A Dynamic Autoregressive Time Series Regression Model for Precipitation Using Particulate Matter and Carbon Dioxide as Exogenous Variables

Abstract

This paper presents the Dynamic Autoregressive Time Series Regression Model (DATSRM) to forecast time series data characterised by complex seasonal patterns and external influences. Even though common models like Autoregressive with Exogenous Variables (ARX), Autoregressive Integrated Moving Average with Exogenous Variables (ARIMAX), Seasonal ARIMAX (SARIMAX), and Lagged Time Series Regression (LTSR) are widely used in time series analysis, they often struggle to effectively manage complex seasonal changes and important outside factors. DATSRM was developed to overcome these limitations by using exogenous variables to account for external factors, like the environment; autoregressive components to capture linear dependencies; and Fourier components to characterise seasonal and cyclical patterns. The model's effectiveness was evaluated using Nigerian datasets that included annual precipitation and air pollution metrics (carbon dioxide and particulate matter) from 1990 to 2022. The model's parameters were determined using the Ordinary Least Squares method. The Durbin-Watson statistic, autocorrelation analysis, Akaike information criterion (AIC) and Bayesian information criterion (BIC), residual diagnostics were used to assess the model's performance. Coefficient of determination (R²), adjusted coefficient of determination  were used for the model accuracy. Mean absolute error (MAE), root mean square error (RMSE), mean absolute percentage error (MAPE) were also used to evaluate the forecast's accuracy. The results obtained indicated that DATSRM outperformed ARX, ARIMAX and LTSR in terms of R² (0.8318, 0.8884, 0.8965) and  (0.7991, 0.8433, 0.8587). DATSRM achieved the lowest AIC (11.1585, 11.3381, 11.2088) and BIC (11.4306, 11.5101, 11.3309) values, indicating better model fit. The forecast evaluation of DATSRM has the smallest value when compared with ARX, ARIMAX and LTSR model, this indicates that DATSRM is a better model compared with existing fitted model. Therefore, DATSRM provides a more accurate and reliable approach to modelling and forecasting datasets characterized by seasonal and periodic behaviors influenced by external variables.

Keywords: Dynamic Autoregressive Time Series Regression, Autoregressive with Exogenous Variable, Lagged Time Series Regression, Autoregressive Integrated Moving Average with Exogenous Variable, Fourier Technique