HIGHER-ORDER SAMPLE AUTOCORRELATIONS AND THE UNIT-ROOT HYPOTHESIS

Hasza (1980) has derived the limiting distributions of sample autocorr elations for ARIMA(p, 1, q) processes; it appears that the sample auto correlations minus one, times the sample size, converge in distributio n to functions of a Wiener process. In this paper we extend Hasza's re sults in the following ways. First, we shall not assume a parametric f orm of the data-generating process, but adopt instead mixing condition s. Second, next to the sample autocorrelation function considered by H asza we also consider a slightly different form of the autocorrelation function, and it appears that the limiting distributions involved are different. Third, we allow the lag length to grow with the sample siz e, leading to limiting distributions that are independent of the covar iance function of the differenced time series under review. Fourth, we also consider the case of detrended time series. Finally, we construc t new tests of the unit root hypothesis, based on higher-order sample autocorrelations.