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Distribution asymptotique des autocorrélations ďun processus saisonnier non stationnaire
Author(s) -
Latour Alain,
Roy Roch
Publication year - 1989
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 - 10.2307/3315480
Subject(s) - mathematics , series (stratigraphy) , distribution (mathematics) , sample (material) , autocorrelation , stationary process , statistics , mathematical analysis , physics , thermodynamics , geology , paleontology
Abstract We examine the behaviour of the sample autocorrelations of a seasonal time series for which the first difference of order s ( s ≥ 1) is stationary. The asymptotic distribution of the autocorrelations r'( k ) based on uncentered data and of the autocorrelations r ( k ) based on centered data are derived. In each case, the asymptotic distribution is characterized as a function of the lag k and the parameters of the process. A simulation study was conducted in order to investigate the rate of convergence of the finite sample distributions of r ( k ) and r'( k ) to their asymptotic counterparts and to evaluate the effect of centering or not centering the data on the distribution of autocorrelations.