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on Econometric Time Series |
| By: | Christian Kascha (Norges Bank (Central Bank of Norway)); Carsten Trenkler (University of Mannheim) |
| Abstract: | We investigate the small-sample size and power properties of bootstrapped likelihood ratio systems cointegration tests via Monte Carlo simulations when the true lag order of the data generating process is unknown. A recursive bootstrap scheme is employed. We estimate the order by minimizing different information criteria. In comparison to the standard asymptotic likelihood ratio test based on an estimated lag order we found that the recursive bootstrap procedure can lead to improvements in small samples even when the true lag order is unknown while the power loss is moderate. |
| Keywords: | Cointegration tests, Bootstrapping, Information criteria |
| JEL: | C15 C32 |
| Date: | 2009–08–04 |
| URL: | http://d.repec.org/n?u=RePEc:bno:worpap:2009_12&r=ets |
| By: | Alessandro De Gregorio; Stefano Iacus (Department of Economics, Business and Statistics, University of Milan, IT) |
| Abstract: | We consider parametric hypotheses testing for multidimensional It\^o processes, possibly with jumps, observed at discrete time. To this aim, we propose the whole class of pseudo $\phi$-divergence test statistics, which include as a special case the well-known likelihood ratio test but also many other test statistics as well as new ones. Although the final goal is to apply these test procedures to multidimensional It\^o processes, we formulate the problem in the very general setting of regular statistical experiments and then particularize the results to our model of interest. In this general framework we prove that, contrary to what happens to true $\phi$-divergence test statistics, the limiting distribution of the pseudo $\phi$-divergence test statistic is characterized by the function $\phi$ which defines the divergence itself. In the case of contiguous alternatives, it is also possible to study in detail the power function of the test. Although all tests in this class are asymptotically equivalent, we show by Monte Carlo analysis that, in small sample case, the performance of the test strictly depends on the choice of the function $\phi$. In particular, we see that even in the i.i.d. case, the power function of the generalized likelihood ratio test ($\phi=\log$) is strictly dominated by other pseudo $\phi$-divergences test statistics. |
| Keywords: | diffusion processes with jumps, Ito processes, power of the test, parametric hypotheses testing, phi-divergences, generalized likelihood ratio test, |
| Date: | 2009–05–21 |
| URL: | http://d.repec.org/n?u=RePEc:bep:unimip:1083&r=ets |
| By: | Emma M. Iglesias; Oliver Linton |
| Abstract: | We propose a method of estimating the Pareto tail thickness parameter of the unconditional distribution of a financial time series by exploiting the implications of a GJR-GARCH volatility model. The method is based on some recent work on the extremes of GARCH-type processes and extends the method proposed by Berkes, Horváth and Kokoszka (2003). We show that the estimator of tail thickness is consistent and converges at rate ?T to a normal distribution (where T is the sample size), provided the model for conditional variance is correctly specified as a GJR-GARCH. This is much faster than the convergence rate of the Hill estimator, since that procedure only uses a vanishing fraction of the sample. We also develop new specification tests based on this method and propose new alternative estimates of unconditional value at risk. We show in Monte Carlo simulations the advantages of our procedure in finite samples; and finally an application concludes the paper |
| Keywords: | Pareto tail thickness parameter, GARCH-type models, Value-at-Risk, Extreme value theory, Heavy tails |
| JEL: | C12 C13 C22 G11 G32 |
| Date: | 2009–06 |
| URL: | http://d.repec.org/n?u=RePEc:cte:werepe:we094726&r=ets |
| By: | Francq, Christian; Zakoian, Jean-Michel |
| Abstract: | This article is concerned by testing the nullity of coefficients in GARCH models. The problem is non standard because the quasi-maximum likelihood estimator is subject to positivity constraints. The paper establishes the asymptotic null and local alternative distributions of Wald, score, and quasi-likelihood ratio tests. Efficiency comparisons under fixed alternatives are also considered. Two cases of special interest are: (i) tests of the null hypothesis of one coefficient equal to zero and (ii) tests of the null hypothesis of no conditional heteroscedasticity. Finally, the proposed approach is used in the analysis of a set of financial data and leads to reconsider the preeminence of GARCH(1,1) among GARCH models. |
| Keywords: | Asymptotic efficiency of tests; Boundary; Chi-bar distribution; GARCH model; Quasi Maximum Likelihood Estimation; Local alternatives |
| JEL: | C12 C22 C01 |
| Date: | 2008 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:16672&r=ets |