| Abstract: | A seasonal random walk is an ARIMA process such that the first difference of order s (s ≥ 1) is a white noise. Given a series of observations from a particular linear transformation of a seasonal random walk, we study the autocovariances c'(k) based on uncentered data and the autocovariances c(k) based on centered data. In both cases, we provide exact, explicit formulae for the mean, variance, and covariance of the sample autocovariances. It is seen that the moments of the c(k)'s are different from those of the c'(k)'s, even asymptotically. Several analytical results presented in the paper were derived by using a symbolic manipulation program. |
