Academic literature on the topic 'Beta-t-EGARCH'

The Beta-Skew-t-EGARCH model was recently proposed in literature to model the volatility of financial returns. The inferences over the parameters of the model are based on maximum likelihood method. These estimators have good asymptotic properties, however in finite sample sizes their performance can be poor. With the purpose of evaluating the finite sample performance of point estimators and of the likelihood ratio test proposed to the presence of two components of volatility, we present a Monte Carlo simulation study. Numerical results indicate that the maximum likelihood estimators of some parameters of the model are considerably biased in sample sizes smaller than 3000. The evaluation results of the proposed two-component test, in terms of size and power of the test, showed its practical usefulness in sample sizes greater than 3000. At the end of the work we present an application in a real data of the proposed two-component test and the model Beta-Skew-t-EGARCH.

No consensus exists in the literature on whether stock prices can be predicted, with most existing studies employing point forecasting to predict returns. By contrast, this study adopts the new perspective of distribution forecasting to investigate the predictability of the stock market using the model combination strategy. Specifically, the Shanghai Composite Index and the Shenzhen Component Index are selected as research objects. Seven models – GARCH-norm, GARCH-sstd, EGARCH-sstd, EGARCH-sstd-M, one-component Beta-t-EGARCH, two-component Beta-t-EGARCH, and the EWMA-based nonparametric model – are employed to perform distribution forecasting of the returns. The results of out-of-sample forecasting evaluation show that none of the individual models is “qualified” in terms of predictive power. Therefore, three combinations of individual models were constructed: equal weight combination, log-likelihood score combination, and continuous ranked probability score combination. The latter two combinations were found to always have significant directional predictability and excess profitability, which indicates that the two combined models may be closer to the real data generation process; from the perspective of economic evaluation, they may have a predictive effect on the conditional return distribution in China’s stock market.

Abstract We present the Beta-t-QVAR (quasi-vector autoregression) model for the joint modelling of score-driven location plus scale of strictly stationary and ergodic variables. Beta-t-QVAR is an extension of Beta-t-EGARCH (exponential generalized autoregressive conditional heteroscedasticity) and Beta-t-EGARCH-M (Beta-t-EGARCH-in-mean). We prove the asymptotic properties of the maximum likelihood (ML) estimator for correctly specified Beta-t-QVAR models. We use Dow Jones Industrial Average (DJIA) data for the period of 1985–2020. We find that the volatility forecasting accuracy of Beta-t-QVAR is superior to the volatility forecasting accuracies of Beta-t-EGARCH, Beta-t-EGARCH-M, A-PARCH (asymmetric power ARCH), and GARCH for the period of 2010–2020.

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior
The Beta-Skew-t-EGARCH model was recently proposed in literature to model the volatility of financial returns. The inferences over the model parameters are based on the maximum likelihood method. The maximum likelihood estimators present good asymptotic properties; however, in finite sample sizes they can be considerably biased. Monte Carlo simulations were used to evaluate the finite sample performance of point estimators. Numerical results indicated that the maximum likelihood estimators of some parameters are biased in sample sizes smaller than 3,000. Thus, bootstrap bias correction procedures were considered to obtain more accurate estimators in small samples. Better quality of forecasts was observed when the model with bias-corrected estimators was considered. In addition, we propose a likelihood ratio test to assist in the selection of the Beta-Skew-t-EGARCH model with one or two volatility components. The numerical evaluation of the two-component test showed distorted null rejection rates in sample sizes smaller than or equal to 1,000. To improve the performance of the proposed test in small samples, the bootstrap-based likelihood ratio test and the bootstrap Bartlett correction were considered. The bootstrap-based test exhibited the closest null rejection rates to the nominal values. The evaluation results of the two-component tests showed their practical usefulness. Finally, an application to the log-returns of the German stock index of the proposed methods was presented.
O modelo Beta-Skew-t-EGARCH foi recentemente proposto para modelar a volatilidade de retornos financeiros. A estimação dos parâmetros do modelo é feita via máxima verossimilhança. Esses estimadores possuem boas propriedades assintóticas, mas em amostras de tamanho finito eles podem ser consideravelmente viesados. Com a finalidade de avaliar as propriedades dos estimadores, em amostras de tamanho finito, realizou-se um estudo de simulações de Monte Carlo. Os resultados numéricos indicam que os estimadores de máxima verossimilhança de alguns parâmetros do modelo são viesados em amostras de tamanho inferior a 3000. Para obter estimadores pontuais mais acurados foram consideradas correções de viés via o método bootstrap. Verificou-se que os estimadores corrigidos apresentaram menor viés relativo percentual. Também foi observada melhor qualidade das previsões quando o modelo com estimadores corrigidos são considerados. Para auxiliar na seleção entre o modelo Beta-Skew-t-EGARCH com um ou dois componentes de volatilidade foi apresentado um teste da razão de verossimilhanças. A avaliação numérica do teste de dois componentes proposto demonstrou taxas de rejeição nula distorcidas em tamanhos amostrais menores ou iguais a 1000. Para melhorar o desempenho do teste foram consideradas a correção bootstrap e a correção de Bartlett bootstrap. Os resultados numéricos indicam a utilidade prática dos testes de dois componentes propostos. O teste bootstrap exibiu taxas de rejeição nula mais próximas dos valores nominais. Ao final do trabalho foi realizada uma aplicação dos testes de dois componentes e do modelo Beta-Skew-t-EGARCH, bem como suas versões corrigidas, a dados do índice de mercado da Alemanha.