Small sample properties of copula-GARCH modelling: a Monte Carlo study

Abstract

Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in February 2009Abstract Copula-GARCH models have been recently proposed in the financial literature as a statistical tool to build flexible multivariate distributions. Our extensive simulation studies investigate the small sample properties of these models and examine how misspecification in the marginals may affect the estimation of the dependence function represented by the copula. We show that the use of normal marginals when the true Data Generating Process is leptokurtic or asymmetric, produces negatively biased estimates of the normal copula correlations. A striking result is that these biases reach their highest value when correlations are strongly negative, and viceversa. This result remains unchanged with both positively skewed and negatively skewed data, while no biases are found if the variables are uncorrelated. Besides, the effect of marginals asymmetry on correlations is smaller than that of leptokurtosis. We finally analyse the performance of these models in terms of numerical convergence and positive definiteness of the estimated copula correlation matrix.

Crypto-Coins and Credit Risk: Modelling and Forecasting Their Probability of Death

“…It is well-known, since the work by Fiorentini et al (1996), that the estimation of GARCH models is complex and requires large samples. Moreover, the large simulation studies of GARCH processes in Hwang and Valls Pereira (2006), Fantazzini (2009) and Bianchi et al (2011) showed that a sample of at least 250-500 observations is needed to have good model estimates and, in case of complex data-generating processes, even larger samples are required.…”

Adaptive Conformal Inference for Computing Market Risk Measures: An Analysis with Four Thousand Crypto-Assets

“…The seminal work by Fiorentini et al (1996) highlighted the issues involved in GARCH model estimation, emphasizing the demand for large datasets. Furthermore, comprehensive simulation studies conducted by Hwang and Valls Pereira (2006), Fantazzini (2009), andBianchi et al (2011) underscored the requirement of a sample size ranging from 250 to 500 observations for obtaining reliable model estimates of basic GARCH models. For scenarios involving more complex data generating processes, even larger sample sizes were necessary to ensure robust estimation.…”

Avaliações numéricas das inferências no modelo Beta-Skew-t-EGARCH

“…Nesse tamanho amostral o viés das estimativas de todos os parâmetrosé próximo a zero. Esses resultados estendem as evidências de simulação identificadas por Bianchi et al (2011), que no entanto, analisam o modelo Cópula GARCH para o caso em que os choques aleatórios seguem a distribuição t-Student. Além disso, percebeu-se que em dados com maior curtose excedente os estimadores apresentam melhores propriedades.…”

“…A estimação dos parâmetros do modeloé baseada no método de máxima verossimilhança. Como relatado ao longo do trabalho esses estimadores podem conduzir a resultados inferenciais distorcidos em pequenas amostras (Hwang & Pereira, 2006, Xie, 2009, Bianchi et al, 2011. Nesse sentido, esse trabalho analisou por meio de simulações de Monte Carlo as propriedades dos estimadores do modelo Beta-Skew-t-EGARCH em amostras de tamanho finito.…”

“…No entanto, em pequenas amostras as aproximações podem ser pobres e produzir estimativas significativamente diferentes do valor do parâmetro (Kenward & Roger, 1997, Hippel, 2013. Ademais, verifica-se que para a classe de modelos GARCH os estimadores de máxima verossimilhança apresentam, em geral, dificuldades em pequenas amostras (Hwang & Pereira, 2006, Bianchi et al, 2011. Detalhes sobre as propriedades assintóticas dos EMV em modelos GARCH podem ser encontradas em Douc et al (2004), Lumsdaine (1995), Chan & McAleer (2002), Xie (2009), Engle et al (1985), Mendes (2000) e Hwang & Pereira (2006), entre outros trabalhos.…”