Université Paris 6
Pierre et Marie Curie
Université Paris 7
Denis Diderot

CNRS U.M.R. 7599
``Probabilités et Modèles Aléatoires''

Testing linearity in AR errors-in-variables model with application to stochastic volatility


Code(s) de Classification MSC:

Résumé: 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 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.

Mots Clés: Autoregression with errors in variables ; stochastic volatility ; testing parametric versus nonparametric fit ; minimax tests

Date: 2000-03-30

Prépublication numéro: PMA-580

Postscript file : PMA-580.ps