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On the partial autocorrelations of once integrated autoregressive-moving average processes 

Author: O.D. Anderson a
Affiliation:   a Department of Mathematics, Nottingham University, University Park, Nottingham, England
DOI: 10.1080/02331887908801495
Publication Frequency: 6 issues per year
Published in: journal Statistics, Volume 10, Issue 3 1979 , pages 389 - 394
Formats available: PDF (English)
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Abstract

An observation, from practical experience with analysing univariate time series, suggests a simple relationship between the partial autocorrelations of a process realisation which requires first differencing, and those for that same sequence of differences. The asymptotic result is proved for a general once integrated autoregressive process, but an extension to twice integrated processes is shown not to be relevant for finite samples. The results are illustrated with examples from the literature.
Keywords: ARIMA processes; differencing; DURBIN's recursive relations for autoregressive estimates; identification of time series; partial autocorrelation
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