Intrinsic Bayesian estimation of linear time series models

Abstract

Intrinsic loss functions (such as the Kullback–Leibler divergence, i.e. the entropy loss) have been used extensively in place of conventional loss functions for independent samples. But applications in serially correlated samples are scant. In the present study, we examine Bayes estimator of Linear Time Series (LTS) model under the entropy loss. We derive the Bayes estimator and show that it involves a frequentist expectation of regressors. We propose a Markov Chain Monte Carlo procedure that jointly simulates the posteriors of the LTS parameters with frequentist expectation of regressors. We conduct Bayesian estimation of an LTS model for seasonal effects in some U.S. macroeconomic variables.

Keywords:

• entropy loss
• latent parameters
• reference prior

AMS 1991 Subject Classifications:

• Primary 62F15
• Secondary 62A15
• 62C10
• 62F25

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Notes on contributors

Shawn Ni

Dr. Shawn Ni holds a PhD in Economics from University of Minnesota. He is currently Middlebush Professor of Economics and Adjunct Professor of Statistics at University of Missouri-Columbia. He conducts research on a wide range of empirical economics topics and Bayesian statistics.

Dongchu Sun

Dr. Dongchu Sun holds a PhD in Statistics from Purdue University. He is a research professor of statistics at the University of Nebraska-Lincoln and East China Normal University. His research interests includes Bayesian analysis, small area estimation, decision theory, business and econometrics, space-time and longitudinal models, and smoothing splines.