Giuseppe Cavaliere, Indeewara Perera, Anders Rahbek
arXiv 28 May 2021 · Econometrics · 1 citations (OpenAlex)
arXiv:2105.14081 · PDF · DOI · OpenAlex · Extracted main text
This paper develops tests for the correct specification of the conditional variance function in GARCH models when the true parameter may lie on the boundary of the parameter space. The test statistics considered are of Kolmogorov-Smirnov and Cram\'{e}r-von Mises type, and are based on a certain empirical process marked by centered squared residuals. The limiting distributions of the test statistics are not free from (unknown) nuisance parameters, and hence critical values cannot be tabulated. A novel bootstrap procedure is proposed to implement the tests; it is shown to be asymptotically valid under general conditions, irrespective of the presence of nuisance parameters on the boundary. The proposed bootstrap approach is based on shrinking of the parameter estimates used to generate the bootstrap sample toward the boundary of the parameter space at a proper rate. It is simple to implement and fast in applications, as the associated test statistics have simple closed form expressions. A simulation study demonstrates that the new tests: (i) have excellent finite sample behavior in terms of empirical rejection probabilities under the null as well as under the alternative; (ii) provide a useful complement to existing procedures based on Ljung-Box type approaches. Two data examples are considered to illustrate the tests.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Cavaliere, G., Nielsen, H. B., Pedersen, R. S., and Rahbek, A (2021) Bootstrap Inference On The Boundary Of The Parameter Space With Application To Conditional Volatility Models self | 0.928 | 5 | 4 | 80% |
| 2 | Hidalgo, J. and Zaffaroni, P (2007) A goodness-of-fit test for ARCH($$) models | 0.843 | 4 | 3 | 75% |
| 3 | Perera, I. and Koul, H. L (2017) Fitting a two phase threshold multiplicative error model self | 0.843 | 3 | 3 | 100% |
| 4 | Koul, H. L., Perera, I., and Silvapulle, M. J (2012) Lack-of-fit testing of the conditional mean function in a class of Markov multiplicative error models self | 0.843 | 3 | 3 | 100% |
| 5 | Francq, C. and Zakoän, J.-M (2010) GARCH models: structure, statistical inference and financial applications | 0.737 | 3 | 2 | 100% |
| 6 | Francq, C. and Zakoian, J.-M (2007) Quasi-maximum likelihood estimation in GARCH processes when some coefficients are equal to zero | 0.693 | 6 | 2 | 50% |
| 7 | Bai, J (2003) Testing parametric conditional distributions of dynamic models | 0.644 | 2 | 2 | 100% |
| 8 | Berkes, I., Horváth, L., and Kokoszka, P (2003) GARCH processes: structure and estimation | 0.644 | 2 | 2 | 100% |
| 9 | Chatterjee, A. and Lahiri, S. N (2011) Bootstrapping lasso estimators | 0.644 | 2 | 2 | 100% |
| 10 | Perera, I., Hidalgo, J., and Silvapulle, M. J (2016) A goodness-of-fit test for a class of autoregressive conditional duration models self | 0.644 | 2 | 2 | 100% |
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