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Goodness‐of‐Fit Tests for Multiplicative Models with Dependent Data
Author(s) -
DETTE HOLGER,
PARDOFERNÁNDEZ JUAN CARLOS,
KEILEGOM INGRID VAN
Publication year - 2009
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/j.1467-9469.2009.00648.x
Subject(s) - mathematics , estimator , goodness of fit , asymptotic distribution , statistics , econometrics , bivariate analysis
. Several classical time series models can be written as a regression model between the components of a strictly stationary bivariate process. Some of those models, such as the ARCH models, share the property of proportionality of the regression function and the scale function, which is an interesting feature in econometric and financial models. In this article, we present a procedure to test for this feature in a non‐parametric context. The test is based on the difference between two non‐parametric 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.