Testing for nonlinearity in mean and volatility for heteroskedastic models

This paper proposes a simple test for threshold nonlinearity in either the mean or volatility equation, or both, of a heteroskedastic time series. Our proposal adopts existing Bayesian Markov chain Monte Carlo methods to fit a general double threshold GARCH model, which may have an explosive regime, then forms posterior credible intervals on model parameters to detect and specify threshold nonlinearity in the mean and/or volatility equations. Simulation experiments demonstrate that the method works favorably in identifying model specifications varying in complexity from the conventional GARCH up to the full double-threshold nonlinear GARCH model and is robust to over-specification in model orders. In an application to nine international financial market indices, clear evidence supporting the hypothesis of threshold nonlinearity in mean and volatility is discovered.