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Unbiased QML Estimation of Log-GARCH Models in the Presence of Zero Returns

Sucarrat, Genaro; Escribano, Álvaro
Fonte: Universidade Carlos III de Madrid Publicador: Universidade Carlos III de Madrid
Tipo: info:eu-repo/semantics/draft; info:eu-repo/semantics/workingPaper
Publicado em 01/09/2013 ENG
Relevância na Pesquisa
25.92%
A critique that has been directed towards the log-GARCH model is that its logvolatility specification does not exist in the presence of zero returns. A common "remedy" is to replace the zeros with a small (in the absolute sense) non-zero value. However, this renders Quasi Maximum Likelihood (QML) estimation asymptotically biased. Here, we propose a solution to the case where actual returns are equal to zero with probability zero, but zeros nevertheless are observed because of measurement error (due to missing values, discreteness approximisation error, etc.). The solution treats zeros as missing values and handles these by combining QML estimation via the ARMA representation with the Expectation-maximisation (EM) algorithm. Monte Carlo simulations confirm that the solution corrects the bias, and several empirical applications illustrate that the biascorrecting estimator can make a substantial difference.

Dynamic conditional score patent count panel data models

Blazsek, Szabolcs; Escribano, Álvaro
Fonte: Universidade Carlos III de Madrid Publicador: Universidade Carlos III de Madrid
Tipo: info:eu-repo/semantics/submitedVersion; info:eu-repo/semantics/workingPaper
Publicado em 01/11/2015 ENG
Relevância na Pesquisa
56.07%
We propose a new class of dynamic patent count panel data models that is based on dynamic conditional score (DCS) models. We estimate multiplicative and additive DCS models, MDCS and ADCS respectively, with quasi-ARMA (QARMA) dynamics, and compare them with the finite distributed lag, exponential feedback and linear feedback models. We use a large panel of 4,476 United States (US) firms for period 1979 to 2000. Related to the statistical inference, we discuss the advantages and disadvantages of alternative estimation methods: maximum likelihood estimator (MLE), pooled negative binomial quasi-MLE (QMLE) and generalized method of moments (GMM). For the count panel data models of this paper, the strict exogeneity of explanatory variables assumption of MLE fails and GMM is not feasible. However, interesting results are obtained for pooled negative binomial QMLE. The empirical evidence shows that the new class of MDCS models with QARMA dynamics outperforms all other models considered.

Monitoring procedure for parameter change in causal time series

Bardet, Jean-Marc; Kengne, William Chakry
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
15.77%
We propose a new sequential procedure to detect change in the parameters of a process $ X= (X_t)_{t\in \Z}$ belonging to a large class of causal models (such as AR($\infty$), ARCH($\infty$), TARCH($\infty$), ARMA-GARCH processes). The procedure is based on a difference between the historical parameter estimator and the updated parameter estimator, where both these estimators are based on a quasi-likelihood of the model. Unlike classical recursive fluctuation test, the updated estimator is computed without the historical observations. The asymptotic behavior of the test is studied and the consistency in power as well as an upper bound of the detection delay are obtained. Some simulation results are reported with comparisons to some other existing procedures exhibiting the accuracy of our new procedure. The procedure is also applied to the daily closing values of the Nikkei 225, S$&$P 500 and FTSE 100 stock index. We show in this real-data applications how the procedure can be used to solve off-line multiple breaks detection.; Comment: arXiv admin note: text overlap with arXiv:1101.5960 by other authors

Global self-weighted and local quasi-maximum exponential likelihood estimators for ARMA--GARCH/IGARCH models

Zhu, Ke; Ling, Shiqing
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 30/01/2012
Relevância na Pesquisa
36.09%
This paper investigates the asymptotic theory of the quasi-maximum exponential likelihood estimators (QMELE) for ARMA--GARCH models. Under only a fractional moment condition, the strong consistency and the asymptotic normality of the global self-weighted QMELE are obtained. Based on this self-weighted QMELE, the local QMELE is showed to be asymptotically normal for the ARMA model with GARCH (finite variance) and IGARCH errors. A formal comparison of two estimators is given for some cases. A simulation study is carried out to assess the performance of these estimators, and a real example on the world crude oil price is given.; Comment: Published in at http://dx.doi.org/10.1214/11-AOS895 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)