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

Samaranayake V. A. | Zendy; Hasza David P. | Zendy

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

Author(s) -

Samaranayake V. A.,

Hasza David P.

Publication year - 1987

Publication title -

journal of time series analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.576

H-Index - 54

eISSN - 1467-9892

pISSN - 0143-9782

DOI - 10.1111/j.1467-9892.1987.tb00422.x

Subject(s) - mathematics , autoregressive model , unit root , autocorrelation , unit circle , series (stratigraphy) , statistics , matrix (chemical analysis) , asymptotic distribution , autocorrelation matrix , sample (material) , partial autocorrelation function , combinatorics , time series , autoregressive integrated moving average , paleontology , materials science , chemistry , chromatography , estimator , composite material , biology

. In this paper the large sample behaviour of the sample autocorrelation matrix R n ( 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 R n ( h ) converges almost surely to a constant matrix. Further, the asymptotic distribution of R n ( h ) is characterized as that of a random matrix which is a function of jointly normal random variables.

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