Testing for linear autoregressive dynamics under heteroskedasticity

One puzzling behavior of asset returns for various frequencies is the often observed positive autocorrelation at lag 1. To some extent this can be explained by standard asset pricing models when assuming time varying risk premia. However, one often finds better results when directly fitting an autoregressive model, for which there is little economic foundation. One may ask whether the underlying process does in fact contain an autoregressive component. It is therefore of interest to have a statistical test at hand that performs well under the stylized facts of financial returns. In this paper, we investigate empirical properties of competing devices to test for autoregressive dynamics in case of heteroskedastic errors. For the volatility process we assume GARCH, TGARCH and stochastic volatility. The results indicate that standard QML inference for the autoregressive parameter is negatively affected by misspecification of the volatility process. We show that bootstrapped versions of a likelihood ratio and White's t-statistic have better size properties and comparable power properties. Applied to German stock data, the alternative tests in many cases yield very different p-values.