Goodness-of-fit tests for multiplicative models with dependent data
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Date
2007-10-25T11:53:12Z
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Abstract
Several classical time series models can be written as a regression model of the
form Y
t
= m(X
t
) + σ(X
t
)ε
t
, where (X
t
,Y
t
), t = 0,±1,±2,..., is a bivariate strictly
stationary process. Some of those models, such as ARCH or GARCH models, share
the property of proportionality of the regression function, m, and the scale function,
σ. In this article, we present a procedure to test for this feature in a nonparametric
context, which is a preliminary step to identify certain time series models. The test is
based on the difference between two nonparametric estimators of the distribution of
the regression error. Asymptotic results are proved and some simulations are shown
in the paper in order to illustrate the finite sample properties of the procedure.
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Keywords
Bootstrap, Dependent data, Error distribution, Kernel smoothing, Location-scale model, Mixing sequences, Multiplicative model, Nonparametric regression