Online modeling of real-world time series through evolving AR models

There is a growing demand to model and predict real-world time series such as natural or financial time series. In this paper, we propose an online modeling approach for real-world time-series through evolving Auto Regressive (eAR) models. At first, it is supposed that a real-world time series can be modeled as a summation of some basic signals. Then, it is shown adaptive AR models which can evolve in the number of lags are suitable models to generate such time series. To evolve an adaptive AR model, it switches to a pre-learned adaptive AR model which has a lag less or more than main model. The capability of the proposed eAR model in detection proper number of lags and prediction is shown through an illustrative example and a real - world application to the prediction of monthly time series of U.S. coal consumption.