TESTING FOR LONG MEMORY
提出一种基于高阶样本自协方差的新检验统计量，用于检验短记忆对长记忆的备择假设，在残差情形下渐近标准正态分布，蒙特卡洛模拟显示其稳健性和功效良好。
This paper introduces a new test statistic for the null hypothesis of short memory against long memory alternatives. The novelty of our statistic is that it is based on only high-order sample autocovariances and by construction eliminates the effects of nuisance parameters typically induced by short memory autocorrelation. For practically relevant situations where the short memory process is not directly observed, but instead appears as the disturbance term in a deterministic linear regression model, we are able to demonstrate that our residual-based statistic has an asymptotic standard normal distribution under the null hypothesis. We also establish consistency of the statistic under long memory alternatives. The finite-sample properties of our procedure are compared to other well-known tests in the literature via Monte Carlo simulations. These show that the empirical size properties of the new statistic can be very robust compared to existing tests and also that it competes well in terms of power.We thank the associate editor and two anonymous referees for their valuable comments on an earlier draft of this paper.