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
The Journal of Futures Markets – Wiley
Published: Apr 1, 1990
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