Modelos estatísticos empregados para a previsão sazonal da precipitação no Brasil

Abstract

This present research aims to apply statistical models of time series for the forecast of seasonal rainfall in sub-regions of the South, Southeast and Midwest regions of Brazil, investigating whether the models of Integrated Autoregressive classes and Moving Averages that take into account the seasonal component (SARIMA), Integrated Autoregressive and Moving Averages that considers a seasonal component and allows the entry of exogenous variables (SARIMAX), Exponential Smoothing and Combined can be used as a support tool for the dynamic models in forecasting monthly accumulation. In order to carry out the study, data from the historical series corresponding to the accumulated monthly combination, extracted from Xavier et al., (2015) from the South, Southeast and Midwest regions of Brazil, between latitudes (20,625° S and 33, 62° S) and longitudes (42.62° W and 57.62° W) in the period from January 1st, 1980 to December 31st, 2013. These data were interpolated to 1o latitude by 1o longitude, being the series the central point. In total, 107 historical series of accumulated monthly graduation were defined, containing each 408 basic series (months). The Sea Surface Temperature (SST) series selected for the same period with 5º latitude by 5º longitude, being the series a central point, comprised in the range between 60ºN and 60ºS, belonging to the ERSSTv5 data set from NOAA (Huang et al., 2017). 1418 historical series of SST were obtained, with each series containing 408 observations. To adjust the models, RStudio software was used. The influence of SST in the sub-regions was determined through the Person correlation. The quality of point forecasts was evaluated by means of the absolute percentage of errors. The predictions were categorized using the quantile technique. The Deibol-Mariano test was used to verify if there is a statistically significant difference between the predictions of the models. The sub-regions with similarities in monthly accumulated precipitation were defined by cluster analysis. The technique determined five similar sub-regions: South Sub-region 1, South Sub-region 2, South Sub-region 3, Southeast / Center 1 and Southeast / Midwest 2. The models proposed for the quarterly seasonal forecasts are adjusted: summer, autumn, winter and spring. The best forecast results for the three South sub-regions were obtained from the autumn and spring period, followed by summer. In the winter period, the models encountered difficulties in adjusting and forecasting, in view of the high variability contained in the time series for these periods. In the Southeast / Midwest regions, models were tested for the months from November to March (extended summer), which is considered a rainy season. The models demonstrated an excellent fit and performance for both regions with errors in point forecasts of around 14% Southeast / Midwest 1 sub-region and 18% Southeast / Midwest 2 sub-region, with no statistically significant difference between the predictions of the tested models. For these sub regions, a strong influence of the SST in the accumulated monthly rainfall must be considered. It is concluded that the proposed ST forecasting models can be used as a tool to support the dynamic models for the forecast of monthly accumulated precipitation in the surveyed regions, with emphasis on the SARIMA model.