A Bayesian Approach to Vector Autoregressive Model Estimation and Forecasting with Unbalanced Data Sets

Abstract

One disadvantage of vector autoregressive (VAR) models is that they require time series to have equal lengths in the estimation process. This requirement induces a loss of potentially valuable information coming from time series that are longer than others. The issue is particularly evident in macroeconometric setups whenever variables have different starting points due to reasons grounded in various data recording and/or collection particularities. In many developing and emerging economies - especially those that were transitioned to market economies in the late 20th century - initial statistical observations on macro variables suffer from uneven availability and/or reliability. In this paper, we offer a remedy through a Bayesian approach: information in longer time series is aggregated into a prior which is then used in the estimation of parameters for the VAR process of clipped and equally-sized time series. Relative model performance is assessed by forecasting ability of resulting models gauged by mean absolute scaled errors (MASE). For illustration purposes, we employ time series from the Georgian economy and find that resulting (Bayesian) VAR models on average perform 7% better than standard alternatives with the same set of variables.