Ensemble properties of high frequency data and intraday trading rules

Baldovin, Fulvio; Camana, Francesco; Caporin, Massimiliano; Caraglio, Michele; Stella, Attilio L.

doi:10.48550/arxiv.1202.2447

Cited by 2 publications

(14 citation statements)

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“…This fine-graining, reverse renormalization group strategy for the description of market dynamics has been already exemplified in previous contributions [23,25,26], especially dealing with high frequency processes [35][36][37]. Unlike in cases for which a single time series is available, in Refs.…”

Section: Scaling As a Guiding Symmetrymentioning

confidence: 89%

“…Unlike in cases for which a single time series is available, in Refs. [35][36][37] we focused on a particular, fixed window of the daily evolution of an asset, and extracted from the available records an ensemble of histories which have been assumed to be independent realizations of the same stochastic process. The manifest time inhomogeneous character of this process and its limited duration in time significantly simplify a modeling approach based on the above fine-graining strategy.…”

Section: Scaling As a Guiding Symmetrymentioning

confidence: 99%

“…( 7): X t = a t Y t . In principle, these rescaling factors convey a time inhomogeneity to the increments X t 's, a property which has been exploited in the modeling of ensembles of histories [35][36][37]. However, a proper randomization of the time argument of the a t 's restores the stationarity of the X t 's, making them suitable for describing single time series whose statistical properties are thought to be independent of time [10].…”

Section: Scaling As a Guiding Symmetrymentioning

confidence: 99%

“…The background ideas exposed in Refs. [23,34] already stimulated some contributions along various lines [23][24][25][26][35][36][37]. In particular, in [25] a model with nonstationary increments and lacking a volatility feedback mechanism has been discussed in detail, pointing out its potential interest and missing features.…”

Section: Introductionmentioning

confidence: 99%

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Scaling symmetry, renormalization, and time series modeling: The case of financial assets dynamics

et al. 2013

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We present and discuss a stochastic model of financial assets dynamics based on the idea of an inverse renormalization group strategy. With this strategy we construct the multivariate distributions of elementary returns based on the scaling with time of the probability density of their aggregates. In its simplest version the model is the product of an endogenous autoregressive component and a random rescaling factor designed to embody also exogenous influences. Mathematical properties like increments' stationarity and ergodicity can be proven. Thanks to the relatively low number of parameters, model calibration can be conveniently based on a method of moments, as exemplified in the case of historical data of the S&P500 index. The calibrated model accounts very well for many stylized facts, like volatility clustering, power-law decay of the volatility autocorrelation function, and multiscaling with time of the aggregated return distribution. In agreement with empirical evidence in finance, the dynamics is not invariant under time reversal, and, with suitable generalizations, skewness of the return distribution and leverage effects can be included. The analytical tractability of the model opens interesting perspectives for applications, for instance, in terms of obtaining closed formulas for derivative pricing. Further important features are the possibility of making contact, in certain limits, with autoregressive models widely used in finance and the possibility of partially resolving the long- and short-memory components of the volatility, with consistent results when applied to historical series.

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Section: Scaling As a Guiding Symmetrymentioning

confidence: 89%

Section: Scaling As a Guiding Symmetrymentioning

confidence: 99%

Section: Scaling As a Guiding Symmetrymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Scaling symmetry, renormalization, and time series modeling: The case of financial assets dynamics

et al. 2013

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“…These limits reflect a lack of adequate modeling for the dynamics of financial indexes, especially in regimes like those covered by the Omori law. In recent contributions [3,4], some of the present authors have proposed a model for the dynamics at high frequency of exchange rates or stock market indexes, which takes into account most of the relevant stylized facts. Among them, the martingale character of index evolution, the manifest non-stationarity of volatility detected in well defined daily windows of trading activity, the anomalous scaling properties of the aggregate return probability density function (PDF) in the same windows, and the strong time autocorrelation of the elementary absolute return.…”

Section: Introductionmentioning

confidence: 99%

Aftershock Prediction for High-Frequency Financial Markets’ Dynamics

Baldovin

Camana

Caraglio

et al. 2013

Econophysics of Systemic Risk and Network Dynamics

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The occurrence of aftershocks following a major financial crash manifests the critical dynamical response of financial markets. Aftershocks put additional stress on markets, with conceivable dramatic consequences. Such a phenomenon has been shown to be common to most financial assets, both at high and low frequency. Its present-day description relies on an empirical characterization proposed by Omori at the end of 1800 for seismic earthquakes. We point out the limited predictive power in this phenomenological approach and present a stochastic model, based on the scaling symmetry of financial assets, which is potentially capable to predict aftershocks occurrence, given the main shock magnitude. Comparisons with S&P high-frequency data confirm this predictive potential.

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Ensemble properties of high frequency data and intraday trading rules

Cited by 2 publications

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Scaling symmetry, renormalization, and time series modeling: The case of financial assets dynamics

Scaling symmetry, renormalization, and time series modeling: The case of financial assets dynamics

Aftershock Prediction for High-Frequency Financial Markets’ Dynamics

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