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Book Consistency of Quasi Maximum Likelihood Estimators for Models with Conditional Heteroskedasticity

Download or read book Consistency of Quasi Maximum Likelihood Estimators for Models with Conditional Heteroskedasticity written by Whitney K. Newey and published by . This book was released on 2008 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Virtually all empirical studies that assume a time-varying conditional variance use a quasi-maximum likelihood estimator (QMLE). If the density from which the likelihood is constructed is assumed to be Gaussian, the QMLE is known to be consistent under correct specification of both the conditional mean and conditional variance. We show that if both the assumed density and the true density are symmetric a QMLE remains consistent. If, however, either the assumed density or the true density is asymmetric, a QMLE is generally not consistent. To ensure that a QMLE is consistent under asymmetric densities, we include the conditional standard deviation as a regressor. We calculate the efficiency loss associated with the added regressor if the densities are symmetric and show that for a QMLE of the conditional variance parameters of a GARCH process there is no efficiency loss. Finally, we develop a test of consistency of a QMLE from the significance of the additional regressor.

Book Quasi Maximum Likelihood Estimation of Semi Strong GARCH Models

Download or read book Quasi Maximum Likelihood Estimation of Semi Strong GARCH Models written by Juan Carlos Escanciano and published by . This book was released on 2008 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This note proves the consistency and asymptotic normality of the Quasi-Maximum Likelihood Estimator (QMLE) of the parameters of a GARCH model with martingale difference centered squared innovations. The results are obtained under mild conditions and generalize and improve those in Lee and Hansen (1994) for the local QMLE in semi-strong GARCH(1,1) models. In particular, no restrictions on the conditional mean are imposed. Our proofs closely follow those in Francq and Zakoian (2004) for independent and identically distributed innovations.

Book Quasi Maximum Likelihood Estimation of GARCH Models with Heavy Tailed Likelihoods

Download or read book Quasi Maximum Likelihood Estimation of GARCH Models with Heavy Tailed Likelihoods written by Jianqing Fan and published by . This book was released on 2012 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The non-Gaussian maximum likelihood estimator is frequently used in GARCH models with the intention of capturing the heavy-tailed returns. However, unless the parametric likelihood family contains the true likelihood, the estimator is inconsistent due to density misspecification. To correct this bias, we identify an unknown scale parameter that is critical to the identification, and propose a two-step quasi maximum likelihood procedure with non-Gaussian likelihood functions. This novel approach is consistent and asymptotically normal under weak moment conditions. Moreover, it achieves better efficiency than the Gaussian alternative, particularly when the innovation error has heavy tails. We also summarize and compare the values of the scale parameter and the asymptotic efficiency for estimators based on different choices of likelihood functions with an increasing level of heaviness in the innovation tails. Numerical studies confirm the advantages of the proposed approach.

Book Quasi maximum Likelihood Estimators in GARCH 1 2 Model

Download or read book Quasi maximum Likelihood Estimators in GARCH 1 2 Model written by Yingfu Xie and published by . This book was released on 2003 with total page 27 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Book On a Buffered Conditional Volatility Process

Download or read book On a Buffered Conditional Volatility Process written by Pak-Hang Lo and published by . This book was released on 2017-01-26 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation, "On a Buffered Conditional Volatility Process" by Pak-hang, Lo, 勞柏衡, was obtained from The University of Hong Kong (Pokfulam, Hong Kong) and is being sold pursuant to Creative Commons: Attribution 3.0 Hong Kong License. The content of this dissertation has not been altered in any way. We have altered the formatting in order to facilitate the ease of printing and reading of the dissertation. All rights not granted by the above license are retained by the author. Abstract: The traditional threshold time series model is famous for its capability in capturing asymmetry. Regime switching takes place immediately when a certain variable crosses the threshold. However, this type of model may not be suitable for data which have no clear cut between regimes. A new generation of threshold type model, buffered time series model, is modified from the traditional threshold time series model. A buffer zone is introduced to replace the role of the threshold; regime switching will not take place within the buffer zone. The regime switching mechanism mimicks a climatological example and the buffered model may be suitable for data in which there is a region where the probabilistic structure of the data is insensitive to changes. Self-exciting buffered generalized autoregressive conditional heteroscedasticity (buffered GARCH) model is considered. Quasi-maximum likelihood is employed for parameter estimation. Strong consistency and asymptotic distributions are derived. Simulation experiments are carried out to verify the properties of the estimators. The buffered GARCH model is applied to two currency exchange rate data sets, US dollar to Moroccan dirham exchange rate and US dollar to Israeli new shekel exchange rate. At the same time, threshold GARCH model is also applied to the data sets in order to have comparison between the buffered GARCH model and threshold GARCH model. It is found that the buffered GARCH model beats the threshold GARCH model in terms of one information criterion, revealing that the buffered GARCH model may have advantage over the threshold GARCH model. DOI: 10.5353/th_b5177344 Subjects: Time-series analysis

Book Consistency of Maximum Likelihood Estimators in Some Reliability Growth Models

Download or read book Consistency of Maximum Likelihood Estimators in Some Reliability Growth Models written by Bernard Sherman and published by . This book was released on 1966 with total page 33 pages. Available in PDF, EPUB and Kindle. Book excerpt: Properties of maximum likelihood estimators of parameters in some sample reliability growth models are investigated. In one model the underlying process is a Markov chain and the estimator of the single unknown parameter is proved consistent. In another model it is shown that no estimators can be consistent. Related estimation problems in sequences of geometric distributions are discussed. (Author).

Book On the Three Step Non Gaussian Quasi Maximum Likelihood Estimation of Heavy Tailed Double Autoregressive Models

Download or read book On the Three Step Non Gaussian Quasi Maximum Likelihood Estimation of Heavy Tailed Double Autoregressive Models written by Dong Li and published by . This book was released on 2020 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This note considers a three-step non-Gaussian quasi-maximum likelihood estimation (TS-NGQMLE) of the double autoregressive model with its asymptotics, which improves efficiency of the GQMLE and circumvents inconsistency of the NGQMLE when the innovation is heavy-tailed. Under mild conditions, the estimator not only can achieve consistency and asymptotic normality regardless of density misspecification of the innovation, but also outperforms the existing estimators, such as the GQMLE and the (weighted) least absolute deviation estimator, when the innovation is indeed heavy-tailed.

Book State space Models with Regime Switching

Download or read book State space Models with Regime Switching written by Chang-Jin Kim and published by Mit Press. This book was released on 1999 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: Both state-space models and Markov switching models have been highly productive paths for empirical research in macroeconomics and finance. This book presents recent advances in econometric methods that make feasible the estimation of models that have both features. One approach, in the classical framework, approximates the likelihood function; the other, in the Bayesian framework, uses Gibbs-sampling to simulate posterior distributions from data.The authors present numerous applications of these approaches in detail: decomposition of time series into trend and cycle, a new index of coincident economic indicators, approaches to modeling monetary policy uncertainty, Friedman's "plucking" model of recessions, the detection of turning points in the business cycle and the question of whether booms and recessions are duration-dependent, state-space models with heteroskedastic disturbances, fads and crashes in financial markets, long-run real exchange rates, and mean reversion in asset returns.

Book Encyclopedia of Statistical Sciences Volume 1

Download or read book Encyclopedia of Statistical Sciences Volume 1 written by and published by John Wiley & Sons. This book was released on 2005-12-16 with total page 722 pages. Available in PDF, EPUB and Kindle. Book excerpt: ENCYCLOPEDIA OF STATISTICAL SCIENCES

Book Hidden Markov and Other Models for Discrete valued Time Series

Download or read book Hidden Markov and Other Models for Discrete valued Time Series written by Iain L. MacDonald and published by CRC Press. This book was released on 1997-01-01 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: Discrete-valued time series are common in practice, but methods for their analysis are not well-known. In recent years, methods have been developed which are specifically designed for the analysis of discrete-valued time series. Hidden Markov and Other Models for Discrete-Valued Time Series introduces a new, versatile, and computationally tractable class of models, the "hidden Markov" models. It presents a detailed account of these models, then applies them to data from a wide range of diverse subject areas, including medicine, climatology, and geophysics. This book will be invaluable to researchers and postgraduate and senior undergraduate students in statistics. Researchers and applied statisticians who analyze time series data in medicine, animal behavior, hydrology, and sociology will also find this information useful.

Book Handbook of Financial Time Series

Download or read book Handbook of Financial Time Series written by Torben Gustav Andersen and published by Springer Science & Business Media. This book was released on 2009-04-21 with total page 1045 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Handbook of Financial Time Series gives an up-to-date overview of the field and covers all relevant topics both from a statistical and an econometrical point of view. There are many fine contributions, and a preamble by Nobel Prize winner Robert F. Engle.