Hybrid LSTM-RNN And Sarima Modeling For Time Series Temperature Prediction: The Case Of Antananarivo, Madagascar

Abstract

This study evaluates various approaches for temperature forecasting in Antananarivo, Madagascar, by comparing the performance of LSTM and SARIMA models, as well as their hybrid combinations. One of the explored strategies involves using an LSTM model to generate an initial forecast, and then modeling its residuals with SARIMA to refine the results. Another approach relies on using SARIMA to produce a preliminary estimate, whose predictions are subsequently incorporated into an LSTM model to better capture the complex dynamics of temperature variations. The goal is to identify the method that offers the best accuracy and stability to improve the reliability of weather forecasts.

While SARIMA has proven effective for linear data, it struggles to capture the non-linear fluctuations of local temperatures. The LSTM model, with its ability to model long-term dependencies and non-linearities, aims to address these limitations.

Our study demonstrated that combining forecasting models, particularly the SARIMA_LSTM hybrid approach, offers superior accuracy compared to other models for temperature forecasting in Antananarivo. This approach, which integrates exogenous variables into the SARIMA model and uses LSTM to refine forecasts by modeling residuals, consistently produced the most accurate results.

The performance of the models was rigorously evaluated using several statistical metrics and tests. We used the Root Mean Square Error (RMSE) to measure forecast accuracy, and Autocorrelation Function (ACF) and Partial Autocorrelation Function (PACF) plots to analyze the temporal structure of the data and residuals. Additionally, we applied the Ljung-Box test to verify the absence of residual autocorrelation, and analyzed skewness and kurtosis to understand the distribution of residuals. Finally, the heteroscedasticity test was performed to evaluate the constancy of error variance.

These analyses confirmed that the SARIMA_LSTM model, by leveraging the strengths of each constituent model, successfully captured both seasonal trends and complex relationships in the temperature data, leading to more reliable forecasts.