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Harmonically Weighted Processes

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  • Uwe Hassler
  • Mehdi Hosseinkouchack

Abstract

We discuss a model for long memory and persistence in time series that amounts to harmonically weighting short memory processes, ∑jxt−j/(j+1). A non‐standard rate of convergence is required to establish a Gaussian functional central limit theorem. Theoretically, the harmonically weighted (HW) process displays less persistence and weaker memory than the classical competitor, fractional integration (FI) of order d. Still, we establish that a test rejects the null hypothesis of d = 0 if the process is HW. Similarly, a bias approximation shows that estimators of d will fail to distinguish between HW and FI given realistic sample sizes. The difficulties to disentangle HW and FI are illustrated experimentally and with USA inflation data.

Suggested Citation

  • Uwe Hassler & Mehdi Hosseinkouchack, 2020. "Harmonically Weighted Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 41(1), pages 41-66, January.
    • Handle: RePEc:bla:jtsera:v:41:y:2020:i:1:p:41-66
    DOI: 10.1111/jtsa.12475
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    Cited by:

    1. Federico Maddanu, 2022. "A harmonically weighted filter for cyclical long memory processes," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 106(1), pages 49-78, March.
    2. Federico Maddanu, 2023. "Forecasting highly persistent time series with bounded spectrum processes," Statistical Papers, Springer, vol. 64(1), pages 285-319, February.
    3. Carlos D. Ramirez, 2024. "The effect of economic policy uncertainty under fractional integration," Portuguese Economic Journal, Springer;Instituto Superior de Economia e Gestao, vol. 23(1), pages 89-110, January.
    4. Hassler, Uwe & Hosseinkouchack, Mehdi, 2020. "Estimating the mean under strong persistence," Economics Letters, Elsevier, vol. 188(C).

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