Testing for Linear Autoregressive Dynamics under Heteroskedasticity

One puzzling behavior of asset returns for various frequencies is the of ten observed positive autocorrelation at lag To some extent this can be explained by standard asset pricing models when assuming time varying risk premia However one often nds better results when directly tting an autoregressive model for which there is little economic foundation One may ask whether the underlying process does in fact contain an au toregressive component It is therefore of interest to have a statistical test at hand that performs well under the stylized facts of nancial 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 aected by misspecication of the volatility pro cess We show that bootstrapped versions of a likelihood ratio andWhites tstatistic have better size properties and comparable power properties Applied to German stock data the alternative tests in many cases yield very dierent pvalue