ar X iv : 1 20 9 . 10 31 v 3 [ m at h . ST ] 1 M ay 2 01 6 Testing the fractional integration parameter revisited : a Fractional Dickey - Fuller Test
نویسنده
چکیده
In this paper, in the first step, we show that the fractional DickeyFuller test proposed by Dolado et al [10] is useless in practice. In the second step, we propose a new testing procedure for the degree of fractional integration of a time series inspired on the unit root test of Dickey-Fuller [7]. The composite null hypothesis is that of d ≥ d0 against d < d0. The test statistics is the same as in Dickey-Fuller test using as output (1− L)0 yt instead of (1− L) yt and as input (1− L)0 yt−1 and eventually some lag of (1 − L)0yt instead some lag of (1 − L)yt, exploiting the fact that if yt is I(d) then ∆ 0yt is I(1) under the null d = d0. If d ≥ d0, using the generalization of Sowell’s result [23], we propose a test based on the least favorable case, d = d0, to control type I error, and when d < d0 we show that the tests statistics diverges to −∞, providing consistency. Through a simulation study, we show the good performance of the test in terms of size and power. Finally, in order to show how to use the new testing procedure, the test is applied to the well-known Nelson and Plosser data.
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تاریخ انتشار 2016