Spectral tests of the martingale hypothesis under conditional heteroscedasticity

摘要: Abstract We study the asymptotic distribution of sample standardized spectral function when observed series is a conditionally heteroscedastic martingale difference. show that no longer Brownian bridge but another Gaussian process. Furthermore, this limiting process depends on covariance structure second moments series. causes test statistics based distribution, such as Cramer von-Mises statistic, to have heavily right skewed distributions, which will lead over-rejection hypothesis in favour mean reversion. A non-parametric correction proposed account for conditional heteroscedasticity. demonstrate corrected version statistic has usual would be obtained absence also present Monte Carlo results finite distributions uncorrected and versions statistic. Our simulation can provide significant gains power over Box–Ljung–Pierce against long-memory alternatives. An empirical application stock returns provided.