Probabilistic Graph Models (PGMs) for Feature Selection in Time Series Analysis and Forecasting

Abstract

Time series or longitudinal analysis has a very important aspect in the field of research. Day by day new and better analyses are getting developed in this field. The main problem of the time series modeling is the presence of heteroskedasticity which was first identified as the autoregressive conditional heteroskedasticitic (ARCH) effect by R. Engle (1969) [15] and then moderated by Bollerslev (1986) [7] in the more generalized form of generalized autoregressive conditional heteroskedasticitic (GARCH) models to explain the conditional dependence and can capture the systematizes evidence of the past variations of the time series variables. And on the other hand, J. Pearl (1985) [33] in the mid-eighties established the use of probabilistic graph models (PGMs), especially it's part where the causation cannot be reversed i.e. directed acyclic graphs (DAGs) as Bayesian Networks (BNs) to determine the conditional independence and is widely used in various fields of life with greater accuracy, precision, and fewer complexities. Fortunately, Bayesian Networks (BNs) are not used to to-date for the analysis of conditional dependencies or conditional independence analysis on the longitudinal data. This paper will review and summarize the uses of GARCH models and the uses of BNs in different fields and the responses of the researchers on the results accuracies and precision in comparison of the other available and applied analyses.