Applications of HMMs to Financial Data: A Data-Motivated Approach

• Activity Number: 247
• Type: Contributed
• Date/Time: Monday, July 30, 2012 : 2:00 PM to 3:50 PM
• Sponsor: Business and Economic Statistics Section
• Author(s): Tessa Childers-Day*+ and Lisa Goldberg
• Companies: University of California at Berkeley and MSCI
• Keywords: Hidden markov model ; Regime switching ; Model selection ; Autoregressive model ; Bootstrap p-value

Abstract

The notion that the behaviors of financial markets are related to unobservable economic states or regimes has both theoretical and empirical bases. Hidden Markov Models (HMMs) are intuitive, flexible models that allow for unobservable states, as well as the heavy tails and skew often present in financial data. We briefly review the literature and illustrate the advantages of HMMs over single-state autoregressive models, using real world financial data. We use established model selection criteria in a multiple state world, and discover via simulation studies that these criteria perform as would be expected in the single-state applications for which they were designed. We also find that, unlike single-state analyses, the assumption of normality in HMMs is not rejected in an empirical example involving the S&P 500. This finding holds in both traditional tests, and those that take the existence of states specifically into account. This paper shows that HMMs provide a better fit to the S&P 500 data than traditional, single-state models, and that existing model selection techniques are appropriate for use in this framework.