Joint parametric specification checking of conditional mean and volatility in time series models with martingale difference innovations

by   Kilani Ghoudi, et al.

Using cumulative residual processes, we propose joint goodness-of-fit tests for conditional means and variances functions in the context of nonlinear time series with martingale difference innovations. The main challenge comes from the fact the cumulative residual process no longer admits, under the null hypothesis, a distribution-free limit. To obtain a practical solution one either transforms the process in order to achieve a distribution-free limit or approximates the non-distribution free limit using a numerical or a re-sampling technique. Here the three solutions will be considered.It is shown that the proposed tests have nontrivial power against a class of root-n local alternatives, and are suitable when the conditioning information set is infinite-dimensional, which allows including models like autoregressive conditional heteroscedastic stochastic models with dependent innovations. The approach presented assumes only certain conditions on the first- and second-order conditional moments, without imposing any autoregression model. The test procedures introduced are compared with each other and with other competitors in terms of their power using a simulation study and a real data application. These simulations have shown that the statistical powers of tests based on re-sampling or numerical approximation of the original statistics are in general slightly better than those based on a martingale transformation of the original process.



There are no comments yet.


page 1

page 2

page 3

page 4


Nonparametric volatility change detection

We consider a nonparametric heteroscedastic time series regression model...

Cauchy or not Cauchy? New goodness-of-fit tests for the Cauchy distribution

We introduce a new characterization of the Cauchy distribution and propo...

Asymptotically Distribution-Free Goodness-of-Fit Testing for Copulas

Consider a random sample from a continuous multivariate distribution fun...

Some multivariate goodness of fit tests based on data depth

Using the fact that some depth functions characterize certain family of ...

Goodness-of-fit tests for complete spatial randomness based on Minkowski functionals of binary images

We propose a class of goodness-of-fit tests for complete spatial randomn...

Feature Shift Detection: Localizing Which Features Have Shifted via Conditional Distribution Tests

While previous distribution shift detection approaches can identify if a...

Combined tests based on restricted mean time lost for competing risks data

Competing risks data are common in medical studies, and the sub-distribu...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.