Time Series Modeling and Forecasting Using Autoregressive Integrated Moving Average and Seasonal Autoregressive Integrated Moving Average Models

Abstract

Time series analysis is pivotal in discerning temporospatial data patterns and facilitating precise forecasts. This study scrutinizes the cardinal challenges associated with time series modeling, namely stationarity, parsimony, and overfitting, focusing on the application of Autoregressive Integrated Moving Average (ARIMA) and Seasonal Autoregressive Integrated Moving Average (SARIMA) models. An examination of six datasets reveals that these models adeptly encapsulate underlying data trends, enabling reliable predictions and yielding insightful conclusions. Relative to baseline methods, the proposed models demonstrate superior performance, as indicated by five evaluation metrics: Mean Squared Error (MSE), Frantic, Root Mean Squared Error (RMSE), Mean Absolute Percentage Error (MAPE), and Theil's U-statistics. The most parsimonious ARIMA or SARIMA model was selected for each dataset, with the resultant forecast summary graphically demonstrating the proximity between original and predicted observations. This study aims to contribute to the discourse on the validity and applicability of ARIMA and SARIMA models in time series analysis and forecasting.