Modeling Sequences of Long Memory Positive Weakly Stationary Random Variables

In this paper we introduce a new class of covariance stationary long-memory models on the positive half-line. The overall structure of the models is related to that of GARCH processes of Engle (1982) and Bollerslev (1986), whereby sequence of random variables of interest have multiplicative shocks structure. Unlike FIGARCH model of Baillie, Bollerslev and Mikkelsen (1996), our models are weakly stationary with non-summable autocovariances and hence belong to the class of long-memory models according to the criteria of McLeod and Hipel (1978). In addition, we are able to ensure positivity of all underlying components of the model, thereby improving on the results of Giraitis, Robinson, and Surgailis (2000). Apart from volatility modeling, the class of models introduced in this paper will find applications in high-frequency financial data econometrics.