Journal of Statistical Theory and Practice

, Volume 3, Issue 3, pp 587–612 | Cite as

Testing for a Constant Coefficient of Variation in Nonparametric Regression

  • Holger DetteEmail author
  • Gabriele Wieczorek


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 L2-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.


Stationary processes Multiplicative error structure Generalized nonparametric regression models 

AMS Subject Classification

62G08 62G10 62G20 


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Copyright information

© Grace Scientific Publishing 2009

Authors and Affiliations

  1. 1.Fakultät für MathematikRuhr-Universität BochumBochumGermany

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