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...

To capture the missed information in the standardized errors by parametric multivariate generalized autoregressive conditional heteroskedasticity (MV-GARCH) model, we propose a new semiparametric MV-GARCH (SM-GARCH) model. This SM-GARCH model is a twostep model: firstly estimating parametric MV-GARCH model, then using nonparametric skills to model the conditional covariance matrix of the standa...

We study the autocorrelation structure and the spectral density function of aggregates from a discrete-time process. The underlying discrete-time process is assumed to be a stationary AutoRegressive Fractionally Integrated MovingAverage (ARFIMA) process, after suitable number of differencing if necessary. We derive closed-form expressions for the limiting autocorrelation function and the normal...

In this paper, we study the dual long memory property of the Korean stock market. For this purpose, the ARFIMA–FIGARCH model is applied to two daily Korean stock price indices (KOSPI and KOSDAQ). Our empirical results indicate that long memory dynamics in the returns and volatility can be adequately estimated by the joint ARFIMA–FIGARCH model. We also found that the assumption of a skewed Stude...

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 brief note offers an explicit algorithm for a multivariate GARCH model, called PC-GARCH, that requires only univariate GARCH estimation. It is suitable for problems with hundreds or even thousands of variables. PC-GARCH is compared to two other techniques of getting multivariate GARCH using univariate estimates.

By design a wavelet’s strength rests in its ability to localize a process simultaneously in time-scale space. The wavelet’s ability to localize a time series in time-scale space directly leads to the computational efficiency of the wavelet representation of a N × N matrix operator by allowing the N largest elements of the wavelet represented operator to represent the matrix operator [Devore, et...