Bayesian Inference and Prediction of a Multiple-Change-Point Panel Model with Nonparametric Priors
Mark Fisher and Mark J. Jensen
Working Paper 2018-2
Change point models using hierarchical priors share in the information of each regime when estimating the parameter values of a regime. Because of this sharing, hierarchical priors have been very successful when estimating the parameter values of short-lived regimes and predicting the out-of-sample behavior of the regime parameters. However, the hierarchical priors have been parametric. Their parametric nature leads to global shrinkage that biases the estimates of the parameter coefficient of extraordinary regimes toward the value of the average regime. To overcome this shrinkage, we model the hierarchical prior nonparametrically by letting the hyperparameter's prior—in other words, the hyperprior—be unknown and modeling it with a Dirichlet processes prior. To apply a nonparametric hierarchical prior to the probability of a break occurring, we extend the change point model to a multiple-change-point panel model. The hierarchical prior then shares in the cross-sectional information of the break processes to estimate the transition probabilities. We apply our multiple-change-point panel model to a longitudinal data set of actively managed, U.S. equity, mutual fund returns to measure fund performance and investigate the chances of a skilled fund being skilled in the future.
JEL classification: C11, C14, C41, G11, G17
Key words: Bayesian nonparametric analysis, change points, Dirichlet process, hierarchical priors, mutual fund performance