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<p>This study evaluates the performance of various linear and nonlinear time series models for simulating monthly precipitation at 12 stations in Algeria. We compare hybrid ARMA–ARCH/GARCH models (CARMA-ARCH, CARMA-GARCH), their optimally tuned versions, and Bayesian-optimized variants, as well as two bilinear hybrid models (BL-ARCH and BL-GARCH). This is the first work to integrate and compare this specific suite of models for precipitation forecasting. Two scenarios were considered: (1) a ‘uniform’ scenario using the same inputs (temperature at lags 0 and 1) for all stations, and (2) a ‘station-specific’ scenario allowing additional lagged inputs (e.g. temperature lag 6, precipitation lags) chosen per station. The results showed that in the first scenario, where model inputs were constant across all stations (temperature with lags 0 and 1), the simple hybrid models and their optimal versions performed well in precipitation simulation, yielding an average error of 17&#xa0;mm. Under the fixed scenario (Scenario 1), the Bilinear-based models exhibited the weakest performance. In the second scenario, where both the number of inputs increased (including precipitation with various lags in addition to temperature and its lags) and input variability differed across stations, the rainfall simulation results for the studied stations showed that the average error decreased by 12&#xa0;mm compared to the first scenario. The findings revealed that in the second scenario, With the addition of temperature at lags 3 and 6 and precipitation at lag 6, the top-performing models shifted toward BL-based models. Although the performance of all examined models was acceptable, BL-based models demonstrated superior performance compared to others due to their ability to better handle increased fluctuations caused by precipitation lags. Additionally, the results indicated that Bayesian optimization did not improve the performance of the base models despite increasing their complexity. Our findings provide a framework for selecting model complexity based on data availability, which can enhance forecasting accuracy.</p>

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Evaluating the role of dimensionality and complexity structure in time series models for precipitation simulation

  • 期刊论文

  • 发表日期：

    2025年10月18日

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  • Issam Rehamnia,
  • Mohammad Nazeri Tahroudi,
  • Mehri Saeidinia

摘要

This study evaluates the performance of various linear and nonlinear time series models for simulating monthly precipitation at 12 stations in Algeria. We compare hybrid ARMA–ARCH/GARCH models (CARMA-ARCH, CARMA-GARCH), their optimally tuned versions, and Bayesian-optimized variants, as well as two bilinear hybrid models (BL-ARCH and BL-GARCH). This is the first work to integrate and compare this specific suite of models for precipitation forecasting. Two scenarios were considered: (1) a ‘uniform’ scenario using the same inputs (temperature at lags 0 and 1) for all stations, and (2) a ‘station-specific’ scenario allowing additional lagged inputs (e.g. temperature lag 6, precipitation lags) chosen per station. The results showed that in the first scenario, where model inputs were constant across all stations (temperature with lags 0 and 1), the simple hybrid models and their optimal versions performed well in precipitation simulation, yielding an average error of 17 mm. Under the fixed scenario (Scenario 1), the Bilinear-based models exhibited the weakest performance. In the second scenario, where both the number of inputs increased (including precipitation with various lags in addition to temperature and its lags) and input variability differed across stations, the rainfall simulation results for the studied stations showed that the average error decreased by 12 mm compared to the first scenario. The findings revealed that in the second scenario, With the addition of temperature at lags 3 and 6 and precipitation at lag 6, the top-performing models shifted toward BL-based models. Although the performance of all examined models was acceptable, BL-based models demonstrated superior performance compared to others due to their ability to better handle increased fluctuations caused by precipitation lags. Additionally, the results indicated that Bayesian optimization did not improve the performance of the base models despite increasing their complexity. Our findings provide a framework for selecting model complexity based on data availability, which can enhance forecasting accuracy.