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Title: An autocovariance-based framework for curve time series Authors:  Cheng Chen - London School of Economics (United Kingdom) [presenting]
Xinghao Qiao - London School of Economics (United Kingdom)
Abstract: It is commonly assumed in functional data analysis (FDA) that samples of each functional variable are independent realizations of an underlying stochastic process, and are observed over a grid of points contaminated by i.i.d. measurement errors. In practice, however, the temporal dependence across curve observations may exist and the parametric assumption on the error covariance structure could be unrealistic. We consider the model setting for serially dependent curve observations, when the contamination by errors is genuinely functional with a fully nonparametric covariance structure. The classical covariance-based methods in the FDA are not applicable here due to the contamination that can result in substantial estimation bias. We propose an autocovariance-based framework to address error-contaminated curve time series problems. Under the proposed framework, we discuss several important problems in FDA, e.g. dimension reduction, functional linear regression, singular component analysis and high dimensional applications.