CMMSE: A Time-Varying Approach to Linear Mixed Models

Linear mixed models (LMMs) are widely utilized for their ability to handle both fixed and random effects, making them versatile tools in statistical analysis. However, traditional LMMs assume constant random effects over time, a limitation when dealing with data where variances and structures change. On the other hand, time series models like ARIMA and GARCH are great at capturing time-related patterns and volatility but cannot handle random effects. In this study, we propose a time-varying linear mixed model (TVLMM) that integrates the strengths of ARIMA, GARCH, and LMMs, allowing for dynamic random effects over time. This novel framework offers a more flexible and realistic approach to modeling data, particularly in contexts where underlying processes evolve, such as in finance, economics, and social sciences. We demonstrate the efficacy of TVLMM through a simulated dataset, highlighting its potential for more accurate and reliable forecasting.