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.

scholarly journals Quasi-maximum likelihood estimator of Laplace (1, 1) for GARCH models

2017 ◽  
Vol 15 (1) ◽  
pp. 1539-1548
Author(s):  
Haiyan Xuan ◽  
Lixin Song ◽  
Muhammad Amin ◽  
Yongxia Shi
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimator ◽  
Strong Consistency ◽  
Garch Model ◽  
Garch Models ◽  
Parameter Vector ◽  
Likelihood Estimator ◽  
Comparison Results ◽  
Quasi Maximum Likelihood ◽  
The Garch Model

Abstract This paper studies the quasi-maximum likelihood estimator (QMLE) for the generalized autoregressive conditional heteroscedastic (GARCH) model based on the Laplace (1,1) residuals. The QMLE is proposed to the parameter vector of the GARCH model with the Laplace (1,1) firstly. Under some certain conditions, the strong consistency and asymptotic normality of QMLE are then established. In what follows, a real example with Laplace and normal distribution is analyzed to evaluate the performance of the QMLE and some comparison results on the performance are given. In the end the proofs of some theorem are presented.

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 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 Asymmetry and Leverage with News Impact Curve Perspective in Australian Stock Returns’ Volatility during COVID-19

2021 ◽  
Vol 14 (7) ◽  
pp. 314
Author(s):  
Najam Iqbal ◽  
Muhammad Saqib Manzoor ◽  
Muhammad Ishaq Bhatti
Keyword(s):  
Stock Returns ◽  
Garch Model ◽  
Bad News ◽  
Good News ◽  
Fiscal Policies ◽  
News Shocks ◽  
Australian Health ◽  
Egarch Model ◽  
Negative Effect ◽  
The Garch Model

This paper studies the effect of COVID-19 on the volatility of Australian stock returns and the effect of negative and positive news (shocks) by investigating the asymmetric nature of the shocks and leverage impact on volatility. We employ a generalised autoregressive conditional heteroskedasticity (GARCH) model and extend the analysis using the exponential GARCH (EGARCH) model to capture asymmetry and allegedly leverage. We proxy the news related to the negative effect of COVID-19 on the Australian health system and its economy as bad news, and on the other hand, measures taken by government economic stimulus packages through their monetary and fiscal policies as good news. The S&P ASX200 (ASX-200) index is used as a proxy to the Australian stock market, and we use value-weighted returns of the stocks listed on ASX-200 for the period 27 January 2020 to 29 December 2020. The empirical results suggest the EGARCH model fits better in capturing asymmetry and leverage than the GARCH model in estimating the volatility of the Australian stock returns. However, another interesting finding is that the EGARCH model with volatility equation without news demonstrates a larger (smaller) leverage effect of the negative (positive) shocks on the conditional volatility compared to its variant with the news.

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.

scholarly journals Comparison of oxygen uptake during and after the execution of resistance exercises and exercises performed on ergometers, matched for intensity

2016 ◽  
Vol 53 (1) ◽  
pp. 179-187 ◽  
Author(s):  
José Vilaça-Alves ◽  
Nuno Miguel Freitas ◽  
Francisco José Saavedra ◽  
Christopher B. Scott ◽  
Victor Machado dos Reis ◽  
...  
Keyword(s):  
Oxygen Uptake ◽  
Ventilatory Threshold ◽  
Lactate Concentration ◽  
Blood Lactate Concentration ◽  
Lower Limbs ◽  
Lower Body ◽  
Load Intensity ◽  
Moment Effect ◽  
The Moment ◽  
The Individual

AbstractThe aim of this study was to compare the values of oxygen uptake (VO2) during and after strength training exercises (STe) and ergometer exercises (Ee), matched for intensity and exercise time. Eight men (24 ± 2.33 years) performed upper and lower body cycling Ee at the individual’s ventilatory threshold (VE/VCO2). The STe session included half squats and the bench press which were performed with a load at the individual blood lactate concentration of 4 mmol/l. Both sessions lasted 30 minutes, alternating 50 seconds of effort with a 10 second transition time between upper and lower body work. The averaged overall VO2 between sessions was significantly higher for Ee (24.96 ± 3.6 ml·kg·min-1) compared to STe (21.66 ± 1.77 ml·kg·min-1) (p = 0.035), but this difference was only seen for the first 20 minutes of exercise. Absolute VO2 values between sessions did not reveal differences. There were more statistically greater values in Ee compared to STe, regarding VO2 of lower limbs (25.44 ± 3.84 ml·kg·min-1 versus 21.83 ± 2·24 ml·kg·min-1; p = 0.038) and upper limbs (24.49 ± 3.84 ml·kg·min-1 versus 21.54 ± 1.77 ml·kg·min-1; p = 0.047). There were further significant differences regarding the moment effect (p<0.0001) of both STe and Ee sessions. With respect to the moment × session effect, only VO2 5 minutes into recovery showed significant differences (p = 0.017). In conclusion, although significant increases in VO2 were seen following Ee compared to STe, it appears that the load/intensity, and not the material/equipment used for the execution of an exercise, are variables that best influence oxygen uptake.

scholarly journals Ramadan Effect and Volatility Risk by Garch Model: Evidence in Indonesia Stock Market

2021 ◽  
pp. 73-82
Author(s):  
Dery Westryananda Putra ◽  
Sri Hasnawati ◽  
Muslimin Muslimin
Keyword(s):  
Stock Market ◽  
Sampling Method ◽  
Stock Exchange ◽  
Garch Model ◽  
Analytical Tool ◽  
Volatility Risk ◽  
Purposive Sampling ◽  
Model Evidence ◽  
The Garch Model

This study aims to analyze the effect of the Ramadan effect and volatility risk on the Indonesian stock market using the GARCH model. The population in this study are companies listed on the LQ45 index on the Indonesia Stock Exchange during 2019. There are 42 companies used as samples in this study. The research sample was taken using purposive sampling method. This study uses the GARCH model as an analytical tool. The results of this study indicate that there is no Ramadan effect on the LQ45 index, but the volatility in the month of Ramadan affects the volatility in the LQ45 index. Keywords: Ramadan Effect, Volatility Risk, GARCH Model Abstrak Penelitian ini bertujuan untuk menganalisis pengaruh Ramadhan effect dan risiko volatilitas terhadap pasar saham Indonesia dengan menggunakan model GARCH. Populasi dalam penelitian ini adalah perusahaan yang terdaftar pada indeks LQ45 di Bursa Efek Indonesia selama tahun 2019. Terdapat 42 perusahaan yang dijadikan sampel dalam penelitian ini. Sampel penelitian diambil dengan menggunakan metode purposive sampling. Penelitian ini menggunakan model GARCH sebagai alat analisis. Hasil penelitian ini menunjukkan bahwa tidak ada pengaruh Ramadhan terhadap indeks LQ45, namun volatilitas pada bulan Ramadhan berpengaruh terhadap volatilitas pada indeks LQ45. Kata Kunci: Ramadhan Effect, Risiko Volatilitas, Model GARCH

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