On Mean and Covariance Estimation for Repeated Time Series Under Long Memory Errors

• Activity Number: 228
• Type: Contributed
• Date/Time: Monday, August 4, 2014 : 2:00 PM to 3:50 PM
• Sponsor: IMS
• Author(s): Jan Beran and Haiyan Liu*+
• Companies: University of Konstanz and University of Konstanz
• Keywords: functional data analysis ; time series ; nonparametric smoothing ; long-range dependence

Abstract

We consider estimation of trend and covariance functions in models of equidistant repeated time series typically encountered in functional data analysis (FDA), with the modification that the random curves are perturbed by error processes that exhibit short- or long-range dependence. Functional limit theorems are obtained for kernel estimators of trend and covariance functions. Since in FDA the mean function plays the role of a nuisance parameter we then focus on the covariance function only. Improved trend free estimators can be defined using a contrast transformation. Under suitable conditions, the same rate of convergence can be obtained as under i.i.d. assumptions. In general, the asymptotic bias term in the covariance estimate needs to be reduced by using higher order kernels. Numerical examples illustrate the results.