Goodness‐of‐Fit Tests for Multiplicative Models with Dependent Data

Abstract

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. Copyright (c) 2009 Board of the Foundation of the Scandinavian Journal of Statistics.

Estimating the error distribution in nonparametric multiple regression with applications to model testing

“…Possible extensions include the case of censored regression (see [22] for one-dimensional covariates), the problem of testing the independence between the error and the covariate (see [23]), and the problem of testing for multiplicative models for dependent data (see [24]). It would also be interesting to study the location-scale model when the covariate is high dimensional, i.e.…”

A note on non‐parametric testing for Gaussian innovations in AR–ARCH models

“…() and Dette et al . (). Selk and Neumeyer () showed in their Theorem 3.1 that (under the assumptions stated in the appendix) uniformly with respect to y, where f denotes the innovation density.…”

“…Details can be found in the work of Neumeyer and Selk (), where we also consider an asymptotically distribution‐free version of the test for multiplicative structure by Dette et al . () under the normality assumption.…”

Scale Checks in Censored Regression

“…In the censored case, González Manteiga, Heuchenne and Sánchez Sellero (2007) considered goodnessof-fit tests for the conditional mean and variance functions while Pardo Fernández, Van Keilegom and González Manteiga (2007) addressed the problem for a specific location function using the process of the difference of residuals distributions. This process has been widely studied, b.e., by Dette, Pardo Fernández and Van Keilegom (2007) or Van Keilegom, González Manteiga and Sánchez Sellero (2007). Indeed, it is more naturally related to the commonly used graphical procedures based on visual examination of the residuals (see Atkinson 1985).…”