Testing for Threshold Diffusion

Abstract

We consider the problem of testing for threshold nonlinearity in the drift and/or diffusion term of a threshold diffusion process, which assumes a piecewise linear drift term and/or a piecewise smooth diffusion term. We do this by developing an approximate likelihood ratio test. Via simulations, the finite sample performance of the proposed approximate likelihood ratio test is studied and compared to an alternative test based on least squares estimation. The proposed test is particularly useful for the empirically relevant case of threshold effects in the diffusion. Finally, the efficacy of our approach is demonstrated with a financial time series. ? Keywords: Irregularly-spaced data; Threshold diffusion process; Nonlinear time series;Stochastic differential equation; Maximum likelihood estimator.