The Hidden States of the Markets A Markov-Switching Implementation of the GARCH framework

Abstract

Financial equity markets exhibit complex, non-linear behaviors characterized by severe volatility clustering and excess kurtosis. Traditional econometric models, such as the standard GARCH(1,1), attempt to capture these dynamics but are fundamentally constrained by the assumption of a single, continuous parameter space. Over extended horizons, this static assumption forces the model to misinterpret transient market shocks as permanent structural shifts, resulting in the overestimation of long-term volatility – a flaw known as the Lamoureux Lastrapes phenomenon. This thesis resolves this structural inefficiency by implementing a Markov-Switching GARCH (MS-GARCH) framework. By allowing the variance parameters to dynamically shift across discrete market states, the model accurately separates transient crises from baseline memory. The empirical analysis applies this framework to the daily logarithmic returns of the S&P 500, Nasdaq 100 and Dow Jones Industrial Average. Using the Bayesian Information Criterion (BIC) for strict parameter penalization and model evaluation, the MS-GARCH framework resoundingly outperforms the single-regime baseline across all indices. The results reveal a clear structural topography: the heavily diversified S&P 500 operates optimally at 4 distinct states. Furthermore, it is demonstrated that market recoveries for the S&P 500 are procedural, multi-stage processes rather than swift re-bounces. In contrast, the more concentrated Nasdaq 100 and Dow Jones optimize at 2 states, characterizing severe volatility as highly transient shocks. Ultimately, this study mathematically suggests that extreme market events are not merely statistical outliers, but distinct structural regimes.