Bayesian Estimation of the Polynomial Time Trend AR(1) Model through Spline Function

Abstract

In this paper, we develop an estimation procedure for an autoregressive model with polynomial time trend approximated by a spline function. Spline function has the advantage of approximating the non-linear time series in an appropriate degree of polynomial time trend model. For Bayesian parameter estimation, the conditional posterior distribution is obtained under two symmetric loss functions. Due to the complex form of the conditional posterior distribution, Markov Chain Monte Carlo (MCMC) approach is used to estimate the Bayes estimators. The performance of Bayes estimators is compared with that of the corresponding maximum likelihood estimators (MLEs) in terms of mean squared error (MSE) and average absolute bias (AB) via a simulation study. To illustrate the proposed study, import series of Brazil, Russia, India, China, and South Africa (BRICS) countries are analyzed.

Keywords and Phrases:

• Bayesian estimation
• MCMC method
• spline function

MATHEMATICS SUBJECT CLASSIFICATIONS:

• 62F15
• 37M10
• 65C05

Acknowledgments

The authors are thankful to the editor-in-chief and two anonymous referees for providing useful comments on an earlier version of this manuscript which led to this improved version.