Theory and Algorithms for Forecasting Time Series
This work addresses forecasting challenges in complex, non-stationary time series, which is incremental as it builds on existing theory with new bounds and algorithms.
The paper tackles the problem of forecasting non-stationary, non-mixing time series by developing data-dependent learning bounds based on sequential complexity and a new discrepancy measure, and reports preliminary experimental results for new algorithms derived from these bounds.
We present data-dependent learning bounds for the general scenario of non-stationary non-mixing stochastic processes. Our learning guarantees are expressed in terms of a data-dependent measure of sequential complexity and a discrepancy measure that can be estimated from data under some mild assumptions. We also also provide novel analysis of stable time series forecasting algorithm using this new notion of discrepancy that we introduce. We use our learning bounds to devise new algorithms for non-stationary time series forecasting for which we report some preliminary experimental results.