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Abstract
This paper proposes an extension of principal component analysis to non-stationary multivariate time series data. A criterion for determining the number of final retained components is proposed. An advance correlation matrix is developed to evaluate dynamic relationships among the chosen components. The theoretical properties of the proposed method are given. Many simulation experiments show our approach performs well on both stationary and non-stationary data. Real data examples are also presented as illustrations. We develop four packages using the statistical software R that contain the needed functions to obtain and assess the results of the proposed method.
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Details
1 University of Strathclyde, Department of Mathematics and Statistics, Glasgow, UK (GRID:grid.11984.35) (ISNI:0000000121138138); Saudi Electronic University, Department of Basic Sciences, Riyadh, Kingdom of Saudi Arabia (GRID:grid.449598.d) (ISNI:0000 0004 4659 9645)
2 University of Strathclyde, Department of Mathematics and Statistics, Glasgow, UK (GRID:grid.11984.35) (ISNI:0000000121138138); Yangze Normal University, School of Mathematics and Statistics, Chongqing, China (GRID:grid.11984.35)