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

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Feldmann D., Härdle W., Hafner C., Hoffmann M., Lepski O., Tsybakov A.

Applicationes Mathematicae

2003

tom 30

nr 4

389-412

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.

Ograniczanie wyników

1 Applicationes Mathematicae

1 Feldmann D.

1 Hafner C.

1 Hoffmann M.

1 Härdle W.

1 Lepski O.

1 Tsybakov A.

1 2003

Wyniki wyszukiwania

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