scholarly journals High-Dimensional Conditional Covariance Matrices Estimation Using a Factor-GARCH Model

Symmetry ◽  
2022 ◽  
Vol 14 (1) ◽  
pp. 158
Author(s):  
Xiaoling Li ◽  
Xingfa Zhang ◽  
Yuan Li
Keyword(s):  
Covariance Matrix ◽  
Factor Model ◽  
Asymptotic Properties ◽  
Garch Model ◽  
Likelihood Estimation ◽  
Least Square ◽  
High Dimensional ◽  
Conditional Covariance ◽  
Financial Application ◽  
Quasi Maximum Likelihood

Estimation of a conditional covariance matrix is an interesting and important research topic in statistics and econometrics. However, modelling ultra-high dimensional dynamic (conditional) covariance structures is known to suffer from the curse of dimensionality or the problem of singularity. To partially solve this problem, this paper establishes a model by combining the ideas of a factor model and a symmetric GARCH model to describe the dynamics of a high-dimensional conditional covariance matrix. Quasi maximum likelihood estimation (QMLE) and least square estimation (LSE) methods are used to estimate the parameters in the model, and the plug-in method is introduced to obtain the estimation of conditional covariance matrix. Asymptotic properties are established for the proposed method, and simulation studies are given to demonstrate its performance. A financial application is presented to support the methodology.

scholarly journals ON DETERMINING THE NUMBER OF SPIKES IN A HIGH-DIMENSIONAL SPIKED POPULATION MODEL

2012 ◽  
Vol 01 (01) ◽  
pp. 1150002 ◽  
Author(s):  
DAMIEN PASSEMIER ◽  
JIAN-FENG YAO
Keyword(s):  
Covariance Matrix ◽  
Population Model ◽  
Factor Model ◽  
Fundamental Problem ◽  
High Dimensional ◽  
Sample Covariance ◽  
Or Economics ◽  
Linear Mixture Model ◽  
The Difference ◽  
Scientific Fields

In a spiked population model, the population covariance matrix has all its eigenvalues equal to units except for a few fixed eigenvalues (spikes). Determining the number of spikes is a fundamental problem which appears in many scientific fields, including signal processing (linear mixture model) or economics (factor model). Several recent papers studied the asymptotic behavior of the eigenvalues of the sample covariance matrix (sample eigenvalues) when the dimension of the observations and the sample size both grow to infinity so that their ratio converges to a positive constant. Using these results, we propose a new estimator based on the difference between two consecutive sample eigenvalues.

scholarly journals NEGATIVE VOLATILITY SPILLOVERS IN THE UNRESTRICTED ECCC-GARCH MODEL

2009 ◽  
Vol 26 (3) ◽  
pp. 838-862 ◽  
Author(s):  
Christian Conrad ◽  
Menelaos Karanasos
Keyword(s):  
Covariance Matrix ◽  
Garch Model ◽  
Positive Definiteness ◽  
Time Varying ◽  
Conditional Covariance ◽  
Conditional Correlation ◽  
Economic Theories ◽  
Model Builder ◽  
Volatility Spillovers ◽  
Volatility Feedback

This paper considers a formulation of the extended constant or time-varying conditional correlation GARCH model that allows for volatility feedback of either the positive or negative sign. In the previous literature, negative volatility spillovers were ruled out by the assumption that all the parameters of the model are nonnegative, which is a sufficient condition for ensuring the positive definiteness of the conditional covariance matrix. In order to allow for negative feedback, we show that the positive definiteness of the conditional covariance matrix can be guaranteed even if some of the parameters are negative. Thus, we extend the results of Nelson and Cao (1992) and Tsai and Chan (2008) to a multivariate setting. For the bivariate case of order one, we look into the consequences of adopting these less severe restrictions and find that the flexibility of the process is substantially increased. Our results are helpful for the model-builder, who can consider the unrestricted formulation as a tool for testing various economic theories.

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.

Asymmetric Laplace Regression: Maximum Likelihood, Maximum Entropy and Quantile Regression

2016 ◽  
Vol 5 (1) ◽  
Author(s):  
Anil K. Bera ◽  
Antonio F. Galvao ◽  
Gabriel V. Montes-Rojas ◽  
Sung Y. Park
Keyword(s):  
Maximum Likelihood ◽  
Quantile Regression ◽  
Maximum Entropy ◽  
Asymptotic Properties ◽  
Likelihood Estimation ◽  
Finite Sample ◽  
Score Functions ◽  
Finite Sample Properties ◽  
Quasi Maximum Likelihood ◽  
Joint Consideration

AbstractThis paper studies the connections among the asymmetric Laplace probability density (ALPD), maximum likelihood, maximum entropy and quantile regression. We show that the maximum likelihood problem is equivalent to the solution of a maximum entropy problem where we impose moment constraints given by the joint consideration of the mean and median. The ALPD score functions lead to joint estimating equations that delivers estimates for the slope parameters together with a representative quantile. Asymptotic properties of the estimator are derived under the framework of the quasi maximum likelihood estimation. With a limited simulation experiment we evaluate the finite sample properties of our estimator. Finally, we illustrate the use of the estimator with an application to the US wage data to evaluate the effect of training on wages.

scholarly journals Identifying Stabilising Effects on Survey Based Life Satisfaction Using Quasi-maximum Likelihood Estimation

2021 ◽  
Author(s):  
Johannes Klement
Keyword(s):  
Life Satisfaction ◽  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Negative Binomial ◽  
Measurement Instrument ◽  
Likelihood Estimation ◽  
Satisfaction Scale ◽  
Quasi Maximum Likelihood ◽  
The Stability

AbstractTo which extent do happiness correlates contribute to the stability of life satisfaction? Which method is appropriate to provide a conclusive answer to this question? Based on life satisfaction data of the German SOEP, we show that by Negative Binomial quasi-maximum likelihood estimation statements can be made as to how far correlates of happiness contribute to the stabilisation of life satisfaction. The results show that happiness correlates which are generally associated with a positive change in life satisfaction, also stabilise life satisfaction and destabilise dissatisfaction with life. In such as they lower the probability of leaving positive states of life satisfaction and increase the probability of leaving dissatisfied states. This in particular applies to regular exercise, volunteering and living in a marriage. We further conclude that both patterns in response behaviour and the quality of the measurement instrument, the life satisfaction scale, have a significant effect on the variation and stability of reported life satisfaction.

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