Harmonically Weighted Processes. (15th May 2019)

• Record Type: Journal Article
• Authors: Hassler, Uwe; Hosseinkouchack, Mehdi
• Is Part Of: Journal of time series analysis. Volume 41:Number 1(2020)
• Page Start: 41
• Page End: 66
• Publication Date: 2019-05-15
• Subjects: Long memory -- persistence -- fractional integration -- inflation; Time-series analysis -- Periodicals; 519.232
• DOI: 10.1111/jtsa.12475
• Languages: English
• ISSNs: 0143-9782

Abstract

Abstract : We discuss a model for long memory and persistence in time series that amounts to harmonically weighting short memory processes, ∑ j x t − 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.