A Comparative Study of Seasonal and Conditional Heteroskedasticity Models in Time Series Using Simulation

Abstract

This study evaluates the performance of the hybrid SARIMA–GARCH model in representing seasonal time series characterized by heteroskedastic volatility, using a Monte Carlo simulation framework under a controlled data-generating process (DGP). The approach combines SARIMA for modelling the conditional mean and GARCH for capturing the conditional variance, under both Gaussian and Student-t error distributions. Results reveal that the SARIMA model suffers from a structural inability to recover the true structure of conditional variance, as its RMSE remains high and unstable even with increasing sample size stemming from its assumption of constant variance. In contrast, the hybrid SARIMA–GARCH model demonstrates a clear methodological improvement: its RMSE declines systematically with larger sample sizes, confirming its capacity to accurately represent volatility dynamics, particularly in heavy-tailed environments. These findings indicate that jointly modelling the mean and variance components constitutes a well-justified methodological choice for analyzing real-world financial time series that exhibit both seasonality and time-varying volatility.