报告人：Degui Li, University of York
题目：Title: Long-Range Dependent Curve Time Series
摘要: We introduce methods and theory for functional time series with long-range dependence. The temporal sum of the curve process is shown to be asymptotically normally distributed. We show that the conditions for this cover 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 more general, semiparametric context, we propose an estimate of the memory parameter, and derive its consistency result. 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 age-specific fertility rates across some developed countries. This is a joint work with P. M. Robinson (LSE) and H. Shang (ANU).