Not all long-memory estimators are born equal: The case of nonstationary functional time series

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Abstract

We study a functional version of fractionally integrated time series that covers the nonstationary case when the memory parameter d is above 0.5. We project time series, with varying levels of nonstationarity, onto a finite-dimensional subspace. We obtain the eigenvalues and eigenfunctions that span a sample version of the dominant subspace through dynamic functional principal component analysis of the sample long-run covariance functions. Within the context of functional autoregressive fractionally integrated moving average models, we evaluate and compare finite-sample bias and mean-squared error among some time- and frequency-domain Hurst exponent estimators via Monte Carlo simulations. We apply the estimators to Canadian female and male life-table death counts.

Original languageEnglish
Number of pages24
JournalCanadian Journal of Statistics
Early online date14 Aug 2021
DOIs
Publication statusE-pub ahead of print - 14 Aug 2021

Keywords

  • Dynamic functional principal component analysis
  • functional autoregressive fractionally integrated moving average
  • long-range dependence
  • long-run covariance
  • nonstationary curve process

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