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. ...

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...

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...

In recent decades, the momentum of global environmental protection has culminated in the Kyoto Agreement of 1998, placing the limelight on “green” issues. This paper argues that the protection of environmental systems involves a fragile balance between the costs of environment preservation and the profit motivations of industrialists. In particular, one of the issues that needs to be addressed ...

This paper is mainly talking about several volatility models and its ability to predict and capture the distinctive characteristics of conditional variance about the empirical financial data. In my paper, I choose basic GARCH model and two important models of the GARCH family which are E-GARCH model and GJR-GARCH model to estimate. At the same time, in order to acquire the forecasting performan...

A semiparametric extension of the GJR model (Glosten et al., 1993. Journal of Finance 48, 1779–1801) is proposed for the volatility of foreign exchange returns. Under reasonable assumptions, asymptotic normal distributions are established for the estimators of the model, corroborated by simulation results. When applied to the Deutsche Mark/US Dollar and the Deutsche Mark/British Pound daily ret...

In this papeT we study the performance of the GARCH model and two of its non-linear modifications to forecast weekly stock market volatility. The models are the Quadratic GARCH (Engle and Ng. 1993) and the Glosten. Jagannathan and Runkle (1992) models which have been proposed to describe, for example, the often observed negative skewness in stock market indices. We find that the QGARCH model is...

The univariate Generalised Autoregressive Conditional Heterscedasticity (GARCH) model has successfully captured the symmetric conditional volatility in a wide range of time series financial returns. Although multivariate effects across assets can be captured through modelling the conditional correlations, the univariate GARCH model has two important restrictions in that it: (1) does not accommo...

The paper develops two Dynamic Conditional Correlation (DCC) models, namely the Wishart DCC (WDCC) model and the Matrix-Exponential Conditional Correlation (MECC) model. The paper applies the WDCC approach to the exponential GARCH (EGARCH) and GJR models to propose asymmetric DCC models. We use the standardized multivariate t-distribution to accommodate heavy-tailed errors. The paper presents a...

The objective of this study is to investigate the predictability of model based forecasts and the VIX index on forecasting future volatility of S&P 500 index daily returns. The study period is from January 1990 to December 2010, including 5291 observations. A variety of time series models were estimated, including random walk model, GARCH (1,1), GJR(1,1) and EGARCH (1,1) models. The study resul...