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# Sign Test for Hypothesis about the Order of Equation in Moving Average Model

 Authors: Goryainov V.B., Goryainova E.R. Published: 06.12.2016 Published in issue: #6(69)/2016 DOI: 10.18698/1812-3368-2016-6-4-15 Category: Mathematics | Chapter: Probability Theory and Mathematical Statistics Keywords: moving average model, hypothesis about the order of the equation, sign test, Tukey distribution

The article deals with constructing the sign test for the hypothesis about the order of equation in moving average. We found the asymptotic distribution of the test statistics which appeared to be the central χ2-distribution under the null hypothesis and the noncentral χ2-distribution under the alternative one. Knowing the asymptotic distribution makes it possible to calculate the asymptotic relative efficiency of the constructed sign test criterion with respect to the known criteria. In our research we give an example of calculating the asymptotic relative efficiency of the constructed sign test criterion in relation to the classical criterion, based on a sample covariance ratio. Moreover, we determine the values of the asymptotic relative efficiency for a normal distribution, the double exponential distribution (Laplace distribution) and contaminated normal distribution (Tukey distribution). It is shown that if the innovation process in the moving average model is contaminated with Gaussian outliers, the asymptotic relative efficiency of this test can be arbitrarily large compared to the traditional criterion, based on a sample correlation coefficient.

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