The Ups and Downs of Modeling Financial Time Series with Wiener Process Mixtures

Challet, Damien; Peirano, Pier Paolo

doi:10.2139/ssrn.1185245

Cited by 2 publications

(5 citation statements)

References 53 publications

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“…The authors of[28] reach a similar conclusion in the most recent update (v3) of their paper. doi:10.1088/1742-5468/2010/02/P02018…”

supporting

confidence: 67%

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Anomalous scaling due to correlations: limit theorems and self-similar processes

Stella¹,

Baldovin²

2010

J. Stat. Mech.

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We derive theorems which outline explicit mechanisms by which anomalous scaling for the probability density function of the sum of many correlated random variables asymptotically prevails. The results characterize general anomalous scaling forms, justify their universal character, and specify universality domains in the spaces of joint probability density functions of the summand variables. These density functions are assumed to be invariant under arbitrary permutations of their arguments. Examples from the theory of critical phenomena are discussed. The novel notion of stability implied by the limit theorems also allows us to define sequences of random variables whose sum satisfies anomalous scaling for any finite number of summands. If regarded as developing in time, the stochastic processes described by these variables are non-Markovian generalizations of Gaussian processes with uncorrelated increments, and provide, e.g., explicit realizations of a recently proposed model of index evolution in finance.

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“…The authors of[28] reach a similar conclusion in the most recent update (v3) of their paper. doi:10.1088/1742-5468/2010/02/P02018…”

supporting

confidence: 67%

“…In particular, the class of scaling functions from which one can construct joint PDFs is specified. This class includes the form used in [21] and also the Student distribution recently considered 1 in [28].…”

Section: Non-markovian Self-similar Stochastic Processesmentioning

confidence: 99%

Anomalous scaling due to correlations: limit theorems and self-similar processes

Stella¹,

Baldovin²

2010

J. Stat. Mech.

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“…(4). This is indeed the case if we choose an inverse-gamma distribution for σ 2 [6]. Equivalently, we may set…”

Section: Model Calibrationmentioning

confidence: 99%

“…In a version of our model suited for describing single, long time series of returns [15,19], the necessity to consider random exogenous factors influencing the market, leads us to switch-on at random times some time-inhomogeneities formally similar to those characterizing the model of the previous Section. This is achieved by setting a t = 1 concomitantly with these random events (See also [2,3,6,1]). In such a context it is not a priori clear whether or not the start of an Omori process should imply putting a t = 1 in correspondence with the time t of the main shock.…”

Section: Aftershock Predictionmentioning

confidence: 99%

“…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. This model for high-frequency data, which applies more general ideas about the time evolution of financial indexes [2,15,6], has also been tested [3] by comparing its predictions with the statistics of ensembles of daily histories all supposed to reproduce the same underlying stochastic process. It has been also shown [4] that some arbitrage opportunities revealed by the model could be successfully exploited by appropriate trading strategies.…”

Section: Introductionmentioning

confidence: 99%

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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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The Ups and Downs of Modeling Financial Time Series with Wiener Process Mixtures

Cited by 2 publications

References 53 publications

Anomalous scaling due to correlations: limit theorems and self-similar processes

Anomalous scaling due to correlations: limit theorems and self-similar processes

Aftershock Prediction for High-Frequency Financial Markets’ Dynamics

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