Homogenized Integral U-statistics for Tests of Non-linearity
نویسنده
چکیده
This paper construct a family of non-linearity tests based on the distance histogram C(m, ε) underlying Grassberger and Procaccias Correlation Dimension (CD), Brock, Dechert and Sheink-mans (BDS) statistic, Mizrachs Simple Non-Parametric Test (SNT) and Mayers Correlation Dimension Ratio (CDR). Two new elements are introduced. The Þrst is homogenizing the data to the uniform or to the normal distribution. This makes conÞdence intervals universal. The second is to use integral measures along intervals of ε (the distance variable of the histogram) to deÞne the family of tests. The resulting statistics use more of the information contained in C(m, ε). A Monte Carlo experiment using the time series in Barnet et. al.s (1996, 1997) single blind controlled competition Þnds some of these tests are more powerful than the CD, BDS, SNT and CDR tests. 1This research was supported by CONACyT grant number 3416P-S9607.
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