Stock Returns and Real Growth: A Bayesian Nonparametric Approach

The study of the joint dynamic behavior between stock market returns and real economic growth rates is an important empirical question in finance and macroeconomics. This paper investigates their linkage by proposing a vector autoregressive infinite hidden Markov model. Our model has two advantages over the existing approaches in the literatures. In contrast to Markov switching models with fixed states, our model will learn the number of states from the data rather than fixing it a priori. The vector autoregressive setting in our model allows the joint time series of stock market returns and real growth rates to share the same unobserved state variable. Compared to existing models, our model shows significant improvements in out-of-sample density forecast accuracy. This paper demonstrates the predictive power of stock market returns for future growth rates are better captured by the unobserved states variables, rather than the lagged stock market returns. key words: hierarchical Dirichlet process prior, beam sampling, Markov switching, MCMC, JEL: C58, C14, C22, C11 ∗I would like to thank John Maheu for his excellent guidance. I am grateful for Martin Burda for support and feedback. I would like to thank Yuanyuan Wan for his valuable comments. I am grateful for comments from conference participants at midwest econometrics annual meeting and seminar participants at University of Toronto. Department of Economics, University of Toronto, [email protected]