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Biometrika 1977 64(2):419-421; doi:10.1093/biomet/64.2.419
© 1977 by Biometrika Trust
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MISCELLANEA

On the asymptotic behaviour of the sample autocovariance function for an integrated moving average process

ROCH ROY

Département d'informatique, Université de Montréal

In this paper, we derive the first two asymptotic moments of the autooovariance function of a time series generated from an integrated moving average process of order (1,1). In particular, it is found that the expected value of the sample autocovariance at lag k is approximately proportional to the length of the series. This result suggests a method of checking whether a nonstationary time series can be described by an integrated moving average process of order (1,1) and its use is illustrated with a simulated series.

Key Words: Integrated moving average process • Model identification • Sample autocovariance • Time series analysis


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