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Some exact results on the sample autocovariances of a seasonal ARIMA model
Author(s) -
Latour Alain,
Roy Roch
Publication year - 1987
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.2307/3314918
Subject(s) - autoregressive integrated moving average , mathematics , random walk , sample (material) , series (stratigraphy) , white noise , statistics , covariance , statistical physics , econometrics , time series , physics , paleontology , biology , thermodynamics
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.