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...

This paper introduces a conditional extreme value volatility estimator (EVT) based on highfrequency returns. The relative performance of the EVT is compared with the discrete-time GARCH and implied volatility models for 1-day and 20-day-ahead forecasts of realized volatility. This is also a first attempt towards detecting any time-series variation in extreme value distributions using high-frequ...

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 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...

In this paper, we propose a Nonlinear Dickey-Fuller test for unit root against first order Logistic Smooth Transition Autoregressive LSTAR (1) model with time as the transition variable. The Nonlinear Dickey-Fuller test statistic is established under the null hypothesis of random walk without drift and the alternative model is a nonlinear LSTAR (1) model. The asymptotic distribution of the test...

We show that, for three common SARV models, fitting a minimum mean square linear filter is equivalent to fitting a GARCH model. This suggests that GARCH models may be useful for filtering, forecasting, and parameter estimation in stochastic volatility settings. To investigate, we use simulations to evaluate how the three SARV models and their associated GARCH filters perform under controlled co...

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...

The paper estimate 1-day Value at Risk (VaR) taking into consideration the financial integration of Indian capital market (BSE-SENSEX and NSE-NIFTY) with other global indicators and its own volatility using daily returns covering the period January 2003 to December 2009. The paper specifies a generalized autoregressive conditional heteroscedasticity (GARCH) framework to model the phenomena of v...