A Long Memory Model with Mixed Normal GARCH for US Inflation Data

We introduce a time series model that captures both long memory and conditional heteroskedasticity and assess their ability to describe the US inflation data. Specifically, the model allows for long memory in the conditional mean formulation and uses a normal mixture GARCH process to characterize conditional heteroskedasticity. We find that the proposed model yields a good description of the salient features, including skewness and heteroskedasticity, of the US inflation data. Further, the performance of the proposed model compares quite favorably with, for example, ARMA and ARFIMA models with GARCH errors characterized by normal, symmetric and skewed Student-t distributions.