THE ASYMPTOTIC PROPERTIES OF THE SAMPLE AUTOCORRELATIONS FOR A MULTIPLE AUTOREGRESSIVE PROCESS WITH ONE UNIT ROOT

V. A. Samaranayake and David P. Hasza

Journal of Time Series Analysis, 1987, vol. 8, issue 1, 79-93

Abstract: Abstract. In this paper the large sample behaviour of the sample autocorrelation matrix Rn(h), (h being the lag, n the sample size), of a multivariate autoregressive time series with one of its characteristic roots equal to unity and the rest of the roots lying inside the unit circle is studied. It is shown that Rn(h) converges almost surely to a constant matrix. Further, the asymptotic distribution of Rn(h) is characterized as that of a random matrix which is a function of jointly normal random variables.

Date: 1987
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