scholarly journals R-estimators in GARCH models; asymptotics and applications

2021 ◽  
Author(s):  
Hang Liu ◽  
Kanchan Mukherjee
Keyword(s):  
Likelihood Estimation ◽  
Real Data ◽  
Superior Performance ◽  
Garch Models ◽  
Fourth Moment ◽  
Asymptotically Normal ◽  
Asymmetric Distributions ◽  
Class Of Estimators ◽  
Heavy Tailed ◽  
Quasi Maximum Likelihood

Abstract The quasi-maximum likelihood estimation is a commonly-used method for estimating the GARCH parameters. However, such estimators are sensitive to outliers and their asymptotic normality is proved under the finite fourth moment assumption on the underlying error distribution. In this paper, we propose a novel class of estimators of the GARCH parameters based on ranks of the residuals, called R-estimators, with the property that they are asymptotically normal under the existence of a finite 2 + δ moment of the errors and are highly efficient. We propose fast algorithm for computing the R-estimators. Both real data analysis and simulations show the superior performance of the proposed estimators under the heavy-tailed and asymmetric distributions.

scholarly journals A New Extension of Thinning-Based Integer-Valued Autoregressive Models for Count Data

Entropy ◽  
2020 ◽  
Vol 23 (1) ◽  
pp. 62
Author(s):  
Zhengwei Liu ◽  
Fukang Zhu
Keyword(s):  
Likelihood Estimation ◽  
Real Data ◽  
Autoregressive Models ◽  
Superior Performance ◽  
Data Sets ◽  
Binomial Thinning ◽  
Free Case ◽  
Two Parameters ◽  
Conditional Maximum ◽  
Thinning Operator

The thinning operators play an important role in the analysis of integer-valued autoregressive models, and the most widely used is the binomial thinning. Inspired by the theory about extended Pascal triangles, a new thinning operator named extended binomial is introduced, which is a general case of the binomial thinning. Compared to the binomial thinning operator, the extended binomial thinning operator has two parameters and is more flexible in modeling. Based on the proposed operator, a new integer-valued autoregressive model is introduced, which can accurately and flexibly capture the dispersed features of counting time series. Two-step conditional least squares (CLS) estimation is investigated for the innovation-free case and the conditional maximum likelihood estimation is also discussed. We have also obtained the asymptotic property of the two-step CLS estimator. Finally, three overdispersed or underdispersed real data sets are considered to illustrate a superior performance of the proposed model.

scholarly journals A Robust Regression by Using Huber Estimator and Tukey Bisquare Estimator for Predicting Availability of Corn in Karanganyar Regency, Indonesia

2018 ◽  
Vol 1 (1) ◽  
pp. 37
Author(s):  
Hasih Pratiwi ◽  
Yuliana Susanti ◽  
Sri Sulistijowati Handajani
Keyword(s):  
Least Squares ◽  
Robust Regression ◽  
Likelihood Estimation ◽  
Corn Production ◽  
Least Squares Fit ◽  
Class Of Estimators ◽  
M Estimation ◽  
Heavy Tailed ◽  
Least Squares Estimates ◽  
Huber Estimator

Linear least-squares estimates can behave badly when the error distribution is not normal, particularly when the errors are heavy-tailed. One remedy is to remove influential observations from the least-squares fit. Another approach, robust regression, is to use a fitting criterion that is not as vulnerable as least squares to unusual data. The most common general method of robust regression is M-estimation. This class of estimators can be regarded as a generalization of maximum-likelihood estimation. In this paper we discuss robust regression model for corn production by using two popular estimators; i.e. Huber estimator and Tukey bisquare estimator.<br />Keywords : robust regression, M-estimation, Huber estimator, Tukey bisquare estimator

scholarly journals Properties and estimation of GARCH(1,1) model

2005 ◽  
Vol 2 (2) ◽  
Author(s):  
Petra Posedel
Keyword(s):  
Fourth Moment ◽  
Asymptotic Covariance Matrix ◽  
Likelihood Estimator ◽  
Consistent Estimation ◽  
Strong Stationarity ◽  
Asymptotic Covariance ◽  
Sampling Behavior ◽  
Garch Processes ◽  
Heavy Tailed ◽  
Quasi Maximum Likelihood

We study in depth the properties of the GARCH(1,1) model and the assumptions on the parameter space under which the process is stationary. In particular, we prove ergodicity and strong stationarity for the conditional variance (squared volatility) of the process. We show under which conditions higher order moments of the GARCH(1,1) process exist and conclude that GARCH processes are heavy-tailed. We investigate the sampling behavior of the quasi-maximum likelihood estimator of the Gaussian GARCH(1,1) model. A bounded conditional fourth moment of the rescaled variable (the ratio of the disturbance to the conditional standard deviation) is sufficient for the result. Consistent estimation and asymptotic normality are demonstrated, as well as consistent estimation of the asymptotic covariance matrix.

scholarly journals Spatial Panel-data Models Using Stata

2017 ◽  
Vol 17 (1) ◽  
pp. 139-180 ◽  
Author(s):  
Federico Belotti ◽  
Gordon Hughes ◽  
Andrea Piano Mortari
Keyword(s):  
Panel Data ◽  
Urban Economics ◽  
Spatial Models ◽  
Likelihood Estimation ◽  
Real Data ◽  
Marginal Effects ◽  
Wide Range ◽  
Spatial Panel Data Models ◽  
Spatial Panel Data ◽  
Quasi Maximum Likelihood

xsmle is a new user-written command for spatial analysis. We consider the quasi–maximum likelihood estimation of a wide set of both fixed- and random-effects spatial models for balanced panel data. xsmle allows users to handle unbalanced panels using its full compatibility with the mi suite of commands, use spatial weight matrices in the form of both Stata matrices and spmat objects, compute direct, indirect, and total marginal effects and related standard errors for linear (in variables) specifications, and exploit a wide range of postestimation features, including the panel-data case predictors of Kelejian and Prucha (2007, Regional Science and Urban Economics 37: 363–374). Moreover, xsmle allows the use of margins to compute total marginal effects in the presence of nonlinear specifications obtained using factor variables. In this article, we describe the command and all of its functionalities using simulated and real data.

The Odd Log-Logistic Log-Normal Distribution with Theory and Applications

2018 ◽  
Vol 10 (04) ◽  
pp. 1850009 ◽  
Author(s):  
Gamze Ozel ◽  
Emrah Altun ◽  
Morad Alizadeh ◽  
Mahdieh Mozafari
Keyword(s):  
Normal Distribution ◽  
Likelihood Estimation ◽  
Real Data ◽  
Estimation Procedure ◽  
Quantile Function ◽  
Logistic Distribution ◽  
Unknown Parameters ◽  
Heavy Tailed ◽  
Log Normal ◽  
Log Normal Distribution

In this paper, a new heavy-tailed distribution is used to model data with a strong right tail, as often occuring in practical situations. The proposed distribution is derived from the log-normal distribution, by using odd log-logistic distribution. Statistical properties of this distribution, including hazard function, moments, quantile function, and asymptotics, are derived. The unknown parameters are estimated by the maximum likelihood estimation procedure. For different parameter settings and sample sizes, a simulation study is performed and the performance of the new distribution is compared to beta log-normal. The new lifetime model can be very useful and its superiority is illustrated by means of two real data sets.

TEST FOR ZERO MEDIAN OF ERRORS IN AN ARMA–GARCH MODEL

2021 ◽  
pp. 1-26
Author(s):  
Yaolan Ma ◽  
Mo Zhou ◽  
Liang Peng ◽  
Rongmao Zhang
Keyword(s):  
Heavy Tails ◽  
Normal Limit ◽  
Garch Model ◽  
Likelihood Estimation ◽  
Fourth Moment ◽  
Economic Data ◽  
Quasi Maximum Likelihood ◽  
Moment Effect ◽  
The Moment ◽  
The Garch Model

Because the ARMA–GARCH model can generate data with some important properties such as skewness, heavy tails, and volatility persistence, it has become a benchmark model in analyzing financial and economic data. The commonly employed quasi maximum likelihood estimation (QMLE) requires a finite fourth moment for both errors and the sequence itself to ensure a normal limit. The self-weighted quasi maximum exponential likelihood estimation (SWQMELE) reduces the moment constraints by assuming that the errors and their absolute values have median zero and mean one, respectively. Therefore, it is necessary to test zero median of errors before applying the SWQMELE, as changing zero mean to zero median destroys the ARMA–GARCH structure. This paper develops an efficient empirical likelihood test without estimating the GARCH model but using the GARCH structure to reduce the moment effect. A simulation study confirms the effectiveness of the proposed test. The data analysis shows that some financial returns do not have zero median of errors, which cautions the use of the SWQMELE.

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