Fitting an Error Distribution in Some Heteroscedastic Time Series Models

By Hira L. Koul, S. Ling. 2006

74 citations recorded by the source corpus.

This paper addresses the problem of fltting a known distribution to the innovation distribution in a class of stationary and ergodic time series models. The asymptotic null distribution of the usual Kolmogorov-Smirnov test based on the residuals generally depends on the underlying model parameters and the error distribution. To overcome the dependence on the underlying model parameters, we propose that tests be based on a vector of certain weighted residual empirical processes. Under the null hypothesis and under minimal moment conditions, this vector of processes is shown to converge weakly to a vector of independent copies of a Gaussian process whose covariance function depends only on the fltted distribution and not on the model. Under certain local alternatives, the proposed test is shown to have nontrivial asymptotic power. The Monte Carlo critical values of this test are tabulated when fltting standard normal and double exponential distributions. The results obtained are shown to be applicable to GARCH and ARMA-GARCH models, the often used models in econometrics and flnance. A simulation study shows that the test has satisfactory size and power for flnite samples at these models. The paper also contains an asymptotic uniform expansion result for a general weighted residual empirical process useful in heteroscedastic models under minimal moment conditions, a result of independent interest.

Subfields: Economics and Econometrics, Finance

View Paper: https://www.semanticscholar.org/paper/e301060af4d4c85834f8b7b98494a7a81657e8c0

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Citations in the corpus

STATISTICAL INFERENCE FOR MULTIVARIATE RESIDUAL COPULA OF GARCH MODELS (2009, unknown): “Currently, there are sporadic results on the convergence of empirical distributions using residuals of non-linear time series; see, for example, Berkes and Horváth (2003), Horváth, Kokoszka and Teyssiére (2001) and Koul and Ling (2006).”
Self-weighted and local quasi-maximum likelihood estimators for ARMA-GARCH/IGARCH models (2007, methodology): “The test statistic in Koul and Ling (2006) can be used to test possible distributions.”
On the least squares estimation of multiple-regime threshold autoregressive models (2012, methodology): “Using a similar technique in Koul and Ling (2006), we can show that I1 = op(1).”