The present study aims at applying different methods i.e GARCH, EGARCH, GJRGARCH, IGARCH & ANN models for calculating the volatilities of Indian stock markets. Fourteen years of data of BSE Sensex & NSE Nifty are used to calculate the volatilities. The performance of data exhibits that, there is no difference in the volatilities of Sensex, & Nifty estimated under the GARCH, EGARCH, GJR GARCH, I...

It is well-known that causal forecasting methods that include appropriately chosen Exogenous Variables (EVs) very often present improved forecasting performances over univariate methods. However, in practice, EVs are usually difficult to obtain and in many cases are not available at all. In this paper, a new causal forecasting approach, called Wavelet Auto-Regressive Integrated Moving Average w...

This paper establishes the strong consistency and asymptotic normality of the quasi-maximum likelihood estimator (QMLE) for a GARCH process with periodically time-varying parameters. We first give a necessary and sufficient condition for the existence of a strictly periodically stationary solution for the periodic GARCH (P -GARCH) equation. As a result, it is shown that the moment of some posit...

It is well-established that the …nancial time series display some stylized fatcs such as volatility clustering, high kurtosis, low starting and slow-decaying autocorrelation function and the Talyor e¤ect as well. In order to evaluate volatility models’capacity in capturing such facts, we apply both standard and robust measures of kurtosis and autocorrelation of squares to GARCH, EGARCH and ARSV...

We consider the parameter restrictions that need to be imposed in order to ensure that the conditional variance process of a GARCH(p, q) model remains non-negative. Previously, Nelson and Cao (1992) provided a set of necessary and sufficient conditions for the aforementioned non-negativity property for GARCH(p, q) models with p ≤ 2, and derived a sufficient condition for the general case of GAR...

In the presence of generalized conditional heteroscedasticity (GARCH) in the residuals of a vector error correction model (VECM), maximum likelihood (ML) estimation of the cointegration parameters has been shown to be efficient. On the other hand, full ML estimation of VECMs with GARCH residuals is computationally difficult and may not be feasible for larger models. Moreover, ML estimation of V...

In this paper we examine the characteristics of market opening news and its impact on the estimated coe cients of the conditional volatility models of the GARCH class. We nd that the di erences between the opening price of one day and the closing price of the day before have di erent characteristics when considering various stock market indices on which options are actively traded. The impact o...

GARCH is one of the most prominent nonlinear time series models, both widely applied and thoroughly studied. Recently, it has been shown that the COGARCH model, which has been introduced a few years ago by Klüppelberg, Lindner and Maller, and Nelson’s diffusion limit are the only functional continuous-time limits of GARCH in distribution. In contrast to Nelson’s diffusion limit, COGARCH reprodu...