Geodesic
Testing Linearity in an AR Errors-in-variables Model with Application to Stochastic Volatility
D. Feldmann 1   ; W. Härdle 1   ; C. Hafner 1   ; M. Hoffmann 2   ; O. Lepski 3   ; A. Tsybakov 4
1 SFB 373 and Institut für Statistik und Ökonometrie Wirtschaftswissenschaftliche Fakultät Humboldt-Universität zu Berlin Spandauer Str. 1 D-10178 Berlin, Germany
2 Laboratoire de probabilités et modèles aléatoires Université Paris 7 pl. Jussieu 2 F-75252 Paris, France
3 Centre des Mathématiques et d'Informatique Université, Aix-Marseille 1 39, rue F. Joliot-Curie F-13453 Marseille, France
4 Laboratoire de probabilités et modèles aléatoires Université Paris 6 pl. Jussieu 4, BP 188 F-75252 Paris, France
Applicationes Mathematicae, Tome 30 (2003) no. 4, pp. 389-412 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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, Dow Jones Industrial Average and for the exchange rate DEM/USD.
DOI : 10.4064/am30-4-3
Keywords: stochastic volatility models widely financial applications decide whether standard parametric restrictions justified given set statistical test required paper develop test linear hypothesis versus general composite nonparametric alternative using state space representation model errors in variables model power test analyzed provide simulation study apply test hfdf set results confirm linear structure log volatility analyzed stock indices amp dow jones industrial average exchange rate dem usd

D. Feldmann  1   ; W. Härdle  1   ; C. Hafner  1   ; M. Hoffmann  2   ; O. Lepski  3   ; A. Tsybakov  4

1 SFB 373 and Institut für Statistik und Ökonometrie Wirtschaftswissenschaftliche Fakultät Humboldt-Universität zu Berlin Spandauer Str. 1 D-10178 Berlin, Germany
2 Laboratoire de probabilités et modèles aléatoires Université Paris 7 pl. Jussieu 2 F-75252 Paris, France
3 Centre des Mathématiques et d'Informatique Université, Aix-Marseille 1 39, rue F. Joliot-Curie F-13453 Marseille, France
4 Laboratoire de probabilités et modèles aléatoires Université Paris 6 pl. Jussieu 4, BP 188 F-75252 Paris, France 
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     title = {Testing {Linearity} in an
 {AR} {Errors-in-variables} {Model} with
 {Application} to {Stochastic} {Volatility}},
     journal = {Applicationes Mathematicae},
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     doi = {10.4064/am30-4-3},
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D. Feldmann; W. Härdle; C. Hafner; M. Hoffmann; O. Lepski; A. Tsybakov. Testing Linearity in an
 AR Errors-in-variables Model with
 Application to Stochastic Volatility. Applicationes Mathematicae, Tome 30 (2003) no. 4, pp. 389-412. doi: 10.4064/am30-4-3

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