For a GJR-GARCH(1, 1) specification with generic innovation distribution we derive analytic expressions for the first four conditional moments of forward and aggregated returns variances. Moments most commonly used GARCH models are stated as special cases. We also limits these time horizon increases, establishing regularity conditions to converge normal moments. A simulation study using produce...

The financial market is the core of national economic development, and stocks play an important role in market. Analyzing stock prices has become focus investors, analysts, people related fields. This paper evaluates volatility Apple Inc. (AAPL) returns using five generalized autoregressive conditional heteroskedasticity (GARCH) models: sGARCH with constant mean, GARCH sstd, GJR-GARCH, AR(1) GJ...

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...

We propose a new approach to density forecast optimisation and apply it to Value-at-Risk estimation. All existing density forecasting models try to optimise the distribution of the returns based solely on the predicted density at the observation. In this paper we argue that probabilistic predictions should be optimised on more than just this accuracy score and suggest that the statistical consi...

In the class of univariate conditional volatility models, the three most popular are the generalized autoregressive conditional heteroskedasticity (GARCH) model of Engle (1982) and Bollerslev (1986), the GJR (or threshold GARCH) model of Glosten, Jagannathan and Runkle (1992), and the exponential GARCH (or EGARCH) model of Nelson (1990, 1991). For purposes of deriving the mathematical regularit...

This paper deals with finding stationarity Condition of GJR-GARCH(Q,P) model by using a local linearization technique in order to reduce this non-linear linear difference equation constant coefficients and then obtain the condition via characteristic equation.
 Finally we apply obtained conditions real data that represents monthly Brent Crude oil prices at closing dollars for period (JUN. ...

In this paper, we estimate GARCH, EGARCH, and GJR-GARCH models assuming normal and heavy-tailed distribution (i.e., GED). Results suggest that when the heavy-tailed distribution is considered, the persistence has found to be reduced in all the cases. Findings also reveal that positive shocks are more common than the negative shocks in this market.

Gold investment is considered safer and has less risk than other types of investment. One the important knowledge in investing gold predicting price future through modeling past. The purpose this study to model past so that it can be used predict prices future. world data a time series heteroscedasticity properties, solve problem GARCH. This an asymmetric effect, GARCH used, namely Glosten-Jaga...

In this paper, we consider a general family of asymmetric volatility models with stationary and ergodic coefficients. This family can nest several non-linear asymmetric GARCH models with stochastic parameters into its ambit. It also generalizes Markovswitching GARCH and GJR models. The geometric ergodicity of the proposed process is established. Sufficient conditions for stationarity and existe...

the direct limit taken over all finite Galois extensions K of k in which the integral closure Y of X is unramified over X, where GKJk denotes the Galois group of such an extension, and where GY denotes the group of points of G with coordinates in Y. For example, if X=k, our notation coincides with that of [10]. For any X, the group H(X,C) is the r-th cohomology group of the profinite group Gjr=...