Type: Seminar

Distribution: World

Expiry: 9 Mar 2019

Auth: shelton(.ststaff;3022.3001)@p819.pc.maths.usyd.edu.au

We introduce methods and theory for functional or curve time series with long range dependence. The temporal sum of the curve process is shown to be asymptotically normally distributed, the conditions for this covering a functional version of fractionally integrated autoregressive moving averages. We also construct an estimate of the long-run covariance function, which we use, via functional principal component analysis, in estimating the orthonormal functions spanning the dominant sub-space of the curves. In a semiparametric context, we propose an estimate of the memory parameter and establish its consistency. A Monte-Carlo study of finite sample performance is included, along with two empirical applications. The first of these finds a degree of stability and persistence in intra-day stock returns. The second finds similarity in the extent of long memory in incremental age-specific fertility rates across some developed nations. *joint work with Degui Li and Han Lin Shang.