DIAGNOSTIC CHECKING FOR THE ADEQUACY OF NONLINEAR TIME SERIES MODELS

Yongmiao Hong and Lee, Tae-Hwy

Econometric Theory, 2003, vol. 19, issue 06, pages 1065-1121

Abstract: We propose a new diagnostic test for linear and nonlinear time series models, using a generalized spectral approach. Under a wide class of time series models that includes autoregressive conditional heteroskedasticity (ARCH) and autoregressive conditional duration (ACD) models, the proposed test enjoys the appealing nuisance-parameter-free property in the sense that model parameter estimation uncertainty has no impact on the limit distribution of the test statistic. It is consistent against any type of pairwise serial dependence in the model standardized residuals and allows the choice of a proper lag order via data-driven methods. Moreover, the new test is asymptotically more efficient than the correlation integral based test of Brock, Hsieh, and LeBaron (1991, Nonlinear Dynamics, Chaos, and Instability: Statistical Theory and Economic Evidence) and Brock, Dechert, Scheinkman, and LeBaron (1996, Econometric Reviews 15, 197 235), the well-known BDS test, against a class of plausible local alternatives (not including ARCH). A simulation study compares the finite-sample performance of the proposed test and the tests of BDS, Box and Pierce (1970, Journal of the American Statistical Association 65, 1509 1527), Ljung and Box (1978, Biometrika 65, 297 303), McLeod and Li (1983, Journal of Time Series Analysis 4, 269 273), and Li and Mak (1994, Journal of Time Series Analysis 15, 627 636). The new test has good power against a wide variety of stochastic and chaotic alternatives to the null models for conditional mean and conditional variance. It can play a valuable role in evaluating adequacy of linear and nonlinear time series models. An empirical application to the daily S P 500 price index highlights the merits of our approach.We thank the co-editor (Don Andrews) and two referees for careful and constructive comments that have lead to significant improvement over an earlier version. We also thank C.W.J. Granger, D. Tj stheim, and Z. Xiao for helpful comments. Hong s participation is supported by the National Science Foundation via NSF grant SES 0111769. Lee thanks the UCR Academic Senate for research support.

Date: 2003
View citations in EconPapers

Downloads: (external link)
http://journals.cambridge.org/abstract_S0266466603196089 link to article abstract page (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: http://EconPapers.repec.org/RePEc:cup:etheor:v:19:y:2003:i:06:p:1065-1121_19

Access Statistics for this article

More articles in Econometric Theory from Cambridge University Press
Address: The Edinburgh Building, Shaftesbury Road, Cambridge CB2 2RU UK
Series data maintained by Mike Eden ().