Nystr"om Regularization for Time Series Forecasting

This paper focuses on learning rate analysis of Nystr"om regularization with sequential sub-sampling for τ-mixing time series. Using a recently developed Banach-valued Bernstein inequality for τ-mixing sequences and an integral operator approach based on second-order decomposition, we succeed in deriving almost optimal learning rates of Nystr"om regularization with sequential sub-sampling for τ-mixing time series. A series of numerical experiments are carried out to verify our theoretical results, showing the excellent learning performance of Nystr"om regularization with sequential sub-sampling in learning massive time series data. All these results extend the applicable range of Nystr"om regularization from i.i.d. samples to non-i.i.d. sequences.