PROVING OPTIMAL MODEL SELECTION AND ZERO COEFFICIENT CASES IN TIME SERIES FORECASTING WITH THE GENERALIZED LEAST DEVIATION ALGORITHM

This article provides a comprehensive analysis and proof of the Generalized Least Deviation Method (GLDM) in the context of time series forecasting, with a particular focus on optimal model order selection and the conditions that lead to zero coefficients. Central to this study is the GLDM Estimator, which determines the coefficients {aj} n(m) j=1 by minimizing the objective function F(a), defined as the sum of the arctangents of the absolute deviations from observed time series data {yt} T t=1 ⊂ R. The research not only proves GLDM’s ability to capture complex data interactions but also demonstrates its adaptability to varying model orders, showing that the selection of the optimal model order is influenced by the underlying characteristics of the data rather than just the data size. For example, temperature data with pronounced seasonal patterns and autocorrelations demands a fifth-order model, whereas wind speed and COVID-19 death cases in Russia are effectively modeled by a second-order structure. The study further examines the implications of higher-order models, advocating for a customized approach to model selection that enhances both predictive accuracy and interpretability in time series forecasting.