Establishing the significance of the coefficients of the quasi-linear equation of n-factor autoregression

This article conducts a thorough analysis of the Generalized Least Deviation Method (GLDM) applied to time series forecasting. The study concentrates on establishing the optimal model order and identifying conditions that lead to zero coefficients. Central to this analysis is the GLDM Estimator, which determines the coefficients {aj}"=^ by minimizing an objective function E(a), expressed as the sum of the arctangents of the absolute deviations from the time series data {y,}/=1 which belongs to R. The adaptability of GLDM to capture complex dataset interactions is examined, highlighting how it adjusts to different model orders. It is shown that the appropriate model order depends not only on the dataset size but also on the inherent data characteristics, which govern the model’s complexity. For example, the data for temperature, with its significant seasonal variations and autocorrelations, requires a fifth-order model, whereas wind speed and COVID-19 death counts in Russia are suitably modeled by a second-order framework. The paper also explores the subtleties of higher-order models and suggests a custom strategy for model selection that enhances the accuracy and interpretability of time series forecasting predictions.