Statistics Seminar: Peter Robinson -- Long-Range Dependent Curve Time Series

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.