Testing Linearity in an AR Errors-in-variables Model with Application to Stochastic Volatility
(2003) Applicationes Mathematicae — Vol. 30, n° 4, p. 389-412 (2003)
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- Authors
- 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.
- Affiliations
Humboldt-Universität zu Berlin Institut für Statistik und Ökonometrie Université de Paris 7 Laboratoire de probabilités et modèles aléatoires Université Aix-Marseille 1 Centre des mathématiques et d'informatique Université Paris 6 Laboratoire de probabilités et modèles aléatoires
Citations
Feldmann, D., Härdle, W., Hafner, C., Hoffmann, M., Lepski, O., & Tsybakov, A. (2003). Testing Linearity in an AR Errors-in-variables Model with Application to Stochastic Volatility. Applicationes Mathematicae, 30(4), 389-412. https://doi.org/10.4064/am30-4-3 (Original work published 2003)