Modeling Persistence and Parameter Instability in Historical Crude Oil Price Data Using a Gibbs Sampling Approach

Abstract

This study aims to analyze two important features of crude oil price data, namely, persistence and parameter instability. We apply an autoregressive fractionally integrated moving average model in which crude oil price persistence measured through the fractional integration parameter, conditional innovation variance and persistence change through Markov-switching dynamics. Model estimation is conducted using Gibbs sampling combined with data augmentation. Applied to monthly West Texas Intermediate crude oil price data from September 1859 to December 2017, we find evidence of four regimes. The main effect of regime switching is in the conditional variance and persistence of the innovations, but there is the possibility that regime switching also affects the fractional integration parameter. Across regimes crude oil price is very persistent with the order of integration estimated close to or slightly higher than one. Finally, discarding parameter instability leads to overestimation of the degree of persistence in the price of crude oil. It also results in inferior density forecasts.