GO-GJRSK Model with Application to Higher Order Risk-Based Portfolio

Abstract

There are three distinguishing features in the financial time series, such as stock prices, are as follows: (1) Non-normality, (2) serial correlation, and (3) leverage effect. All three points need to be taken into account to model the financial time series. However, multivariate financial time series modeling involves a large number of stocks, with many parameters to be estimated. Therefore, there are few examples of multivariate financial time series modeling that explicitly deal with higher-order moments. Furthermore, there is no multivariate financial time series model that takes all three characteristics above into account. In this study, we propose the generalized orthogonal (GO)-Glosten, Jagannathan, and Runkle GARCH (GJR) model which extends the GO-generalized autoregressive conditional heteroscedasticity (GARCH) model and incorporates the three features of the financial time series. We confirm the effectiveness of the proposed model by comparing the performance of risk-based portfolios with higher-order moments. The results show that the performance with our proposed model is superior to that with baseline methods, and indicate that estimation methods are important in risk-based portfolios with higher moments.

The asymmetric effects of climate risk on higher-moment connectedness among carbon, energy and metals markets

“…The financial time series is not strictly subject to normal distribution, but has the characteristics of leptokurtosis, fat-tail and leverage effect. To measure the conditional volatility, skewness, and kurtosis of carbon, energy and metal markets, we use the GJRSK model proposed by Nakagawa and Uchiyama 36 which is the GARCHSK model with a leverage effect to establish a high-order moment model. The GJRSK model is based on the GJR framework, which allows for asymmetric responses to positive and negative shocks.…”

“…In this work, we employ the GJRSK model proposed by Nakagawa and Uchiyama 36 , the spillover method introduced by Baruník and Krehlík 37 , and the quantile-on-quantile method to investigate the influence of climate risk on high-order time-frequency spillover effects. First, we explore the risk spillover effects in the carbon-energymetals nexus from the perspective of higher-order moment risk, adding to the previous studies, which mainly investigate the spillover effects of returns and volatility.…”

Entropy Based Student’s t-Process Dynamical Model

“…Various families of GARCH model have been developed and proposed in the area of econometrics and quantitative finance [ 17 ]. For instance, asymmetric effect has been introduced into a multivariate GARCH model [ 18 , 19 ].…”