Comparative Analysis of Sarima and Holt-Winters Models for Rainfall Prediction in Cajamarca, Peru

Abstract

The research compares two models for rainfall prediction in the Cajamarca Valley, Peru, for the period 2021-2024 using the SARIMA econometric models and the Holt-Winters Additive Exponential Smoothing. The analysis of monthly rainfall in the Cajamarca Valley reveals considerable variability in the data. The rainiest year was 2012 with a total of 823.9 mm, while 2020 was the least rainy recording only 340.2 mm. Rainfall is unpredictable for agricultural activities, as well as for human consumption. In the Cajamarca valley there are significant fluctuations over the years, with months of less rainfall generally between May and September. When performing the comparative analysis of the statistics corresponding to both models in order to evaluate their predictive capacity, it has been observed that the Holt-Winters Additive Exponential Smoothing Model stands out significantly compared to the SARIMA Model. In this sense, the Root Mean Squared of Errors (RMSE) shows values of 28,697 versus 41,546, and the Mean Absolute Error (MAE) shows values of 20,044 as opposed to 29,260, both results being lower in the SARIMA model. It is worth noting that lower values in these metrics indicate greater model precision. In addition, the R² (Coefficient of Determination) evaluates the effectiveness of the fit of a model, where a higher value indicates a better quality of fit. In this situation, a value of 0.657 is observed, which exceeds the 0.287 corresponding to the SARIMA model. This high R² value suggests that the Holt-Winters Additive Exponential Smoothing model provides superior tuning and more accurate predictions of rainfall in the Cajamarca Valley. The methodology to predict rainfall in the Cajamarca Valley can be applicable to any city in the country and other places with similar characteristics.