Abstract

INVESTIGATING A STATIONARITY PROPERTY OF MULTIVARIATE TIME SERIES USING NIGERIA CONSUMER PRICE INDEX RETURN SERIES

Usoro, Anthony Effiong,1 Awakessien, Clement E.2 and Omekara, Chukwuemeka O.3

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The motivation behind this research was to investigate stationarity of multivariate time series through positive definiteness property of the cross-autocovariance/cross-autocorrelation functions. Three vector series which represent the Nigeria Average, Urban and Rural Consumer Price Indices were used with data collected from CBN Statistical Bulletin from 1995-2018. The covariances and autocorrelation matrices of individual vector return series constituted the components of cross-covariance and cross-autocorrelation matrices. Firstly, the positive definiteness of the sub-autocorrelation matrices were investigated, and stationarity were ascertained. This was followed by the investigation on the cross-autocorrelation functions. The results of the principal minors and determinants revealed positive definiteness of the multivariate process. This paper recommends that in multivariate time series, investigation of stationarity should incorporate the sub-autocovariance or autocorrelation matrices of individual vector processes as components of the cross-covariance or cross-autocorrelation matrix. Keywords: Stationarity, Positive-definiteness, cross-autocovariance and cross-autocorrela-tions.

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