Functional Time-Series Prediction and Applications

• Activity Number: 639
• Type: Invited
• Date/Time: Thursday, August 2, 2012 : 10:30 AM to 12:20 PM
• Sponsor: IMS
• Author(s): Anestis Antoniadis*+
• Companies: University Joseph Fourier
• Keywords: Wavelets ; Time series prediction ; nonparametric regression ; functional data ; functional clustering

Abstract

We consider the prediction problem of a continuous time series on a whole time interval in terms of its past.? Such problems arise when a long record of a continuous time series can be naturally split into segments of equal length. Each individual segment can then be treated as a different, functional, realization, and methods of functional data analysis can then be used to perform different kinds of tasks. To predict such stochastic processes on an entire time-interval, we adopt an approach based on functional kernel nonparametric regression estimation techniques. To achieve some kind of stationarity that is necessary for efficient prediction, clustering groups of similar segments are considered, the reasoning being that segments within clusters will exhibit less non-stationary behaviors and hence, provide more powerful forecasting as a result. A common technique used within the talk, is to convert the segments into a multivariate dataset using a wavelet transform. The proposed methodology is illustrated via an application of short-term electrical demand forecasting. These results are derived from a long standing collaborative work.