A note on Chambers's "long memory and aggregation in macroeconomic time series"

Chambers (1998) explores the interaction between long memory and aggregation. For continuous-time processes, he takes the aliasing effect into account when studying temporal aggregation. For discrete-time processes, however, he seems to fail to do so. This note gives the spectral density function of temporally aggregated long memory discrete-time processes in light of the aliasing effect. The results are different from those in Chambers (1998) and are supported by a small simulation exercise. As a result, the order of aggregation may not be invariant to temporal aggregation, specifically if d is negative and the aggregation is of the stock type.

The aliasing effect, the Fejer Kernel and temporally aggregated long memory processes

This paper derives the spectral density function of aggregated long memory processes in light of the aliasing effect. The results are different from previous analyses in the literature and a small simulation exercise provides evidence in our favour. The main result point to that flow aggregates from long memory processes shall be less biased than stock ones, although both retain the degree of long memory. This result is illustrated with the daily US Dollar/ French Franc exchange rate series.

Spectral properties of temporally aggregated long memory processes

This paper derives the spectral density function of aggregated long memory processes in light of the aliasing effect. The results are different from previous analyses in the literature and a small simulation exercise provides evidence in our favour. The main result point to that flow aggregates from long memory processes shall be less biased than stock ones, although both retain the degree of long memory. This result is illustrated with the daily US Dollar/ French Franc exchange rate series.