Nonfractional Long-Range Dependence: Long Memory, Antipersistence, and Aggregation

Abstract

This paper used cross-sectional aggregation as the inspiration for a model with long-range dependence that arises in actual data. One of the advantages of our model is that it is less brittle than fractionally integrated processes. In particular, we showed that the antipersistent phenomenon is not present for the cross-sectionally aggregated process. We proved that this has implications for estimators of long-range dependence in the frequency domain, which will be misspecified for nonfractional long-range-dependent processes with negative degrees of persistence. As an application, we showed how we can approximate a fractionally differenced process using theoretically-motivated cross-sectional aggregated long-range-dependent processes. An example with temperature data showed that our framework provides a better fit to the data than the fractional difference operator.

Credit-to-GDP ratios – non-linear trends and persistence: evidence from 44 OECD economies

“…2. In the I(d) framework, mean reversion takes place when the differencing parameter d is smaller than 1, while lack of it occurs if d ≥ 1 (Vera-Valdes, 2021). …”

On long memory origins and forecast horizons

“…LongMemory.jl uses multiple dispatch, a novel feature of Julia, to provide a unified interface to generate long memory by cross-sectional aggregation using a finite number of autoregressive processes and the asymptotic version using the fast algorithm proposed by Vera-Valdés (2021a). The finite version of the algorithm is used if a finite number of autoregressive processes is provided.…”