Linearized Ridge Regression Modeling with MM-Estimator in Statistical Downscalling for Rainfall Forecasting

Rainfall is one of the important climate variables to be predicted because it affects various sectors, such as agriculture, health, and disasters. One method that can be used to forecast rainfall is statistical downscaling, which is the process of relating large-scale climate variables to local-scale climate variables. However, this method has several challenges, such as the presence of heteroscedasticity, multicollinearity, and outliers in the data. To overcome these challenges, this study proposes linearized ridge regression modelling with MM-estimator in statistical downscaling for rainfall forecasting. Linearized ridge regression is a linear regression method that can reduce the influence of multicollinearity by adding a penalty parameter to the covariance matrix. MM-estimator is a robust method that can handle outliers by using two estimators, namely the initial estimator (S-estimator) and the final estimator (M-estimator). This research uses daily rainfall data from BMKG Pangkep station and Global Circulation Model (GCM) output data as predictors. The results showed that linearized ridge regression modelling with MM-estimator has better performance than linearized ridge regression modelling without MM-estimator in terms of accuracy and resilience to outliers with a correlation value of 0.94 against the acute rainfall data, the Root Means Square Error value obtained is 97.26 and 86.57% of determinant coefisient value. Therefore, linearized ridge regression modelling with MM-estimator can be used as an alternative statistical downscaling method for rainfall forecasting. Based on the forecasting results for January - December 2023, it shows that the highest rainfall in Pangkep Regency is in January and the lowest rainfall is in September.