The impact of data frequency on market efficiency tests of commodity futures prices

• Published date: 01 June 2018
• Author: Jeffrey H. Dorfman,Berna Karali,Xuedong Wu
• DOI: http://doi.org/10.1002/fut.21912
• Date: 01 June 2018

Received: 30 September 2016

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Accepted: 4 February 2018

DOI: 10.1002/fut.21912

RESEARCH ARTICLE

The impact of data frequency on market efficiency

tests of commodity futures prices

Xuedong Wu

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Jeffrey H. Dorfman

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Berna Karali

The University of Georgia, Athens, Georgia

Correspondence

Jeffrey H. Dorfman, University of Georgia,

312 Conner Hall, Athens, GA 30602.

Email: jdorfman@uga.edu

We investigate the impacts of sampling frequency and model specification

uncertainty on the outcome of unit root tests, commonly employed as market

efficiency tests, using a new, robust Bayesian test on seven commodity futures prices

at three different sample frequencies (daily, weekly, and monthly). Using Bayesian

model averaging to account for different possible mean and error variance

specifications, we show that sample frequency does affect the unit root test results:

the higher the frequency, the higher the support for stationarity. We further show that

not accounting for model specification uncertainty can produce unit root test results

that are not robust.

KEYWORDS

Bayesian model averaging, commodity futures, GARCH, model uncertainty, stationarity,

unit root tests

JEL CLASSIFICATION

C11, C58, Q11

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INTRODUCTION

When analyzing asset prices, the time series properties of the data have a very important economic meaning. If an asset price

series follows a unit root, then the market is deemed efficient in the sense that profitable predictions are unlikely to be possible.

Alternative tests of market efficiency are many, for example, based on cointegration. Researchers have tested whether spot and

futures prices are cointegrated to investigate price discovery and market efficiency in a variety of markets. Examples include

Bessler and Covey (1991), Chowdhury (1991), Lai and Lai (1991), Fortenbery and Zapata (1993), Schwarz and Szakmary

(1994), Chow (1998), and Yang, Bessler, and Leatham (2001). However, such cointegration tests are based on nonstationarity of

price series, and therefore require dependable tests of a unit root in order to proceed. Thus, for many empirical studies of asset

prices, model specification depends crucially on whether such market efficiency is assumed; for two recent examples in this

Journal, see Tong, Wang, and Yang (2016) and Fan, Li, and Park (2016). For these reasons, economists need a reliable, accurate,

and statistically efficient manner of testing such series for nonstationarity. Complicating the matter is the fact that existing tests

have low statistical power, which has led many researchers to seek larger samples of data to test.

To obtain more data one has two choices: a longer time span of data or a higher frequency of sampling within the same time

span. Using a longer time series (in calendar terms) is commonly believed to provide more information related to the stationarity,

thus leading to a more reliable testing result. Using higher frequency data while maintaining the same time span is generally

believed not to provide much additional information since intuitively, stationarity requires a series to pass its mean regularly

within the test sample, and increasing the sampling frequency may not change this mean reversion within the sample (Boswijk &

Klaassen, 2012). However, this is not necessarily the case if the low frequency data is constructed by systematic sampling, that is,

skipping certain intermediate observations from a high frequency process, because systematic sampling at a lower frequency can

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reduce observed mean reversions as well as impacting sample moments such as the mean and variance. This is worrisome

because systematic sampling is exactly the method employed to produce commonly used asset price series such as monthly

(weekly, daily) futures prices.

For example, researchers often pick the price of one day each week to construct weekly data from daily data. Choi (1992)

demonstrated by simulation that this kind of data aggregation will lower the power of augmented Dickey–Fuller (ADF) and

Phillips–Perron (PP) tests, although Chambers (2004) showed that this is a finite sample effect and asymptotically it is still

possible to consistently test for a unit root when sampling frequency varies.

Recently, Boswijk and Klaassen (2012) proved that the effects of systematic sampling on unit root testing is not negligible,

when a high-frequency sample has volatility clustering with fat-tailed innovations, the famous autoregressive conditional

heteroskedasticity which is typical of financial market data. Using simulated data they showed that likelihood ratio-based tests

were more powerful than the traditional ADF test on data processes displaying the aforementioned behavior characteristics. This

leads to a second way to test for unit roots more accurately: improve the testing method.

Unit root tests which focus on non-normal errors can be found in Lucas (1995) and Rothenberg and Stock (1997).

Seo (1999), Boswijk (2001), and Ling and Li (2003) present unit root tests when the time series being tested has Gaussian

GARCH (Generalized Autoregressive Conditional Heteroskedasticity) stochastics. Although these tests have increased

power when testing financial data, a common trait for the existing testing methods is that they all require some specific

model specification assumption, either in terms of mean functional form (e.g., the ADF test requires the number of

autoregressive lags to be specified) or the error term distribution (ARCH–Autoregressive Conditional Heteroscedasticity–,

GARCH, normal, t, etc.). This is a non-trivial issue, because while the question of interest is the presence or absence of a

unit root, not the specification of the time series model, Moral-Benito (2015) showed that inappropriate model

assumptions will produce erroneous unit root test results—and that is certainly something with which economists are

concerned.

In this paper, we present an improved method of testing for market efficiency using a Bayesian unit root test which averages

over multiple possible specifications of the underlying time series model, thus providing robust test results. Our method is

demonstrated using futures price data on seven futures prices: five agricultural commodities (corn, soybean, cotton, live cattle,

and lean hog) and two industrial (crude oil and silver), all of which display typical financial data characteristics. We first show

that systematic sampling can have significant effects on the results of unit root testing using three different frequency samples

(daily, weekly, and monthly) using the traditional testing methods. Then, more importantly, we test the stationarity of the seven

series by averaging 24 diverse models using our Bayesian model averaging (BMA) unit root test and compare the results with

traditional unit root test results to show the performance of the BMA method, as well as its ability to handle the model

specification issue.

The rest of the paper is orga nized as follows. The next s ection introduces the rob ust Bayesian unit root test and the

specific models averaged for th is application. Next, the dat a used in the analysis are introdu ced, followed by the priors,

posterior distributions , and the sampling methods. We the n present and discuss the res ults of the tests, followed by

conclusions.

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A ROBUST BAYESIAN UNIT ROOT TEST ACCOUNTING FOR MODEL

UNCERTAINTY

Because traditional unit root tests have very low power and use a null hypothesis of a unit root, they are biased in favor of finding

market efficiency (i.e., nonstationarity). Further, when testing financial asset price series it is important to incorporate the

distributional features commonly found in such time series, such as fatter tails and conditional heteroskedasticity. To this end, we

introduce a new testing approach which relies on Bayesian model averaging to produce probabilities in favor of and against a unit

root while accounting for uncertainty over both model and error specifications.

2.1

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Model parameterization

Although the error specification is a key for financial data such as the futures prices considered in this paper, it is also of equal

importance to specify the mean function accurately as model uncertainty arises in both areas. In this paper, we adopt a standard

autoregressive model with maximum lag pas the mean function. This can be written as

ALðÞxt¼εtð1Þ

WU ET AL.

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