A Long Memory Model with Normal Mixture GARCH

We present an exploratory analysis of a class of long memory models with a normal mixture generalized autoregressive conditional heteroskedasticity innovation process. Monte Carlo results are used to infer the performance of the maximum likelihood estimator. The estimation biases are associated with, amongst others, the mixing parameter, and these biases are usually insignificant. As an illustration, we fit the proposed model to four countries inflation data. It is found that the performance of the long memory model with normal mixture generalized autoregressive conditional heteroskedasticity is better than, say, both autoregressive moving average and long memory models with a standard generalized autoregressive conditional heteroskedasticity specification in terms of the flexibility to describe both the time-varying conditional skewness and kurtosis.