Multi‐model Forecasts of the West Texas Intermediate Crude Oil Spot Price

• Date: 01 July 2017
• DOI: http://doi.org/10.1002/for.2440
• Author: Laura Ryan,Bronwen Whiting
• Published date: 01 July 2017

Journal of Forecasting,J. Forecast. 36, 395–406 (2017)

Published online 13 September 2016 in Wiley Online Library (wileyonlinelibrary.com)DOI: 10.1002/for.2440

Multi-model Forecasts of the West Texas Intermediate Crude Oil

Spot Price

LAURA RYAN1AND BRONWEN WHITING2

1

PIMCO Australia Pty Ltd, Sydney, NSW, Australia

2

Research School of Finance, Actuarial Studies and Statistics, College of Business and Economics,

Australian National University, Acton, ACT, Australia

ABSTRACT

We measure the performance of multi-model inference (MMI) forecasts compared to predictions made from a single

model for crude oil prices. We forecast the West Texas Intermediate (WTI) crude oil spot prices using total OECD

petroleum inventory levels, surplus production capacity, the Chicago Board Options Exchange VolatilityIndex and an

implementation of a subset autoregression with exogenous variables (SARX). Coefficient and standard error estimates

obtained from SARX determined by conditioning on a single ‘best model’ ignore model uncertainty and result in

underestimated standard errors and overestimated coefficients. We find that the MMI forecast outperforms a single-

model forecast for both in- and out-of-sample datasets over a variety of statistical performance measures, and further

find that weighting models according to the Bayesian information criterion generally yields superior results both in

and out of sample when compared to the Akaike information criterion. Copyright © 2016 John Wiley & Sons, Ltd.

KEY WORDS Akaike; Bayesian information criterion; model uncertainty; information theoretic; autore-

gression; petroleum inventories

INTRODUCTION

Traditionally, any model selection process used will identify a single ‘best’ model from a set of candidate models.

The model selected is then reported as the winner and we disregarded any losing models. Most of the research into

oil price forecasting follows this pattern, presenting a final ‘winning model’ based on some model selection process.

The final model reported is treated as though there is no uncertainty with respect to the size of the coefficients,

significance of the coefficients, variables included or variables excluded. However, many different types of model

selection processes exist and, for any given dataset, use of a different model selectionprocess may result in a different

model being selected. Conversely,for any given model selection process, a different final winning model would likely

result if we obtained a new dataset. This leads us to pose the question: if the final winning model is dependent on the

model selection process, how certain can we be about the final model form? It further leads to the conclusion that any

coefficient estimates we find should also account for this model uncertainty.

In the realm of traditional forecasting, combining models has been discussed extensively, from Bates and Granger

(1969), with Winkler (1983) discussing methods of combination (weighted averages vs. simple averages vs. other

methods), Reeves and Lawrence (1982) considering combining forecasts for multiple objectives and Palmand Zellner

(1992) discussing issues in combining forecasts with different Bayesian techniques. These methods all relate to

combining forecast values; our paper deals with averaging models themselves. Something approaching this idea was

considered by Bates and Granger (1969), where it was commented that when dealing with forecasts which make

‘different assumption(s) about the form of the relationship between the variables’ this case ‘does not necessarily lead

to a situation in which a combined forecast improves upon the better individual forecast’. This paper aims to show

that when we combine the models themselves we can improve our inference.

Many researchers have identified the issues associated with model uncertainty resulting from the model selection

process (see Clyde 2000; Anderson et al., 2001; Clyde and George, 2004; Bernanke et al., 2004; Austin, 2008). These

issues include such problems as noise variables being identified as true predictors, true predictors being excluded,

p-values being too small (leading to overestimation of significance), and coefficients being biased away from zero.

These problems result because we only have a single realisation of the data-generating process (DGP) to analyse.

Any model that we fit may be capturing characteristics specific to the single-sample path and may not generalise to

the population. This leads to downwardly biased standard error estimates, overestimation of coefficients and therefore

overestimation of the importance of the variables themselves. When we attempt to model a large number of variables

and therefore consider a large set of initial candidate models, model uncertainty is exacerbated (see Miller, 1990). For

Correspondence to: Bronwen Whiting, Research School of Finance, Actuarial Studies and Statistics, College of Business and Economics,

Australian National University,Acton, ACT 2601, Australia. E-mail: bronwen.whiting@anu.edu.au

Copyright © 2016 John Wiley & Sons, Ltd