Estimating the predictability of economic and financial time series

Quentin Giai Gianetto, Jean-Marc Le Caillec () and Erwan Marrec
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Quentin Giai Gianetto: Arkéa
Jean-Marc Le Caillec: Lab-STICC_M3 - Equipe Marine Mapping & Metrology - Lab-STICC - Laboratoire des sciences et techniques de l'information, de la communication et de la connaissance - ENIB - École Nationale d'Ingénieurs de Brest - UBS - Université de Bretagne Sud - UBO - Université de Brest - ENSTA Bretagne - École Nationale Supérieure de Techniques Avancées Bretagne - IMT - Institut Mines-Télécom [Paris] - CNRS - Centre National de la Recherche Scientifique - UBL - Université Bretagne Loire - IMT Atlantique - IMT Atlantique - IMT - Institut Mines-Télécom [Paris], IMT Atlantique - ITI - Département lmage et Traitement Information - IMT Atlantique - IMT Atlantique - IMT - Institut Mines-Télécom [Paris]
Erwan Marrec: Arkéa

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Abstract: The predictability of a time series is determined by the sensitivity to initial conditions of its data generating process. In this paper our goal is to characterize this sensitivity from a finite sample by assuming few hypotheses on the data generating model structure. In order to measure the distance between two trajectories induced by a same noisy chaotic dynamic from two close initial conditions, a symmetric Kullback-Leiber divergence measure is used. Our approach allows to take into account the dependence of the residual variance on initial conditions. We show it is linked to a Fisher information matrix and we investigated its expressions in the cases of covariance-stationary processes and ARCH($\infty$) processes. Moreover, we propose a consistent non-parametric estimator of this sensitivity matrix in the case of conditionally heteroscedastic autoregressive nonlinear processes. Various statistical hypotheses can so be tested as for instance the hypothesis that the data generating process is "almost" independently distributed at a given moment. Applications to simulated data and to the stock market index S&P500 illustrate our findings. More particularly, we highlight a significant relationship between the sensitivity to initial conditions of the daily returns of the S&P 500 and their volatility.

Keywords: Chaotic Dynamics (nlin.CD); Applications (stat.AP); FOS: Physical sciences; FOS: Computer and information sciences (search for similar items in EconPapers)
Date: 2023-11-30
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Persistent link: https://EconPapers.repec.org/RePEc:hal:wpaper:hal-04315088

DOI: 10.48550/arXiv.1212.2758

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