Aggregation of Seasonal Long-Memory Processes

Abstract

To understand the impact of temporal aggregation on the properties of a seasonal long-memory process, the e¤ects of skip and cumulation sampling on both stationary and nonstationary processes with poles at several potential frequencies are analyzed. By allowing for several poles in the disaggregated process, their interaction in the aggregated series is investigated. Further, by de…ning the process according to the truncated Type II de…nition, the proposed approach encompasses both stationary and nonstationary processes without requiring prior knowledge of the case. The frequencies in the aggregated series to which the poles in the disaggregated series are mapped can be directly deduced. Speci…cally, unlike cumulation sampling, skip sampling can impact on non-seasonal memory properties. Moreover, with cumulation sampling, seasonal long-memory can vanish in some cases. Using simulations, the mapping of the frequencies implied by temporal aggregation is illustrated and the estimation of the memory at the di¤erent frequencies is analyzed.

Asymptotic normality of simultaneous estimators of cyclic long-memory processes

“…Time series with cyclic long-memory behaviours attracted increasing attention in recent years, see [2,3,4,5,15] and the references therein. It was due to importance of such time series in finance, hydrology, cosmology, internet modelling, and other applications to data with non-seasonal cyclicities, see [3,4,6,13,18,32].…”