phenomenon · claim-type · cross-domain-transfer · mechanism · claim-relation · replication-status · limitation — grounded in the full text| phenomenon | smoothness (roughness) of the volatility process— “Estimating volatility from recent high frequency data, we revisit the question of the smoothness of the volatility process.” | |
| claim-type | existence— “Our main result is that log-volatility behaves essentially as a fractional Brownian motion with Hurst exponent H of order 0.1, at any reasonable time scale.” | |
| method — evidence | — “We now proceed to estimate the smoothness parameter sq for each q by computing the m(q, ∆) for different values of ∆ and regressing log m(q, ∆) against log ∆.” | |
| transfer | from stochastic processes / statistical physics (fractional Brownian motion, the Hurst exponent): fractional Brownian motion with a Hurst exponent below 1/2 used as the model of log-volatility, in place of the standard semimartingale volatility models of finance— “Our main result is that log-volatility behaves essentially as a fractional Brownian motion with Hurst exponent H of order 0.1, at any reasonable time scale.” | transfers[0] |
| mechanism | THE TERM'S TWO SENSES ARE SEPARATED BY THEIR HISTORY: 'long memory' initially meant the slow decay of the autocorrelation function - anything slower than exponential - and over time acquired the more precise meaning that the function is not integrable, and more precisely still that it decays as a power law with exponent less than one— “Initially, it appears that the term long memory referred to the slow decay of the autocorrelation function (of absolute returns for example), anything slower than exponential. Over time however, it seems that this term has acquired the more precise meaning that the autocorrelation function is not integrable, see [8], and even more precisely… | mechanisms[0] |
| mechanism | THE TECHNICAL SENSE IS DEFENDED AS THE ONLY ESTIMABLE ONE: the recent literature assumes long memory in the technical sense, and the authors add that meaningful results can probably ONLY be obtained under such a specification, since the asymptotic behaviour of the covariance function cannot be estimated without assuming a specific form for it— “Much of the more recent literature, for example [7, 11, 13], assumes long memory in volatility in this more technical sense. Indeed, meaningful results can probably only be obtained under such a specification, since it is not possible to estimate the asymptotic behavior of the covariance function without assuming a specific form.” | mechanisms[1] |
| mechanism | THE QUESTION IS DECLARED UNANSWERABLE AS POSED, and the authors then supply a different instrument rather than a different answer: stated in terms of the asymptotic behaviour of the autocorrelation function the long memory question simply cannot be answered, but explicit expressions still allow the dependence structure to be analysed— “that when stated in term of the asymptotic behavior of the autocorrelation function, the long memory question can simply not be answered. Nevertheless, we are able to provide explicit expressions enabling us to analyze thoroughly the dependence structure of the volatility process.” | mechanisms[2] |
| mechanism | A WIDELY ACCEPTED STYLIZED FACT IS EXPLAINED AS AN ARTEFACT OF ITS OWN DETECTOR: the model has no long memory property, and yet the classical statistical procedures designed to detect volatility persistence TEND TO CONCLUDE THAT LONG MEMORY IS PRESENT in data the model generated— “Our main finding is that although the RFSV model does not have any long memory property, classical statistical procedures aiming at detecting volatility persistence tend to conclude the presence of long memory in data generated from it. This sheds new light on the supposed long memory in the volatility of financial data.” | mechanisms[3] |
| mechanism | the evidence for the stylized fact is dated rather than dismissed: the analyses supporting it use data that PREDATE high-frequency electronic trading, and the authors note the evidence has never satisfied the remaining doubters— “Nevertheless, analyses such as that of Andersen et al. [3] use data that predate the advent of high-frequency electronic trading, and the evidence for long memory has never been sufficient to satisfy remaining doubters” | mechanisms[4] |
| mechanism | THE NEW NAME IS CHOSEN TO CARRY THE DEPARTURE: an existing model is adopted and renamed, with the new word picked to underline the single parameter inequality that separates it from its parent— “Specifically we adopt the fractional stochastic volatility (FSV) model of Comte and Renault [16]. We call our model Rough FSV (RSFV) to underline that, in contrast to FSV, we take H < 1/2.” | mechanisms[5] |
| mechanism | in the process used, ONE PARAMETER CONTROLS BOTH PROPERTIES AT ONCE - regularity and long memory stand in one-to-one correspondence through the Hurst parameter - so a claim about smoothness is inseparably a claim about memory— “Note that in the case of the fBM, there is a one to one correspondence between regularity and long memory through the Hurst parameter H.” | mechanisms[6] |
| mechanism | A WIDESPREAD BELIEF IS MET WITH A COUNTEREXAMPLE RATHER THAN AN ARGUMENT: the model is offered as a counterexample to the widespread belief that the explosion of the volatility smile at short expiries implies the presence of jumps— “This is interesting in and of itself in that it provides a counterexample to the widespread belief that the explosion of the volatility smile as τ → 0 (as clearly seen in Figures 1.1 and 1.2) implies the presence of jumps” | mechanisms[7] |
| mechanism | THE MODEL IS OFFERED AGAINST TWO SEPARATE REQUIREMENTS rather than one - consistency with the empirically observed properties of the volatility time series AND consistency with the shape of the volatility surface - and the claim is stated as POTENTIAL, not as achievement— “The volatility model that we will specify in Section 3.1, driven by fBM with H < 1/2, therefore has the potential to be not only consistent with the empirically observed properties of the volatility time series but also consistent with the shape of the volatility surface.” | mechanisms[8] |
| mechanism | the smoothness estimate is reported as a RANGE ACROSS ASSETS rather than a single fitted number, and it is accompanied by two further empirical properties of the increments - approximate normality and a monofractal scaling of the moments - which together are what licenses the modelling choice— “In Section 2, we report our estimates of the smoothness of the log-volatility for selected assets. This smoothness parameter lies systematically between 0.08 and 0.2 (in the sense of H¨older regularity for example). Furthermore, we find that increments of the log-volatility are approximately normally distributed and that their moments enjoy a… | mechanisms[9] |
| builds-on | fractional Brownian motion (from mathematics/physics)— “log-volatility behaves essentially as a fractional Brownian motion with Hurst exponent H of order 0.1” | claim_relations[0] |
| builds-on | the fractional stochastic volatility (FSV) model of Comte and Renault [16]— “This leads us to adopt the fractional stochastic volatility (FSV) model of Comte and Renault [16].” | claim_relations[1] |
| extends | the FSV model of Comte and Renault [16], modified to H < 1/2— “We call our model Rough FSV (RFSV) to underline that, in contrast to FSV, H < 1/2.” | claim_relations[2] |
| contradicts | the accepted stylized fact of power-law long memory in volatility— “Once again, our conclusion is that although the (log-)volatility may exhibit some form of persistence, it does not present any long memory in the classical power law sense.” | claim_relations[3] |
| replicates | the stylized fact of near-Gaussian log-volatility increments reported by Andersen et al. ([2], [3])— “That the distribution of increments of logvolatility is close to Gaussian is a well-established stylized fact reported for example in the papers [2] and [3] of Andersen et al.” | claim_relations[4] |
| builds-on | Fukasawa [25] on the ATM volatility skew generated by fBM-driven volatility— “As already shown by Fukasawa [25], such a model with a small H reproduces the observed decay of at-the-money volatility skew with respect to time to expiry, asymptotically for short times.” | claim_relations[5] |
| sense | long memory - SENSE 1, THE ORIGINAL AND LOOSE ONE: slow decay of the autocorrelation function, meaning anything slower than exponential— “Initially, it appears that the term long memory referred to the slow decay of the autocorrelation function (of absolute returns for example), anything slower than exponential” | senses[0] |
| sense | long memory - SENSE 2, THE LATER TECHNICAL ONE the field drifted to: a non-integrable autocorrelation function, more precisely one decaying as a power law with exponent below 1, and the recent literature assumes this sense— “Over time however, it seems that this term has acquired the more precise meaning that the autocorrelation function is not integrable, see [8], and even more precisely that it decays as a power-law with exponent less than 1. Much of the more recent literature, for example [7, 11, 13], assumes long memory in volatility in this more technical… | senses[1] |
| sense | volatility - AS A PROXY, ALWAYS: the process is not directly observable, so every quantity here is computed from an estimated daily stand-in taken at a fixed time of day— “Of course, the volatility process is not directly observable, and an exact computation of m(q, ∆) is not possible in practice. We must therefore proxy spot volatility values by appropriate estimated values” | senses[2] |
| sense | Local volatility - exact European-option fit with time-inhomogeneous and unrealistic future dynamics— “In the derivatives world, log-prices are often modeled as continuous semimartingales. For a given asset with log-price Yt, such a process takes the form dYt = µtdt + σtdWt, where µt is a drift term and Wt is a one-dimensional Brownian motion. The term σt denotes the volatility process and is the most important ingredient of the model. In the… | senses[3] |
| sense | Conventional stochastic volatility - more realistic dynamics without exact consistency with observed European option prices— “In the derivatives world, log-prices are often modeled as continuous semimartingales. For a given asset with log-price Yt, such a process takes the form dYt = µtdt + σtdWt, where µt is a drift term and Wt is a one-dimensional Brownian… | senses[4] |
| sense | Local-stochastic volatility - market hybrid targeting both exact fit and reasonable dynamics | senses[5] |
| sense | Implied volatility - the Black-Scholes volatility input required to reproduce an option's market price Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | senses[6] |
| sense | Volatility surface - implied volatility plotted across strike price and time to expiry Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | senses[7] |
| sense | Short-maturity volatility-smile explosion - reproducible without jumps when volatility is fractionally rough Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | senses[8] |
| sense | Rough FSV - fractional stochastic volatility with H below one half rather than the long-memory H above one half Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | senses[9] |
| sense | Spot-volatility observation - intrinsically latent and therefore replaced by daily fixed-time proxies Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | senses[10] |
| sense | Whole-day realized variance - a regularized spot proxy expected to bias smoothness upward Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | senses[11] |
| sense | Stationary rough-volatility specification - fractional Ornstein-Uhlenbeck process with a very long reversion scale Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | senses[12] |
| sense | Practitioner mean reversion - unusually high volatility tends down and unusually low volatility tends up Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | senses[13] |
| sense | Window-length bias - longer integration raises estimated H and lowers estimated volatility-of-volatility Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | senses[14] |
| sense | RFSV scale resemblance - a daily volatility path qualitatively resembles a decade-long path Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | senses[15] |
| sense | Spurious memory diagnosis - standard estimators report power-law memory on simulations whose model has none Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | senses[16] |
| sense | RFSV forecast parsimony - one H parameter rather than horizon-dependent AR/HAR coefficients Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | senses[17] |
| sense | Forecast-history rule - past window approximately matches the future horizon Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | senses[18] |
| sense | Hawkes endogeneity - one order triggers many more as algorithms respond to other participants' orders Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | senses[19] |
| sense | Order splitting - many observed orders belong to a slowly executed metaorder Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | senses[20] |
| sense | Microstructural roughness mechanism - near-critical endogenous feedback plus long-tailed order influence produces a fractional macroscopic limit Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | senses[21] |
| control | a detailed test of the model against observed option prices - NOT performed, and deferred to a future article — absent-declared-unreported — rules out the model fitting volatility time series while failing on the option prices it would be used to compute, which is the comparison the paper itself says its predecessors fail Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | controls[0] |
| edge | long memory —operationalised-as→ Hurst parameter Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concept_edges[0] |
| audit | spot volatility —operationalised-as→ realized volatility — Audit 2026-09-28: DOUBTFUL - read against its full span and kept, but the span writes 'daily spot variances' and 'daily realized variance estimates', not 'spot volatility' / 'realized volatility'. Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concept_edges[1] |
| note | stochastic volatility dynamics —contrasted-with→ local volatility dynamics — The stochastic dynamics are said to be more realistic than local-volatility dynamics, though still price-inconsistent. Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concept_edges[2] |
| note | power-law function of time to expiry —contrasted-with→ sum of decaying exponentials — Observed skew is a power law, in contrast to the conventional model's constant/exponential shape. Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concept_edges[3] |
| note | Rough FSV —same-as→ RFSV — The model name is immediately followed by its acronym in parentheses. Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concept_edges[4] |
| note | Rough FSV (RFSV) —distinct-from→ FSV — The paper explicitly contrasts the rough H below one-half regime with FSV. Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concept_edges[5] |
| note | choice H < 1/2 —causes→ observed smoothness of the volatility process — The choice enables the model to reproduce the observed smoothness. Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concept_edges[6] |
| note | choice H < 1/2 —causes→ term structure of volatility skew — The same choice enables agreement with the observed skew term structure. Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concept_edges[7] |
| note | one given order —causes→ many other orders — The paper states that one order endogenously generates many others. Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concept_edges[8] |
| audit | superposition effect —causes→ irregular volatility — Audit 2026-09-28: DOUBTFUL - read against its full span and kept, but 'We believe' the two phenomena lead to the superposition effect; hedged. Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concept_edges[9] |
| note | superposition effect —causes→ irregular volatility — The authors say they believe the combined phenomena induce irregular volatility. Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concept_edges[9] |
| weight | superposition effect —causes→ irregular volatility — 0.6 Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concept_edges[9] |
| note | Rough Fractional Stochastic Volatility (RFSV) model —distinct-from→ FSV model — The models are separated by the explicitly named major difference H below versus above one half. Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concept_edges[10] |
| evidence status note | concept — PAGE FURNITURE IS SPLICED INTO THE 'evidence' QUOTE - the text of footnote 1 ('1Actually H corresponds…') and a page number, between 'This implies' and 'that when stated'. The words on either side of it were never continuous on the page; read the quote with it deleted. Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[28] |
| outcome (stated by the tagger, no quotation) | control — absent-declared-unreported | controls[0] |
| for which use | limitation — the scaling result, over the range examined: AT LEAST AT USUAL TIME SCALES OF OBSERVATION Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | limitations[0] |
| for which use | limitation — the smoothness estimates specifically: WE EXPECT ESTIMATES OF THE SMOOTHNESS OF THE VOLATILITY PROCESS TO BE BIASED UPWARDS, INTEGRATION BEING A REG[ularising operation] - the direction of the bias is stated Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | limitations[1] |
| for which use | limitation — every quantity computed in the paper: THE VOLATILITY PROCESS IS NOT DIRECTLY OBSERVABLE, AND AN EXACT COMPUTATION OF m(q, delta) IS NOT POSSIBLE IN PRACTICE Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | limitations[2] |
| for which use | limitation — the option-pricing implications: A MORE DETAILED ANALYSIS OF THE CONSISTENCY OF OUR MODEL WITH OPTION PRICES IS LEFT FOR A FUTURE ARTICLE Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | limitations[3] |
| for which use | limitation — any estimate of long memory in volatility: the asymptotic behaviour of the covariance function cannot be estimated without assuming a specific form for it, so the specification is an input to the result rather than an output Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | limitations[4] |
| for which use | limitation — the debate over whether volatility has long memory: stated in terms of the asymptotic behaviour of the autocorrelation function, the paper says the question simply cannot be answered Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | limitations[5] |
| for which use | limitation — the widely accepted stylized fact that volatility has long memory: classical procedures for detecting volatility persistence conclude it is present in data simulated from a model that has no long memory property at all Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | limitations[6] |
| evidence status note | mechanism — Span re-sliced at drafting: the staged text splices footnote 1 AND a page number between 'This implies' and its own subordinate clause ('…see Section 2.1. 3 that when stated in term…'), so the quote begins after the splice. Extraction damage, not authorial. Damage class C. Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | mechanisms[2] |
| evidence status note | mechanism — The span contains 'H¨older' for 'Hölder' - the diaeresis is emitted BEFORE its base letter by the PDF extraction. The quote is still an exact substring and anchors correctly; the damage is in what a reader of the tag sees, not in the provenance. None of the four shapes an internal tool looks for covers this, so it is annotated by hand. Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | mechanisms[9] |
| evidence status note | sense — PAGE FURNITURE IS SPLICED INTO THE 'evidence' QUOTE - the text of footnotes 13 and 14 and a page number, between 'requires the parameter' and 'H to forecast'. The words on either side of it were never continuous on the page; read the quote with it deleted. Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | senses[17] |
| weight | classical statistical procedures → long memory — 0.8 Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | unhoused_relations[1] |
| weight | macroscopic scaling limit of Hawkes processes → integrated fractional process — 0.8 Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | unhoused_relations[4] |
| replication | untested | |
| no type for this | RFSV model → improved forecasts of realized volatility — The RFSV model enables improved forecasts of realized volatility. Enables is absent from the eight governed types and is not direct physical causation. Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | unhoused_relations[0] |
| no type for this | classical statistical procedures → long memory — Classical persistence diagnostics tend to conclude long memory in data generated by a model that has none. Misidentifies-as is absent from the edge vocabulary. Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | unhoused_relations[1] |
| no type for this | RFSV forecast → AR and HAR forecasts — The RFSV forecast consistently outperforms AR and HAR, especially at longer horizons. Outperforms is absent from the eight types and contrast alone would discard the direction of performance. Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | unhoused_relations[2] |
| no type for this | relevant regression window → forecasting horizon — The relevant history window is linear in the forecasting horizon. Proportional-to is absent from the governed edge types. Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | unhoused_relations[3] |
| no type for this | macroscopic scaling limit of Hawkes processes → integrated fractional process — The near-critical long-tail Hawkes scaling limit can be seen as an integrated fractional process. Scaling-limit-is-represented-by is absent and a plain is-a would overstate an asymptotic result. Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | unhoused_relations[4] |
| no type for this | cumulated order flow → integrated variance — The paper reports a linear relation between cumulated order flow and integrated variance. Correlates-with/linearly-related-to is absent from the eight types. Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | unhoused_relations[5] |
| limitation | the scaling result is established at usual observation time scales Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | limitations[0] |
| limitation | Smoothness estimates based on whole-trading-day realized variance are expected to be biased upwards because integration smooths the process. Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | limitations[1] |
| limitation | Volatility is never observed directly, so the key quantity m(q, Δ) can only be computed from proxies. Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | limitations[2] |
| limitation | The paper only treats the volatility time series; whether the model is consistent with observed option prices is deferred. Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | limitations[3] |
| limitation | The property cannot be estimated without first assuming the functional form whose presence is at issue. Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | limitations[4] |
| limitation | As the term is now defined, the field's central question about volatility cannot be answered at all. Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | limitations[5] |
| limitation | Standard procedures report the property in data generated by a model that does not have it, which the authors offer as the reason the field accepted it as a stylized fact. Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | limitations[6] |
finding · quantity · variable · definition · key-term — grounded in the full text| finding | Log-volatility acts essentially like fractional Brownian motion with a Hurst exponent near 0.1 at any reasonable time scale, which leads to the Rough FSV (RFSV) model with H < 1/2. Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.findings[0] |
| finding | Although volatility is NOT long-memory under RFSV, classical persistence tests spuriously detect long memory in RFSV-generated data — explaining why long memory became an accepted stylized fact. Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.findings[1] |
| quantity | H ≈ 0.1 — Hurst exponent of log-volatility (H<1/2 means rough) Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.quantities[0] |
| quantity | H = 1/2 — the classical Brownian-motion boundary case Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.quantities[1] |
| variable | Hurst parameter H (independent) Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.variables[0] |
| definition | RFSV model Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.definitions[0] |
| definition | EVIDENCE CORRECTED (RE-GROUNDED) · fractional Brownian motion Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.definitions[1] |
| retracted | definition — RE-GROUNDED. The old span welded 'model the log of volatility using' - Gatheral's OWN model, a fBM with H < 1/2 - to 'motion (fBM for…' 5,695 characters EARLIER, which belongs to Comte and Renault's H > 1/2 model. It conflated the two Hurst regimes, which is the single distinction this paper exists to draw. | content_tags.definitions[1] |
| key-terms | volatility, fractional, Brownian, Hurst, log-volatility, exponent, memory, realized, rough |
| concept | fractional Brownian motion Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[1] |
| concept | realized volatility Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[3] |
| concept | long memory Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[5] |
| concept | Hurst parameter Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[6] |
| concept | spot volatility Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[7] |
| concept | volatility surface Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[8] |
| concept | continuous semimartingales — not defined in this paper's own words; standard process class used for derivative log-prices Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[9] |
| concept | volatility process — not defined in this paper's own words; time-varying scale term treated as the key model ingredient Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[10] |
| concept | Black-Scholes framework — not defined in this paper's own words; framework using constant or deterministic-time volatility Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[11] |
| concept | deterministic function of time — not defined in this paper's own words; non-random volatility specification available in Black-Scholes Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[12] |
| concept | local volatility model — not defined in this paper's own words; price-and-time deterministic model calibrated to European options Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[13] |
| concept | time-inhomogeneous — not defined in this paper's own words; status assigned to local-volatility dynamics Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[14] |
| concept | future volatility surfaces — not defined in this paper's own words; model-generated surfaces criticized as unrealistic Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[15] |
| concept | exotic options — not defined in this paper's own words; contracts whose local-volatility prices can be off-market Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[16] |
| concept | stochastic volatility models — not defined in this paper's own words; Brownian-semimartingale volatility models including Heston and SABR Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[17] |
| concept | continuous Brownian semi-martingale — not defined in this paper's own words; process form assigned to conventional stochastic volatility Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[18] |
| concept | local volatility dynamics — not defined in this paper's own words; deterministic price-and-time dynamics contrasted with stochastic dynamics Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[19] |
| concept | stochastic volatility dynamics — not defined in this paper's own words; more realistic dynamics that still miss observed European prices Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[20] |
| concept | local-stochastic-volatility (LSV) models — not defined in this paper's own words; market-practice hybrids fitting prices while retaining reasonable dynamics Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[21] |
| concept | reasonable dynamics — not defined in this paper's own words; dynamical behavior jointly targeted with exact market fit Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[22] |
| concept | slow decay of the autocorrelation function — not defined in this paper's own words; original loose meaning of long memory Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[23] |
| concept | not integrable — not defined in this paper's own words; later technical requirement imposed on the autocorrelation function Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[24] |
| concept | power-law with exponent less than 1 — not defined in this paper's own words; most precise long-memory definition described Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[25] |
| concept | asymptotic behavior of the covariance function — not defined in this paper's own words; quantity that requires a specified form to estimate Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[26] |
| concept | usual time scales of observation — not defined in this paper's own words; finite scales at which volatility autocorrelation is tested Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[27] |
| concept | dependence structure — not defined in this paper's own words; object analyzed explicitly despite unresolved asymptotic memory Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[28] |
| concept | implied volatility — not defined in this paper's own words; Black-Scholes volatility value that matches an option's market price Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[29] |
| concept | volatility parameter — not defined in this paper's own words; Black-Scholes input adjusted to reproduce an observed price Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[30] |
| concept | market price of that option — not defined in this paper's own words; calibration target defining implied volatility Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[31] |
| concept | strike price — not defined in this paper's own words; one coordinate of the volatility surface Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[32] |
| concept | time to expiry — not defined in this paper's own words; second coordinate of the volatility surface Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[33] |
| concept | power-law function of time to expiry — not defined in this paper's own words; empirical form of the short-maturity skew term structure Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[34] |
| concept | term structure of at-the-money (ATM) skew — not defined in this paper's own words; conventional-model prediction contrasted with the observed power law Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[35] |
| concept | sum of decaying exponentials — not defined in this paper's own words; large-maturity skew shape generated by conventional stochastic-volatility models Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[36] |
| concept | explosion of the volatility smile — not defined in this paper's own words; short-maturity option feature not requiring price jumps Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[37] |
| concept | presence of jumps — not defined in this paper's own words; widespread explanation countered by fractional-volatility skew Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[38] |
| concept | ATM volatility skew — not defined in this paper's own words; option-surface feature generated by fractional Brownian volatility Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[39] |
| concept | smoothness parameter — not defined in this paper's own words; estimated log-volatility regularity lying around 0.08 to 0.2 Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[40] |
| concept | increments of the log-volatility — not defined in this paper's own words; empirical changes found close to normally distributed Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[41] |
| concept | approximately normally distributed — not defined in this paper's own words; distributional regularity of log-volatility increments Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[42] |
| concept | monofractal scaling property — not defined in this paper's own words; moment scaling whose smoothness is constant across orders Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[43] |
| concept | fractional stochastic volatility (FSV) model — not defined in this paper's own words; Comte–Renault model adopted with a rough-H modification Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[44] |
| concept | Rough FSV (RSFV) — not defined in this paper's own words; rough fractional stochastic-volatility model as spelled in the paper's overview Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[45] |
| concept | Rough FSV — not defined in this paper's own words; short model name introduced before the RFSV acronym Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[46] |
| concept | RFSV — not defined in this paper's own words; abbreviation for the authors' rough fractional stochastic-volatility model Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[47] |
| concept | FSV — not defined in this paper's own words; fractional stochastic-volatility predecessor with H above one half Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[48] |
| concept | Rough FSV (RFSV) — not defined in this paper's own words; rough model name and abbreviation as printed in the abstract Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[49] |
| concept | RFSV model — not defined in this paper's own words; rough fractional stochastic-volatility model used for forecasting and diagnostics Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[50] |
| concept | improved forecasts of realized volatility — not defined in this paper's own words; forecasting capability attributed to the RFSV model Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[51] |
| concept | volatility persistence — not defined in this paper's own words; dependence behavior reexamined through RFSV simulations Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[52] |
| concept | classical statistical procedures — not defined in this paper's own words; estimators shown capable of reporting spurious long memory Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[53] |
| concept | RFSV volatility forecasts — not defined in this paper's own words; model-based forecasts compared with AR and HAR Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[54] |
| concept | conventional AR and HAR volatility forecasts — not defined in this paper's own words; benchmark forecasting approaches Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[55] |
| concept | market microstructure explanation — not defined in this paper's own words; order-flow account of macroscopic roughness Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[56] |
| concept | high degree of endogeneity of the market — not defined in this paper's own words; algorithmic-order feedback component of the proposed explanation Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[57] |
| concept | algorithmic trading — not defined in this paper's own words; market automation linked to endogenous order generation Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[58] |
| concept | integrated variance — not defined in this paper's own words; short-window quantity used to proxy unobservable spot variance Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[59] |
| concept | model with uncertainty zones — not defined in this paper's own words; high-frequency estimator used for futures data Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[60] |
| concept | very short time intervals — not defined in this paper's own words; windows over which integrated variance approximates spot variance Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[61] |
| concept | daily realized variance estimates — not defined in this paper's own words; whole-day proxy used for S&P and NASDAQ spot variance Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[62] |
| concept | Oxford-Man Institute of Quantitative Finance Realized Library — not defined in this paper's own words; source of precomputed realized-variance series Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[63] |
| concept | integration — not defined in this paper's own words; regularizing operation expected to bias estimated smoothness upward Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[64] |
| concept | biased upwards — not defined in this paper's own words; direction of smoothness-estimation bias from whole-day integration Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[65] |
| concept | smoothness parameter sq — not defined in this paper's own words; quantity estimated for each moment order by log-log regression Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[66] |
| concept | regressing log m(q, ∆) against log ∆ — not defined in this paper's own words; empirical procedure for estimating smoothness Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[67] |
| concept | fractional Ornstein-Uhlenbeck process — not defined in this paper's own words; stationary log-volatility model with locally fractional behavior Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[68] |
| concept | mathematical tractability — not defined in this paper's own words; one reason stationarity is imposed Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[69] |
| concept | reasonableness of the model at very large times — not defined in this paper's own words; second motivation for a stationary specification Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[70] |
| concept | very long reversion time scale — not defined in this paper's own words; mean-reversion scale chosen for the stationary process Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[71] |
| concept | choice H < 1/2 — not defined in this paper's own words; roughness choice enabling joint time-series and skew fit Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[72] |
| concept | observed smoothness of the volatility process — not defined in this paper's own words; first empirical feature reproduced by small H Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[73] |
| concept | term structure of volatility skew — not defined in this paper's own words; second empirical feature reproduced by small H Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[74] |
| concept | mean reversion by practitioners — not defined in this paper's own words; tendency of unusually high or low volatility to reverse Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[75] |
| concept | fBM like-behavior of the log-volatility — not defined in this paper's own words; local behavior retained by taking a small reversion coefficient Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[76] |
| concept | stationarity property — not defined in this paper's own words; global property combined with local fractional behavior Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[77] |
| concept | one-hour window — not defined in this paper's own words; uncertainty-zone window yielding a near-true H estimate Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[78] |
| concept | daily eight-hour windows — not defined in this paper's own words; realized-variance window yielding a higher H estimate Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[79] |
| concept | regularizing effect of the integral operator — not defined in this paper's own words; source of upward H bias under longer windows Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[80] |
| concept | volatility of volatility — not defined in this paper's own words; interpretation of nu whose estimate falls with longer windows Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[81] |
| concept | persistent periods of high volatility — not defined in this paper's own words; visual regime shared by observed and simulated paths Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[82] |
| concept | low volatility periods — not defined in this paper's own words; alternating visual regime shared by both paths Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[83] |
| concept | fractal-type behavior — not defined in this paper's own words; qualitative scale resemblance reproduced by RFSV Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[84] |
| concept | range of observation scales — not defined in this paper's own words; interval over which small-H rescaled paths retain similar laws Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[85] |
| concept | volatility process over one day — not defined in this paper's own words; short-scale path resembling the long-scale path Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[86] |
| concept | volatility process over a decade — not defined in this paper's own words; long-scale path resembling the daily path Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[87] |
| concept | straight lines with slope 1.86 — not defined in this paper's own words; simulation-and-data pattern that would imply a spurious memory exponent Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[88] |
| concept | power law behavior of the autocorrelation function — not defined in this paper's own words; incorrect inference induced by the first diagnostic Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[89] |
| concept | wrongly convinced — not defined in this paper's own words; epistemic failure produced when the diagnostic is applied to RFSV-like data Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[90] |
| concept | classical estimation procedures — not defined in this paper's own words; procedures collectively shown to identify spurious long memory Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[91] |
| concept | spurious long memory of volatility — not defined in this paper's own words; false property reported for RFSV simulations Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[92] |
| concept | classical power law sense — not defined in this paper's own words; long-memory definition rejected for log-volatility Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[93] |
| concept | RFSV forecast — not defined in this paper's own words; one-parameter forecast evaluated against AR and HAR Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[94] |
| concept | AR and HAR forecasts — not defined in this paper's own words; multi-coefficient benchmarks for the RFSV predictor Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[95] |
| concept | longer horizons — not defined in this paper's own words; forecast ranges where the RFSV advantage is greatest Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[96] |
| concept | more parsimonious — not defined in this paper's own words; one-parameter advantage claimed for the RFSV method Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[97] |
| concept | forecast time horizon — not defined in this paper's own words; quantity on which benchmark coefficients depend Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[98] |
| concept | relevant regression window — not defined in this paper's own words; amount of past volatility required for forecasting Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[99] |
| concept | forecasting horizon — not defined in this paper's own words; future interval proportional to the relevant history window Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[100] |
| concept | volatility over the last week — not defined in this paper's own words; history suggested for a one-week forecast Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[101] |
| concept | volatility over the last month — not defined in this paper's own words; history suggested for a one-month forecast Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[102] |
| concept | Hawkes processes — not defined in this paper's own words; self-exciting point processes used to analyze order flow Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[103] |
| concept | extensions of Poisson processes — not defined in this paper's own words; class description given for Hawkes processes Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[104] |
| concept | intensity at a given time — not defined in this paper's own words; conditional event rate depending on prior jumps Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[105] |
| concept | past jumps — not defined in this paper's own words; history on which Hawkes intensity depends Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[106] |
| concept | point process — not defined in this paper's own words; transaction-count process assumed to follow Hawkes dynamics Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[107] |
| concept | kernel — not defined in this paper's own words; nonnegative function weighting effects of past jump times Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[108] |
| concept | L1 norm — not defined in this paper's own words; kernel norm calibrated close to one Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[109] |
| concept | power law tail — not defined in this paper's own words; second recurring feature of calibrated Hawkes kernels Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[110] |
| concept | degree of endogeneity of the market — not defined in this paper's own words; near-critical feedback implied by the kernel norm Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[111] |
| concept | one given order — not defined in this paper's own words; order capable of endogenously generating further orders Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[112] |
| concept | many other orders — not defined in this paper's own words; endogenous descendants of a given order Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[113] |
| concept | electronic high frequency trading — not defined in this paper's own words; algorithmic setting associated with market endogeneity Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[114] |
| concept | splitting of large orders — not defined in this paper's own words; explanation offered for long-lived order influence Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[115] |
| concept | metaorder — not defined in this paper's own words; large parent order whose execution spans many child orders Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[116] |
| concept | superposition effect — not defined in this paper's own words; combined near-critical and long-tail mechanism proposed to induce roughness Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[117] |
| concept | irregular volatility — not defined in this paper's own words; macroscopic property induced by the proposed superposition Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[118] |
| concept | macroscopic scaling limit of Hawkes processes — not defined in this paper's own words; large-scale limit described as integrated fractional Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[119] |
| concept | integrated fractional process — not defined in this paper's own words; limit process with H below one half Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[120] |
| concept | cumulated order flow — not defined in this paper's own words; large-scale order-flow quantity linked to integrated variance Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[121] |
| concept | Rough Fractional Stochastic Volatility (RFSV) model — not defined in this paper's own words; expanded model name used in the conclusion Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[122] |
| concept | FSV model — not defined in this paper's own words; long-memory predecessor distinguished by H above one half Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[123] |
| concept | one major difference — not defined in this paper's own words; opposite Hurst regimes separating FSV and RFSV Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | concepts[124] |
| mean μ | as written: mean of Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.statistics[1] |
| evidence status note | mean — THE QUOTE STARTS INSIDE A FORMULA AND ENDS IN A TABLE: it opens on the tail of the flattened expectation symbol that its sentence defines; this copy places that sentence's last words (the period the mean is taken over) before the quote; and after the quote's last words the text runs into the labels of the forecasting results table. | content_tags.statistics[1] |
| regression β | as written: linear regression Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.statistics[2] |
| sample-size n/N | Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.statistics[3] |
| evidence status note | sample-size — QUOTE REPAIRED: the extractor split a hyphen-space and the quote was recorded faithfully with the damage in it, which made it unanchorable. The repaired string is an EXACT SUBSTRING of the staged text - that is why it was accepted, not because a rule produced it. The text as originally recorded is kept in evidence as extracted. | content_tags.statistics[3] |
| standard-error SE | Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.statistics[4] |
| variance σ² | Quotation withheld — this paper is not ours to reproduce, and the page has already quoted as much of it as the rights layer allows. The tag, its field and its confidence stand; the sentence is at the publisher. | content_tags.statistics[6] |
| evidence status note | variance — A FOOTNOTE CALL SITS INSIDE THIS QUOTE: the '6' between 'the S&P and' and 'NASDAQ indices' is the paper's footnote marker, not part of the sentence; read the quote with it deleted. | content_tags.statistics[6] |
When we have changed our mind. Some entries in the table begin with a word in capitals and the reason for it. EVIDENCE CORRECTED — the finding still stands, but we had quoted the wrong sentence from the paper, and the quotation has been replaced with the right one. RETRACTED — the entry itself was wrong; it stays on the page, marked, with the reason, rather than being deleted. WITHDRAWN AND REPLACED — the entry was wrong, and a corrected version of it appears in the entries below. Each mark carries its own reason, in brackets, because the reasons differ from one entry to the next. An entry we have WITHDRAWN is removed from this page and kept in the record, with its reason. A line reading Audit and a date is a later re-reading of the entry against its whole sentence: DOUBTFUL means it was kept, and the reason says what is loose about it. Quotation marks inside the tagger's sentence. Where a tag is the tagger's own sentence, a phrase in quotation marks inside it is borrowed from the paper — the tagger's wording around it is not. The paper's own sentence is the evidence quote for that row; on this page it is withheld with the article, and the article is at its publisher. Nothing inside quotation marks anywhere on this page is ours: if it is quoted, it is the paper's. Whose words a concept carries. A concept entry records a term the paper itself uses, so the term, the sense given for it, and its evidence are the paper's own words, quoted where the paper fixes them. This is the opposite of a sense entry in the tag table, which is the tagger's sentence about how the paper uses a term. Where a concept entry could not be grounded in the paper's words, the entry says so on its own row.
Tag layer © the Meta-Tagging Project, CC BY 4.0. The paper text is © its authors/publisher
and is linked, not reproduced. Excerpts shown are short quotations for identification and verification.
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