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Title: Long-range dependent curve time series Authors:  Degui Li - University of York (United Kingdom) [presenting]
Peter Robinson - London School of Economics (United Kingdom)
Han Lin Shang - Australian National University (Australia)
Abstract: Methods and theory for functional time series with long-range dependence are introduced. 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.