Abstract: We consider the application of the limiting aggregate model derived by Tsai and Chan (2005d) for modeling aggregated long-memory data. The model is characterized by the fractional integration order of the original process and may be useful for (i) modeling discrete-time data with sufficiently long sampling intervals, for example, annual data, and/or (ii) studying the fractional integration order of the original process. The fractional integration parameter is estimated by maximizing the Whittle likelihood. It is shown that the quasi-maximum likelihood estimator is asymptotically normal, and its finite-sample properties are studied through simulation. The efficacy of the proposed approach is demonstrated with three data analyses.
Key words and phrases: ARFIMA models, asymptotic normality, temporal aggregation, Whittle likelihood.