Bayesian nonparametric vector autoregressive models

Jim E. Griffin,Maria Kalli

doi:10.1016/j.jeconom.2017.11.009

Abstract

Vector autoregressive (VAR) models are the main work-horse models for macroeconomic forecasting, and provide a framework for the analysis of complex dynamics that are present between macroeconomic variables. Whether a classical or a Bayesian approach is adopted, most VAR models are linear with Gaussian innovations. This can limit the model’s ability to explain the relationships in macroeconomic series. We propose a nonparametric VAR model that allows for nonlinearity in the conditional mean, heteroscedasticity in the conditional variance, and non-Gaussian innovations. Our approach differs from that of previous studies by modelling the stationary and transition densities using Bayesian nonparametric methods. Our Bayesian nonparametric VAR (BayesNP-VAR) model is applied to US and UK macroeconomic time series, and compared to other Bayesian VAR models. We show that BayesNP-VAR is a flexible model that is able to account for nonlinear relationships as well as heteroscedasticity in the data. In terms of short-run out-of-sample forecasts, we show that BayesNP-VAR predictively outperforms competing models.

Highlights

Introduced by Sims (1980), vector autoregressive (VAR) models provide a systematic way of capturing the dynamics and interactions of multiple time-series
We introduce a novel stationary model for multivariate time series where the stationary and transition densities are directly modelled using Bayesian nonparametric methods, which place a prior on an infinite dimensional parameter space and adapt their complexity to the data
We extend their work to multivariate stationary time series and we call our model Bayesian nonparametric VAR (BayesNP-VAR)

Summary

Introduction

Introduced by Sims (1980), vector autoregressive (VAR) models provide a systematic way of capturing the dynamics and interactions of multiple time-series. Mixtures of experts are extensions of smooth regression models and popular within the machine learning community They are used in regression to estimate the conditional density p(y|x) of a univariate y for all values of a (often, high-dimensional) covariate x, using mixtures where the component weights depend on a x, see Jacobs et al (1991), Jordan and Jacobs (1994), Geweke and Keane (2007) and Villani et al (2012). Antoniano-Villalobos and Walker (2016) describe a Gibbs sampler for their univariate model but truncate the centring distribution for the stationary variance of each component away from zero To avoid this truncation, we use an adaptive truncation method introduced by Griffin (2016) which adaptively truncates the infinite sum in the numerator and denominator and tends to avoid large truncation errors in the posterior.

Evalulate

Simulated data

Data sets

Impulse Response Functions

Out-of-sample predictive performance

Discussion

Findings

A Appendix