We introduce a new concept in time series analysis: a Time-Threshold Decomposition (TTD) for time series, where (i) the time series gets decomposed in a wavelet basis, (ii) the wavelet coefficients get thresholded using all threshold values simultaneously. The TTD is defined as the resulting sequence of wavelet reconstructions, considered jointly as a function of time and threshold value. We discuss some probabilistic properties of this object, and apply it to time series classification.
Keywords: Wavelets; Thresholding; Time series; Classification
Biography: Piotr is with the Department of Statistics, London School of Economics. His research interests are in multiscale modelling and estimation, time series (especially nonstationary time series), sparse modelling and estimation, and the applications of statistics in finance and in neuroscience.