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A nonparametric test of serial independence for time series and residuals. (English) Zbl 1004.62043

From the introduction: This paper develops nonparametric tests of independence and serial independence. The tests proposed here apply when testing the independence of \(p\) random variables or the serial independence of time series data and residuals. These tests are Cramér-von Mises or Kolmogorov Smirnov functionals of some empirical processes. This paper shows that under the independence (serial independence) hypothesis these empirical processes converge to Gaussian limits with quite convenient covariance functions.
It is also shown that if the \(U_i\)’s have continuous distribution function then the limiting distributions of the test statistics do not depend on the underlying law of the \(U_i\)’s. This holds when testing independence of \(p\) random variables, serial independence of time series data and serial independence of residuals of a classical linear regression. In other cases, such as residuals of an autoregressive model, the limiting distribution depends, in general, on the law of the \(U_i\)’s.

MSC:

62G10 Nonparametric hypothesis testing
62G20 Asymptotic properties of nonparametric inference
60F05 Central limit and other weak theorems
62E20 Asymptotic distribution theory in statistics
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References:

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