The asymmetric power ARCH model is a recent addition to time series models that may be used for predicting volatility. Its performance is compared with that of standard models of conditional heteroskedasticity such as GARCH. This has previously been done empirically. In this paper the same issue...

We consider a family of GARCH(1,1) processes introduced in He and Teräsvirta (1999a). This family contains various popular GARCH models as special cases. A necessary and sufficient condition for the existence of a strictly stationary solution is given.

This paper is concerned with efficient GMM estimation and inference in GARCH models. Sufficient conditions for the estimator to be consistent and asymptotically normal are established for the GARCH(1,1) conditional variance process. In addition efficiency results are obtained in the general...

Properties of three well-known and frequently applied first-order models for modelling and forecasting volatility in financial series such as stock and exchange rate returns are considered. These are the standard Generalized Autoregressive Conditional Heteroskedasticity (GARCH), the Exponential...

This paper contains a survey of univariate models of conditional heteroskedasticity. The classical ARCH model is mentioned, and various extensions of the standard GARCH model are highlighted. This includes the Exponential GARCH model. Stochastic volatility models remain outside this review.

This paper investigates the presence of asymmetric GARCH effects in a number of equity return series, and compare the modeling performance of seven different conditional variance models, within the parametric GARCH class of models. The data consists of daily returns for 45 Nordic stocks, during...

In this paper the autocorrelation structure of the Exponential GARCH(p,q) process of Nelson (1991) is considered. Conditions for the existence of any arbitrary unconditional moment are given. Furthermore, the expressions for the kurtosis and the autocorrelations of squared observations are...

This paper examines the effect of using Black and Scholes formula for pricing and hedging options in a discrete time heteroskedastic environment. This is done by a simulation procedure where asset returns are generated from a GARCH (1,1)-t model. In the simulation a hypothetical trader writes an...

In the classical ARCH model of Engle [1982] the conditional variance is a linear function of lagged squared residuals. In this paper I introduce nonlinearity, by adding a term that consists of a constant parameter multiplied by a transition function. Two different transition functions are...

In this paper I present two new Lagrange multiplier test statistics designed for testing the null of GARCH (1,1), against the alternative of asymmetric GARCH. For one test the alternative is the generalized QARCH (1,1) model of Sentana [1995], and for the other the alternative is the logistic...