Abstract

The analysis of time series using Autoregressive and Moving Average (ARMA) models constitutes a cornerstone of data analysis, yet selecting the appropriate model order (p, q) remains a pivotal challenge. Traditionally, this process involves examining empirical Autocorrelation Function (ACF) and Partial Autocorrelation Function (PACF) plots and evaluating numerous candidate models using Information Criteria (IC). Automated methodologies have been developed to streamline this task, which typically involves the analysis of a predefined set of orders or systematically exploring all feasible combinations within specified ranges. While systematic, they can be computationally expensive. In this context, sequential search strategies for the model order, like the Hyndman-Khandakar (HK) algorithm, represent more efficient alternatives. This algorithm defines a range of models with different (p,q) and each combination undergoes evaluation using IC. At each step of the algorithm, the model with the lowest criterion value is identified and iteratively adjusts parameters to explore adjacent models, continuing until no further improvements are observed.
This study aims to assess the effectiveness of commonly employed algorithms to determine optimal model orders, considering factors such as time series length and underlying model parameters. Additionally, it introduces an innovative post-processing step designed to enhance algorithmic performance by systematically removing non-significant coefficients. This enhancement underscores the advantages of integrating significance-based decision rules with traditional IC approaches.