Examining the validity of a test of futures market efficiency: A comment

Examining the validity of a test of futures market efficiency: A comment St+l = a + bS, + e,,, (1) where Sr+iis the spot price at period t + i . Pricing is considered efficient if a = 0 and b = 1. Elam and Dixon are aware that the F-distribution might be invalid in this case but they do not know it has been already derived. Phillips (1986, 1987) shows that S,will converge to the Wiener process if S,has the unit root. The simple intuition of the Wiener process convergence theory can be understood easily by studying the definition of white noise. White noise is defined as the first difference of a univariate Wiener process when sample size goes to infinity. Phillips proves that if the first difference of a univariate time series is white noise, then that series must converge to Wiener process. If S, converges to Wiener process, then Phillips and Durlauf (1987) show that conventional t - and F- statistics also converge to the Wiener process. In addition, if S, has the unit root, the distribution of OLS estimate of b skews to the left (Fuller (1976)), then the critical value of the 5 percent significant level moves to the right making the conventional test reject http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png The Journal of Futures Markets Wiley

Examining the validity of a test of futures market efficiency: A comment

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Publisher
Wiley
Copyright
Copyright © 1990 Wiley Periodicals, Inc., A Wiley Company
ISSN
0270-7314
eISSN
1096-9934
DOI
10.1002/fut.3990100209
Publisher site
See Article on Publisher Site

Abstract

St+l = a + bS, + e,,, (1) where Sr+iis the spot price at period t + i . Pricing is considered efficient if a = 0 and b = 1. Elam and Dixon are aware that the F-distribution might be invalid in this case but they do not know it has been already derived. Phillips (1986, 1987) shows that S,will converge to the Wiener process if S,has the unit root. The simple intuition of the Wiener process convergence theory can be understood easily by studying the definition of white noise. White noise is defined as the first difference of a univariate Wiener process when sample size goes to infinity. Phillips proves that if the first difference of a univariate time series is white noise, then that series must converge to Wiener process. If S, converges to Wiener process, then Phillips and Durlauf (1987) show that conventional t - and F- statistics also converge to the Wiener process. In addition, if S, has the unit root, the distribution of OLS estimate of b skews to the left (Fuller (1976)), then the critical value of the 5 percent significant level moves to the right making the conventional test reject

Journal

The Journal of Futures MarketsWiley

Published: Apr 1, 1990

References

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