Economic significance of commodity return forecasts from the fractionally cointegrated VAR model

• Author: Sepideh Dolatabadi,Ke Xu,Morten Ørregaard Nielsen,Paresh Kumar Narayan
• Published date: 01 February 2018
• Date: 01 February 2018
• DOI: http://doi.org/10.1002/fut.21866

Received: 5 January 2017

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Accepted: 1 August 2017

DOI: 10.1002/fut.21866

RESEARCH ARTICLE

Economic significance of commodity return forecasts from the

fractionally cointegrated VAR model

Sepideh Dolatabadi

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Paresh Kumar Narayan

2

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Morten Ørregaard Nielsen

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Ke Xu

4

1

Queen's University, Kingston, Ontario,

Canada

2

Deakin University, Burwood, Victoria,

Australia

3

Queen's University, Kingston, Ontario,

Canada, and CREATES, Aarhus, Denmark

4

University of Victoria, Victoria, British

Columbia, Canada

Correspondence

Morten Ørregaard Nielsen, Department of

Economics, Queen's University, Dunning

Hall Room 307, 94 University Avenue,

Kingston, Ontario K7L 3N6, Canada.

Email: mon@econ.queensu.ca

Funding information

Center for Research in Econometric

Analysis of Time Series, Aarhus, Denmark;

Canada Research Chairs; Social Sciences

and Humanities Research Council of

Canada

We model and forecast commodity spot and futures prices using fractionally

cointegrated vector autoregressive (FCVAR) models generalizing the well-known

(non-fractional) CVAR model to accommodate fractional integration. In our

empirical analysis to daily data on 17 commodity markets, the fractional model is

statistically superior in terms of in-sample fit and out-of-sample forecasting. We

analyze economic significance of the forecasts through dynamic (mean-variance)

trading strategies, leading to statistically significant and economically meaningful

profits in most markets. We generally find that the fractional model generates higher

profits on average, especially in the futures markets.

JEL CLASSIFICATION

C32, G11

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INTRODUCTION

The forecastability of commodity market returns is a very active area of research in financial economics. In particular, recent

research has shown that commodity spot and futures prices are fractionally cointegrated: see, inter alia, Baillie and Bollerslev

(1994), Lien and Tse (1999), Maynard and Phillips (2001), Coakley, Dollery, and Kellard (2011), and Dolatabadi, Nielsen, and

Xu (2016). An implication is that a fractionally cointegrated model may provide a better statistical fit for commodity prices and

returns. Relatedly, the understanding of how commodity market return forecasts can be used to devise trading strategies appears

still rather limited.

In this paper, we make two contributions to this literature. Our first contribution is methodological. We propose to model and

forecast commodity spot and futures prices using the recently developed fractionally cointegrated vector autoregressive

(FCVAR) model of Johansen (2008) and Johansen and Nielsen (2012). Specifically, we derive the best linear predictor for the

FCVAR model and show that it takes a relatively simple form due to the autoregressive structure. We thus demonstrate how to

forecast commodity spot and futures prices and returns based on the FCVAR model, and we evaluate these using statistical

measures of forecast performance. Our second contribution is to investigate the economic significance of the FCVAR model

forecasts through a dynamic trading strategy based on a portfolio of two assets with portfolio weights derived from a

J Futures Markets. 2018;38:219–242. wileyonlinelibrary.com/journal/fut © 2017 Wiley Periodicals, Inc.

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mean-variance utility function and from return forecasts. Throughout, we compare with forecasts from the more standard

(non-fractional) cointegrated vector autoregressive (CVAR) model of Johansen (1995).

In our empirical analysis, we consid er spot and futures prices of 17 commodit ies, and we demonstrate that the FCVAR

model provides superior sta tistical in-sample fit compa red with the more standard CVAR mo del. We also estimate price

discovery from both models (e .g., Dolatabadi, Nielsen, & Xu, 2015, and references therein ), which may be important from a

forecasting point of view since his torical information from the domi nant market could be useful in forecasti ng prices and

returns in the non-dominant m arket. In any case, both the FCV AR and CVAR models are joint mode ls of the two prices

series, and as such they automa tically take into account the pric e discovery information in mod eling and forecasting. With

both the CVAR and FCVAR models we find that there is signific ant price discovery in both the spot and futures markets for

many commodities, althou gh the general tendency is that the futures market ha s a larger share of the price discovery process,

as much theory predicts (e.g., Hasbro uck, 1995).

For the statistical forecast comparison we consider several forecast horizons and a variety of out-of-sample forecast

evaluation metrics. The general finding is that the FCVAR model outperforms the CVAR model. Specifically, in terms of

statistical tests of forecast superiority at the short horizon (h=1), these favor the FCVAR model in almost all cases and are

statistically significant at standard levels in most cases. At longer horizons, most statistical tests continue to favor the FCVAR

model, although fewer are now statistically significant. Among those that are statistically significant for longer horizon

forecasting (h=5orh=21), 22 out of 23 favor the FCVAR model.

Finally, as an additional metric of forecast performance and comparison, we also examine the economic—as opposed to

purely statistical—significance of return forecasts. We do this by investigating whether the return forecasts can generate

significant excess returns when implemented in a dynamic portfolio trading strategy. For our main empirical analysis we find

that using return forecasts from both FCVAR and CVAR models in simple mean-variance trading strategies leads to statistically

significant and economically meaningful profits in most commodity markets, although there is much heterogeneity in profits

across different markets. Furthermore, we find that profits are higher on average when based on forecasts from the FCVAR

model rather than the CVAR model, especially in the futures markets where trading is also more practical.

Our finding that profits from commodity markets are statistically significant and economically meaningful is consistent with

a broad range of studies which show, using different approaches, that commodity markets are profitable. For example, Miffre and

Rallis (2007) and Narayan, Ahmed, and Narayan (2014) show profitability using technical and momentum trading strategies.

However, given the profitability of these approaches, only limited focus has been on using a model-based forecasting approach to

estimate profits (an exception is Narayan, Narayan, & Sharma, 2013).

In spite of the limited attention to model-based forecasting approaches, there is a clear acceptance of the fact that a

forecasting based trading model that draws its profitability analysis from a utility function, such as a mean-variance utility

function, has theoretical appeal, see, for example, Marquering and Verbeek (2004) and Campbell and Thompson (2008). On the

basis of this evidence, commodity markets are treated as an investment class. As the focus on theoretically motivated profitability

analysis gains momentum, following, for example, the works mentioned above, the emphasis on and hence demand for

appropriate forecasting models will increase.

We note from the outset that, although trading strategies based on commodity spot prices are not really feasible, because it

would be too expensive to take possession of the commodity, we nonetheless consider simultaneous modeling of commodity

spot and futures prices. In terms of applying these as forecasting models for futures returns, it has no relevance whether spot

prices can be traded on or not, and hence this point is irrelevant for all our results regarding futures markets, futures price, and

return forecasting, and trading strategies involving commodity futures. For trading strategies involving commodity spot markets,

these can still be considered a useful metric for comparison of forecast performance in terms of economic significance, even if

the trading strategies are infeasible; a related point was also made in, for example, Graham-Higgs, Rambaldi, and Davidson

(1999), Wang (2000), and Narayan et al. (2013). Thus, even if portfolios involving commodity spot positions are infeasible, we

consider such “artificial portfolios”as a means of forecast evaluation and comparison.

To demonstrate the robustness of our empirical results, our analysis is conducted with several different variations. First, we

forecast returns over both short and long horizons. Second, we use several statistical out-of-sample forecast evaluation metrics.

Third, when estimating profits using the mean-variance investor utility function, where the choice of the investor's risk-aversion

coefficient influences portfolio weights, we consider low, medium, and high risk-aversion investors. Fourth, we calculate Sharpe

ratios. Finally, when estimating profits we consider several alternative restrictions on short-selling and leverage/borrowing. In

general, all these results confirm (i) that portfolio excess returns are statistically different from zero and economically

meaningful in many commodity markets and (ii) that portfolio returns derived from CVAR and FCVAR model forecasts are

similar, although the latter are slightly higher on average.

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