Abstract
In this paper we propose a new test for the hypothesis of a constant coefficient of variation in the common nonparametric regression model. The test is based on an estimate of the L 2-distance between the square of the regression function and the variance function. We prove asymptotic normality of a standardized estimate of this distance under the null hypothesis and fixed alternatives. The finite sample properties of a corresponding bootstrap test are investigated by means of a simulation study. The results are applicable to stationary processes with the common mixing conditions and are used to construct tests for ARCH assumptions in financial time series.
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Dette, H., Wieczorek, G. Testing for a Constant Coefficient of Variation in Nonparametric Regression. J Stat Theory Pract 3, 587–612 (2009). https://doi.org/10.1080/15598608.2009.10411949
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DOI: https://doi.org/10.1080/15598608.2009.10411949