On the computational estimation of high order GARCH model

2021 ◽  
Vol 8 (4) ◽  
pp. 797-806
Author(s):  
A. Settar ◽  
◽  
N. I. Fatmi ◽  
M. Badaoui ◽  
◽  
...  
Keyword(s):  
Monte Carlo ◽  
Kalman Filter ◽  
Monte Carlo Simulations ◽  
Garch Model ◽  
Real Data ◽  
Conditional Variance ◽  
High Order ◽  
Computational Estimation ◽  
Necessary And Sufficient ◽  
The Garch Model

To guarantee the non-negativity of the conditional variance of the GARCH process, it is sufficient to assume the non-negativity of its parameters. This condition was empirically violated besides rendering the GARCH model more restrictive. It was subsequently relaxed for some GARCH orders by necessary and sufficient constraints. In this paper, we generalized an approach for the QML estimation of the GARCH(p,q) parameters for all orders $p\geq 1$ and $q\geq1$ using a constrained Kalman filter. Such an approach allows a relaxed QML estimation of the GARCH without the need to identify and/or apply the relaxed constraints to the parameters. The performance of our method is demonstrated through Monte Carlo simulations and empirical applications to real data.

A NOTE ON INEQUALITY CONSTRAINTS IN THE GARCH MODEL

2008 ◽  
Vol 24 (3) ◽  
pp. 823-828 ◽  
Author(s):  
Henghsiu Tsai ◽  
Kung-Sik Chan
Keyword(s):  
Generating Function ◽  
Sufficient Conditions ◽  
Inequality Constraints ◽  
Conditional Variance ◽  
Necessary Condition ◽  
Sufficient Condition ◽  
Economic Statistics ◽  
Absolute Monotonicity ◽  
Necessary And Sufficient ◽  
The Garch Model

We consider the parameter restrictions that need to be imposed to ensure that the conditional variance process of a GARCH(p,q) model remains nonnegative. Previously, Nelson and Cao (1992, Journal of Business ’ Economic Statistics 10, 229–235) provided a set of necessary and sufficient conditions for the aforementioned nonnegativity property for GARCH(p,q) models with p ≤ 2 and derived a sufficient condition for the general case of GARCH(p,q) models with p ≥ 3. In this paper, we show that the sufficient condition of Nelson and Cao (1992) for p ≥ 3 actually is also a necessary condition. In addition, we point out the linkage between the absolute monotonicity of the generalized autoregressive conditional heteroskedastic (GARCH) generating function and the nonnegativity of the GARCH kernel, and we use it to provide examples of sufficient conditions for this nonnegativity property to hold.

scholarly journals Structural nonlinear damage identification using penalty conversion index of GARCH model

2020 ◽  
Vol 12 (11) ◽  
pp. 168781402097117
Author(s):  
Hui-Yong Guo ◽  
Heng Zuo
Keyword(s):  
Damage Identification ◽  
Detection Method ◽  
Garch Model ◽  
Exact Expression ◽  
Conditional Variance ◽  
Major Influence ◽  
Engineering Structures ◽  
Service Period ◽  
Stiffness Characteristic ◽  
The Garch Model

In the service period, some engineering structures may have cracks or other nonlinear damages. The nonlinear damages are the major influence to the safety of engineering structures, which should be detected as early as possible. Currently, the effective nonlinear damage detection method is still lacking. Therefore, a penalty conversion index based on generalized autoregressive conditional heteroskedasticity (GARCH) model is presented to identify the nonlinear damage. First, an exact expression of GARCH model is described, the bilinear stiffness characteristic of nonlinear damage is given, and acceleration responses are used to establish the GARCH model. Then, through the GARCH model analysis of nonlinear damages responses, it can be found that the variance of conditional variance are sensitive to the nonlinear damage information of acceleration responses, so a basic conversion index based on the variance of conditional variance is proposed. Finally, a penalty conversion index based on GARCH model is presented, which can reduce the interference induced by the adjacent unrelated factors. Numerical and experimental examples show that the identification results of the proposed penalty conversion index based on GARCH model are superior to those of the basic conversion index and the cepstral metric (CM) index.

scholarly journals Small area estimation in the case of nonesponse

2009 ◽  
Vol 50 ◽  
Author(s):  
Vilma Nekrašaitė-Liegė
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Small Area ◽  
Finite Population ◽  
Real Data ◽  
Area Estimation ◽  
Empirical Results ◽  
Different Types ◽  
Business Survey ◽  
Repeated Samples

In this paper the effect of model and nonresponseadjustment on different types of estimators for the totals of small area domains is examined. The empirical results are based on Monte Carlo simulations with repeated samples drawn from a finite population constructed from the real data from the Lithuanian Business Survey.

scholarly journals Simulasi Monte Carlo untuk Memprediksi Persediaan Darah

2020 ◽  
Author(s):  
Rahmi Darnis ◽  
Gunadi Widi Nurcahyo ◽  
Yuhandri Yunus
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Blood Supply ◽  
Transport System ◽  
Real Data ◽  
Transportation System ◽  
Production Data ◽  
Accuracy Rate ◽  
Simulation Results

Blood is a special organ as a communication and transportation system whose job is to circulate nutrients and oxygen. As a very vital transport system and its very useful existence for many people, blood must be managed properly. Monte Carlo simulations can predict problems related to blood stock and demand for blood. The data that is processed to predict blood supply is blood production data in 2018 and 2019, Simulation results data for 2018 are compared with real data for 2019 and simulation results for 2019 are compared with real data for 2020. The results of the simulations that have been carried out have an accuracy rate of 96.21% for 2018 and 79.22% for 2019. Based on the results of the tests that have been done, it can provide information that can help in the management of forecasting future blood stocks.

Adjacency matrix comparison for stochastic block models

2019 ◽  
Vol 08 (03) ◽  
pp. 1950010
Author(s):  
Guangren Yang ◽  
Songshan Yang ◽  
Wang Zhou
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Adjacency Matrix ◽  
Real Data ◽  
Finite Sample ◽  
Adjacency Matrices ◽  
Block Models

In this paper, we study whether two networks arising from two stochastic block models have the same connection structures by comparing their adjacency matrices. We conduct Monte Carlo simulations study to examine the finite sample performance of the proposed method. A real data example is used to illustrate the proposed methodology.

scholarly journals Estimation Methods of Alpha Power Exponential Distribution with Applications to Engineering and Medical Data

2020 ◽  
pp. 149-166 ◽  
Author(s):  
Mazen Nassar ◽  
Ahmed Z. Afify ◽  
Mohammed Shakhatreh
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Exponential Distribution ◽  
Real Data ◽  
Medical Data ◽  
Estimation Methods ◽  
Alpha Power ◽  
Unknown Parameters ◽  
Data Set ◽  
Distribution Parameters

This paper addresses the estimation of the unknown parameters of the alphapower exponential distribution (Mahdavi and Kundu, 2017) using nine frequentist estimation methods. We discuss the nite sample properties of the parameterestimates of the alpha power exponential distribution via Monte Carlo simulations. The potentiality of the distribution is analyzed by means of two real datasets from the elds of engineering and medicine. Finally, we use the maximumlikelihood method to derive the estimates of the distribution parameters undercompeting risks data and analyze one real data set.

scholarly journals The Generalized Transmuted Poisson-G Family of Distributions: Theory, Characterizations and Applications

2018 ◽  
pp. 759-779 ◽  
Author(s):  
Haitham Yousof ◽  
Ahmed Z Afify ◽  
Morad Alizadeh ◽  
G. G. Hamedani ◽  
S. Jahanshahi ◽  
...  
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Order Statistics ◽  
Real Data ◽  
Model Parameters ◽  
Data Sets ◽  
Continuous Distributions ◽  
New Class ◽  
Mathematical Properties ◽  
Family Of Distributions

In this work, we introduce a new class of continuous distributions called the generalized poissonfamily which extends the quadratic rank transmutation map. We provide some special models for thenew family. Some of its mathematical properties including Rényi and q-entropies, order statistics andcharacterizations are derived. The estimations of the model parameters is performed by maximumlikelihood method. The Monte Carlo simulations is used for assessing the performance of the maximumlikelihood estimators. The ‡exibility of the proposed family is illustrated by means of two applicationsto real data sets.

scholarly journals TESTING THE GARCH MODEL IN THE VIETNAMESE STOCK MARKET

2010 ◽  
Vol 13 (4) ◽  
pp. 5-14
Author(s):  
Hien Thu Nguyen ◽  
Nghi Dinh Le
Keyword(s):  
Stock Market ◽  
Stock Returns ◽  
Stock Markets ◽  
Trading Volume ◽  
Garch Model ◽  
Conditional Variance ◽  
Investment Risk ◽  
The Garch Model

An important factor of interest of investors on stock markets is investment risk. Risk can undergo a quantitative process through volatility, be measured by conditional variance of stock returns. GARCH is an effective and popularly used model for volatility effect on stock returns. This study tests the GARCH model and analyzes other aspects of volatility on stock returns on the two stock markets of Vietnam. In addition, the study provides evidence of the existence of GARCH effect on Vietnamese stock markets. Besides, the study also assesses price margin policy, trading volume and leverage effects on volatility of stock returns.

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