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

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Abstract

This paper develops a theoretically-based framework to analyse long-range dependence in time series data. We use cross-sectional aggregation as inspiration for a model with long-range dependence that arises in actual data. We argue that one of the reasons behind the appeal of the fractional difference operator is the existence of efficient algorithms for simulation and estimation. Thus, this paper develops efficient algorithms to generate long-range dependent processes by cross-sectional aggregation. Moreover, we show that the antipersistent phenomenon is not present for cross-sectionally aggregated processes. We prove that this has implications for estimators of long-range dependence in the frequency domain, which will be misspecified for cross-sectionally aggregated processes with negative degrees of persistence. Hence, we develop the maximum likelihood estimator for long-range dependent series generated by cross-sectional aggregation. As an application, we show how we can approximate a fractionally diffeerenced process using theoretically-based long-range dependent processes.
Original languageEnglish
Publication statusSubmitted - 20 Jun 2020

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