In the paper the asymptotic distributions of sample optimal portfolio weights are derived. This is done under the weak assumption on the data generating process. It is assumed that the k -dimensional vector of asset returns follows a VARMA( 1 1 , p q )GARCH( 2 2 , p q ) process with the elliptically distributed error process. The estimators of the mean vector and the covariance matrix of the as...

This paper characterizes the term structure of risk measures such as Value at Risk (VaR) and expected shortfall under different econometric approaches including multivariate regime switching, GARCH-in-mean models with student-t errors, two-component GARCH models and a non-parametric bootstrap. We show how to derive the risk measures for each of these models and document large variations in term...

The frequent and sharp fluctuations in garlic prices seriously affect the sustainable development of industry. Accurate prediction can facilitate correct evaluation scientific decision making by practitioners, thereby avoiding market risks promoting healthy To improve accuracy prices, this paper proposes a garlic-price-prediction method based on combination long short-term memory (LSTM) multipl...

This paper investigates the forecasting ability of five different versions of GARCH models. The five GARCH models applied are bivariate GARCH, GARCH-ECM, BEKK GARCH, GARCH-X and GARCH-GJR. Forecast errors based on four emerging stock futures portfolio return (based on forecasted hedge ratio) forecasts are employed to evaluate out-ofsample forecasting ability of the five GARCH models. Daily data...

In the empirical finance literature findings on the risk-return tradeoff in excess stock market returns are ambiguous. In this study, we develop a new QR-GARCH-M model combining a probit model for a binary business cycle indicator and a regime switching GARCH-in-mean model for excess stock market return with the business cycle indicator defining the regime. Estimation results show that there is...

ARCH/GARCH modelling has been successfully applied in empirical finance for many years. This paper surveys the semiparametric and nonparametric methods in univariate andmultivariate ARCH/GARCHmodels. First, we introduce some specific semiparametric models and investigate the semiparametric and nonparametrics estimation techniques applied to: the error density, the functional form of the volatil...

The augmented GARCH model is a unification of numerous extensions of the popular and widely used ARCH process. It was introduced by Duan and besides ordinary (linear) GARCH processes, it contains exponential GARCH, power GARCH, threshold GARCH, asymmetric GARCH, etc. In this paper, we study the probabilistic structure of augmented GARCH(1,1) sequences and the asymptotic distribution of various ...

This paper adopts a new approach to estimating the conditional probability distribution of asset returns. It is evident that the exact conditional mean or variance is inherently unobservable for time series. In practice, the popular way is to derive from different models such as GARCH by assuming distributions such as normal, student t, or skewed t. Thus the accuracy of forecast strongly depend...