Time-series forecasting models

Abstract

Statistical and mathematical models of forecasting are of paramount importance for the understanding and study of databases, especially when applied to data of climatological variables, which enables the atmospheric study of a city or region, enabling greater management of the anthropic activities and actions that suffer the direct or indirect influence of meteorological parameters, such as precipitation and temperature. Therefore, this article aimed to analyze the behavior of monthly time series of Average Minimum Temperature, Average Maximum Temperature, Average Compensated Temperature, and Total Precipitation in Belém (Pará, Brazil) on data provided by INMET, for the production and application forecasting models. A 30-year time series was considered for the four variables, from January 1990 to December 2020. The Box and Jenkins methodology was used to determine the statistical models, and during their applications, models of the SARIMA and Holt-Winters class were estimated. For the selection of the models, analyzes of the Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), Autocorrelation Correlogram (ACF), and Partial Autocorrelation (PACF) and tests such as Ljung-Box and Shapiro-Wilk were performed, in addition to Mean Square Error (NDE) and Absolute Percent Error Mean (MPAE) to find the best accuracy in the predictions. It was possible to find three SARIMA models: (0,1,2) (1,1,0) [12], (1,1,1) (0,0,1) [12], (0,1,2) (1,1,0) [12]; and a Holt-Winters model with additive seasonality. Thus, we found forecasts close to the real data for the four-time series worked from the SARIMA and Holt-Winters models, which indicates the feasibility of its applicability in the study of weather forecasting in the city of Belém. However, it is necessary to apply other possible statistical models, which may present more accurate forecasts.