Title

The Asymptotic Properties of the Sample Autocorrelations for a Multiple Autoregressive Process with One Unit Root

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.

Department(s)

Mathematics and Statistics

Keywords and Phrases

multivariate time series; autoregression; nonstationarity; asymptotic behaviour; sample autocorrelations

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 1987 Wiley-Blackwell, All rights reserved.


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