Bull, bear or any other states in US stock market?

a r t i c l e i n f o Keywords: Markov switching model Optimal number of states S&P 500 returns A stock market is traditionally considered to shift between bull and bear markets, reflecting the states of high mean and low mean in stock returns, respectively. In this paper, we attempt to detect more different states in a stock market by applying a Bayesian Markov switching model, where the optimal number of states is determined according to the marginal likelihoods. An application to US stock market indicates that there exist four dis-tinguishable states and each state represents different characteristics of US stock market. Traditionally speaking, a stock market trend is usually considered to switch between two states, bull and bear markets. The terms bull market and bear market describe upward and downward trends of stock index or positive and negative stock index returns over a period of time, respectively. Since the switching between bull and bear markets is similar to the switching of GDP growth between expansions and contractions , methodologies that originally developed to identify the business cycle were naturally applied to identify the bull market and the bear market. There exist two main categories of methods in general, non-parametric method and parametric method. Non-parametric method directly deals with the time series data and attempts to determine the time points of peak (market top) and trough (market bottom) in the business cycle (stock index). An early study by Bry and Boschan (1971) developed a criterion to detect peaks and troughs and the method was applied by NBER to study the US business cycle. Harding and Pagan (2002) made adjustments to this method. Applications of non-parametric method to identify the bull market and the bear market include those of Pagan and Sossounov (2003) and Edvards et al. (2003). Parametric method develops econometric models to quantitatively study the time series. Among many models, a widely and frequently used model is the Markov switching model that allows parameter values to vary across states and models the switching mechanism between states by a first-order Markov process. The expansion (bull market) and contraction (bear market) in business cycle (stock market) exactly represent the two states of high mean and low mean in GDP growth (stock returns), respectively. Hamilton (1989) introduced a 2-state Markov switching model that allows switching in the mean parameter of GDP growth and applied it to identify the US …