Utilizing Trajectory Matrices and Singular Value Decomposition (SVD) for Multivariate Transformation in Time Series Analysis Dina Prariesa1, Udjianna Sekteria Pasaribu2, Utriweni Mukhaiyar2
1Doctoral Program in Mathematics, Faculty of Mathematics and Natural Science, Institut Teknologi Bandung, Jalan Ganesha no 10, Bandung 40132, Indonesia
2Statistics Research Division, Faculty of Mathematics and Natural Science, Institut Teknologi Bandung, Jalan Ganesha no 10, Bandung, 40132, Indonesia
Abstract
The trajectory matrix provides a mechanism for converting univariate time series data into multivariate form. This study utilizes the structural properties of the Hankel matrix (H), which supports weakly stationary processes with a lag of 1. Research on data matrices in Time Series Analysis (TSA) remains limited. Consequently, this study examines the Box-Jenkins TSA technique to investigate autocorrelation behavior in the Autoregressive (AR) model using the Singular Value Decomposition (SVD) approach on the H matrix. SVD, a multivariate analysis technique, aims to reduce dimensionality while preserving critical information from the observed data. The role of SVD in TSA is expanded by considering parameter properties, stationarity, and matrix embedding in time series models. An alternative approach with SVD explores the construction and significance of the trajectory matrix in AR modeling. This research focuses on the properties and requirements of the H and matrix dimension considerations in SVD. The initial research phase involved numerical simulations of time series models, particularly the AR(1) and AR(2) models. The results of PACF and scree plots from SVD generally exhibit similar patterns. This leads to the hypothesis that SVD on the H matrix could serve as an alternative method for order identification in the AR model, in addition to PACF. The findings provide an initial indication of future research potential. The methodology involves exploring, adapting, and generalizing previous research results. By examining these aspects, this research aims to offer new insights and methodological advancements in the field of TSA.
Keywords: Time Series, Singular Value Decomposition, Hankel Matrix
