Author: Daniel Straumann
Publisher:
ISBN: 9788778345219
Category :
Languages : en
Pages : 36

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Author: Daniel Straumann
Publisher: Springer Science & Business Media
ISBN: 3540269789
Category : Business & Economics
Languages : en
Pages : 239

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Book Description
In his seminal 1982 paper, Robert F. Engle described a time series model with a time-varying volatility. Engle showed that this model, which he called ARCH (autoregressive conditionally heteroscedastic), is well-suited for the description of economic and financial price. Nowadays ARCH has been replaced by more general and more sophisticated models, such as GARCH (generalized autoregressive heteroscedastic). This monograph concentrates on mathematical statistical problems associated with fitting conditionally heteroscedastic time series models to data. This includes the classical statistical issues of consistency and limiting distribution of estimators. Particular attention is addressed to (quasi) maximum likelihood estimation and misspecified models, along to phenomena due to heavy-tailed innovations. The used methods are based on techniques applied to the analysis of stochastic recurrence equations. Proofs and arguments are given wherever possible in full mathematical rigour. Moreover, the theory is illustrated by examples and simulation studies.

Author: Florian Ziel
Publisher:
ISBN:
Category :
Languages : en
Pages : 17

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Author: Giuseppe Cavaliere
Publisher:
ISBN:
Category :
Languages : en
Pages : 41

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Author: Whitney K. Newey
Publisher:
ISBN:
Category :
Languages : en
Pages :

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Book Description
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.

Author: Mirko Armillotta
Publisher:
ISBN:
Category :
Languages : en
Pages : 0

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We propose a novel estimation approach for a general class of semi-parametric time series models where the conditional expectation is modeled through a parametric function. The proposed class of estimators is based on a Gaussian quasi-likelihood function and it relies on the specification of a parametric pseudo-variance that can contain parametric restrictions with respect to the conditional expectation. The specification of the pseudo-variance and the parametric restrictions follow naturally in observation-driven models with bounds in the support of the observable process, such as count processes and double-bounded time series. We derive the asymptotic properties of the estimators and a validity test for the parameter restrictions. We show that the results remain valid irrespective of the correct specification of the pseudo-variance. The key advantage of the restricted estimators is that they can achieve higher efficiency compared to alternative quasi-likelihood methods that are available in the literature. Furthermore, the testing approach can be used to build specification tests for parametric time series models. We illustrate the practical use of the methodology in a simulation study and two empirical applications featuring integer-valued autoregressive processes, where assumptions on the dispersion of the thinning operator are formally tested, and autoregressions for double-bounded data with application to a realized correlation time series.

Author: Christopher C. Heyde
Publisher: Springer Science & Business Media
ISBN: 0387226796
Category : Mathematics
Languages : en
Pages : 236

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Book Description
The first account in book form of all the essential features of the quasi-likelihood methodology, stressing its value as a general purpose inferential tool. The treatment is rather informal, emphasizing essential principles rather than detailed proofs, and readers are assumed to have a firm grounding in probability and statistics at the graduate level. Many examples of the use of the methods in both classical statistical and stochastic process contexts are provided.

Author: Whitney K. Newey
Publisher:
ISBN:
Category :
Languages : en
Pages :

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Author: T. Fomby
Publisher: Elsevier
ISBN: 0762310758
Category : Business & Economics
Languages : en
Pages : 266

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Book Description
Comparative study of pure and pretest estimators for a possibly misspecified two-way error component model / Badi H. Baltagi, Georges Bresson, Alain Pirotte -- Estimation, inference, and specification testing for possibly misspecified quantile regression / Tae-Hwan Kim, Halbert White -- Quasimaximum likelihood estimation with bounded symmetric errors / Douglas Miller, James Eales, Paul Preckel -- Consistent quasi-maximum likelihood estimation with limited information / Douglas Miller, Sang-Hak Lee -- An examination of the sign and volatility switching arch models under alternative distributional assumptions / Mohamed F. Omran, Florin Avram -- estimating a linear exponential density when the weighting matrix and mean parameter vector are functionally related / Chor-yiu Sin -- Testing in GMM models without truncation / Timothy J. Vogelsang -- Bayesian analysis of misspecified models with fixed effects / Tiemen Woutersen -- Tests of common deterministic trend slopes applied to quarterly global temperature data / Thomas B. Fomby, Timothy J. Vogelsang -- The sandwich estimate of variance / James W. Hardin -- Test statistics and critical values in selectivity models / R. Carter Hill, Lee C. Adkins, Keith A. Bender -- Introduction / Thomas B Fomby, R. Carter Hill.

Author: Scott R. Eliason
Publisher: SAGE
ISBN: 9780803941076
Category : Mathematics
Languages : en
Pages : 100

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Book Description
This is a short introduction to Maximum Likelihood (ML) Estimation. It provides a general modeling framework that utilizes the tools of ML methods to outline a flexible modeling strategy that accommodates cases from the simplest linear models (such as the normal error regression model) to the most complex nonlinear models linking endogenous and exogenous variables with non-normal distributions. Using examples to illustrate the techniques of finding ML estimators and estimates, the author discusses what properties are desirable in an estimator, basic techniques for finding maximum likelihood solutions, the general form of the covariance matrix for ML estimates, the sampling distribution of ML estimators; the use of ML in the normal as well as other distributions, and some useful illustrations of likelihoods.