Utilizing Trajectory Matrices and Singular Value Decomposition (SVD) for Multivariate Transformation in Time Series Analysis

The trajectory matrix transforms univariate time series data into multivariate form using the structural properties of the Hankel Matrix (HM). Research on data matrices within Time Series Analysis (TSA) remains limited. This study examines AR models with stationary properties and applies Singular Value Decomposition (SVD) to HM in the Box-Jenkins framework. It focuses on HM properties, matrix dimension considerations in SVD, and order identification. Numerical simulations of the AR(1) and AR(2) models reveal that the PACF and SVD scree plots exhibit similar patterns. This indicates that applying SVD to HM could serve as an alternative to PACF for AR order selection. The findings highlight potential future research directions by refining, adapting, and generalizing previous studies to advance the TSA methodology.