Testing Linearity in an AR Errors-in-variables Model with Application to Stochastic Volatility

Volume 30 / 2003

D. Feldmann, W. Härdle, C. Hafner, M. Hoffmann, O. Lepski, A. Tsybakov Applicationes Mathematicae 30 (2003), 389-412 MSC: 62G07, 62G10, 62M10. DOI: 10.4064/am30-4-3

Abstract

Stochastic Volatility (SV) models are widely used in financial applications. To decide whether standard parametric restrictions are justified for a given data set, a statistical test is required. In this paper, we develop such a test of a linear hypothesis versus a general composite nonparametric alternative using the state space representation of the SV model as an errors-in-variables AR(1) model. The power of the test is analyzed. We provide a simulation study and apply the test to the HFDF96 data set. Our results confirm a linear AR(1) structure in log-volatility for the analyzed stock indices S&P500, Dow Jones Industrial Average and for the exchange rate DEM/USD.

Authors

  • D. FeldmannSFB 373 and
    Institut für Statistik und Ökonometrie
    Wirtschaftswissenschaftliche Fakultät
    Humboldt-Universität zu Berlin
    Spandauer Str. 1
    D-10178 Berlin, Germany
  • W. HärdleSFB 373 and
    Institut für Statistik und Ökonometrie
    Wirtschaftswissenschaftliche Fakultät
    Humboldt-Universität zu Berlin
    Spandauer Str. 1
    D-10178 Berlin, Germany
  • C. HafnerSFB 373 and
    Institut für Statistik und Ökonometrie
    Wirtschaftswissenschaftliche Fakultät
    Humboldt-Universität zu Berlin
    Spandauer Str. 1
    D-10178 Berlin, Germany
  • M. HoffmannLaboratoire de probabilités
    et modèles aléatoires
    Université Paris 7
    pl. Jussieu 2
    F-75252 Paris, France
    e-mail
  • O. LepskiCentre des Mathématiques
    et d'Informatique
    Université, Aix-Marseille 1
    39, rue F. Joliot-Curie
    F-13453 Marseille, France
    e-mail
  • A. TsybakovLaboratoire de probabilités
    et modèles aléatoires
    Université Paris 6
    pl. Jussieu 4, BP 188
    F-75252 Paris, France
    e-mail

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