Uwe Hassler (Goethe University Frankfurt)

We discuss a model for long memory and persistence in time series that amounts to harmonically weighting short memory processes. A nonstandard 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 U.S. inflation data.

VIEW PAPER