Finite-Sample Properties of the Maximum Likelihood Estimator in GARCH(1,1) and IGARCH(1,1) Models: A Monte Carlo Investigation

Abstract: In this article, we analyze a maximum likelihood estimator using Data Cloning for Stochastic Volatility models. This estimator is constructed using a hybrid methodology based on Integrated Nested Laplace Approximations to calculate analytically the auxiliary Bayesian estimators with great accuracy and computational efficiency, without requiring the use of simulation methods such as Markov Chain Monte Carlo. We analyze the performance of this estimator compared to methods based on Monte Carlo simulations (Simulated Maximum Likelihood, MCMC Maximum Likelihood) and approximate maximum likelihood estimators using Laplace Approximations. The results indicate that this data cloning methodology achieves superior results over methods based on MCMC, comparable to results obtained by the Simulated Maximum Likelihood estimator. The methodology is extended to models with leverage effects, continuous time formulations, multifactor and multivariate stochastic volatility.

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Asymptotic Theory for Regressions with Smoothly Changing Parameters

Journal of Time Series Econometrics ◽

10.1515/jtse-2012-0024 ◽

2013 ◽

Vol 5 (2) ◽

pp. 133-162 ◽

Cited By ~ 4

Author(s):

Eric Hillebrand ◽

Marcelo C. Medeiros ◽

Junyue Xu

Keyword(s):

Maximum Likelihood ◽

Asymptotic Theory ◽

Asymptotic Properties ◽

Smooth Transition ◽

Finite Sample ◽

Likelihood Estimator ◽

Output Data ◽

Asymptotically Normal ◽

Finite Sample Properties ◽

Quasi Maximum Likelihood

Abstract: We derive asymptotic properties of the quasi-maximum likelihood estimator of smooth transition regressions when time is the transition variable. The consistency of the estimator and its asymptotic distribution are examined. It is shown that the estimator converges at the usual -rate and has an asymptotically normal distribution. Finite sample properties of the estimator are explored in simulations. We illustrate with an application to US inflation and output data.

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Using ranked set sampling with extreme ranks in estimating the population proportion

Statistical Methods in Medical Research ◽

10.1177/0962280218823793 ◽

2019 ◽

Vol 29 (1) ◽

pp. 165-177 ◽

Cited By ~ 10

Author(s):

Ehsan Zamanzade ◽

M Mahdizadeh

Keyword(s):

Maximum Likelihood ◽

Maximum Likelihood Estimator ◽

Simple Random Sampling ◽

Ranked Set Sampling ◽

Finite Sample ◽

Likelihood Estimator ◽

Population Proportion ◽

Health And Nutrition ◽

Finite Sample Size ◽

Using Data

This article studies the properties of the maximum likelihood estimator of the population proportion in ranked set sampling with extreme ranks. The maximum likelihood estimator is described and its asymptotic distribution is derived. Finite sample size properties of the estimator are investigated using simulation studies. It turns out that the proposed estimator is substantially more efficient than its simple random sampling and ranked set sampling analogs, as the true population proportion tends to zero/unity. The method is illustrated using data from the National Health and Nutrition Examination Survey.

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