Testing Linearity in an AR Errors-in-variables Model with Application to Stochastic Volatility
Volume 30 / 2003
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.
