Asymmetric long memory GARCH: a reply to Hwang’s model

Periodic Long Memory GARCH models

A distinguishing feature of the intra-day time-varying volatility of financial time series is given by the presence of long-range dependence of periodic type due mainly to time-of-the-day phenomena. In this work we introduce a model able to describe the empirical evidence given by this periodic longmemory behaviour. The model, named PLM-GARCH (Periodic Long Memory GARCH), represents a natural e...

Long memory with Markov-Switching GARCH

A Smooth Transition GARCH Model with Asymmetric Transition Phases

This paper develops a smooth transition GARCH model with an asymmetric transition function, which allows for an asymmetric response of volatility to the size and sign of shocks, and an asymmetric transition dynamics for positive and negative shocks. We apply our model to the empirical financial data: the NASDAQ index and the individual stock IBM daily returns. The empirical evidence shows that ...

Asymmetric multivariate normal mixture GARCH

An asymmetric multivariate generalization of the recently proposed class of normal mixture GARCH models is developed. Issues of parametrization and estimation are discussed. Conditions for covariance stationarity and the existence of the fourth moment are derived, and expressions for the dynamic correlation structure of the process are provided. In an application to stock market returns, it is ...

Misspecification tests for periodic long memory GARCH models

Distributional theory for Quasi-Maximum Likelihood estimators in long memory conditional heteroskedastic models is not formally defined, even asympotically. Because of that, this paper analyses the performance of the Likelihood Ratio and the Lagrange Multiplier misspecification tests for Periodic Long Memory GARCH models. The real size and power of these tests are studied by means of Monte Carl...