Segmenting the Time Series of a Market Index Using a Hidden Markov Model

• Activity Number: 135
• Type: Contributed
• Date/Time: Monday, August 1, 2011 : 8:30 AM to 10:20 AM
• Sponsor: Business and Economic Statistics Section
• Author(s): Ziqian Tony Huang*+ and Stanley L. Sclove
• Companies: University of Illinois at Chicago and University of Illinois at Chicago
• Keywords: time series ; stock market index ; S&P500 ; Bull and Bear ; hidden Markov model

Abstract

The time series of monthly rates of return (RORs) of the S&P 500 stock index for January, 1950, through September, 2010 (729 months, 728 RORs), was segmented by several methods, the up-down method, in which a month is declared to be a Bull month if the ROR was positive and a Bear month if it was negative, a Bull-Bear scoring method comparing one month's high, low and close to those of the preceding month, and some hidden Markov models (HMMs). HMMs with two and three states were fit and compared with a single distribution for the RORs. The single distribution appears to be non-Normal. State-conditional Normal distributions with different means and variances were fit for two and three states. The HMMs were scored by BIC. The model with two states was better. One state had a positive mean ROR, the other, a negative mean ROR. This corresponds to conventional notions of Bull and Bear states. The Bear state has a higher variance. Some comparison with ARIMA and ARCH models was made. Among these, there is evidence that an ARCH(3) model would be best, but not as good as the HMM model with two states.