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Mathematical Problems in Engineering
Volume 2014 (2014), Article ID 572173, 9 pages
Research Article

Autoregressive Prediction with Rolling Mechanism for Time Series Forecasting with Small Sample Size

Research Center of Small Sample Technology, School of Aeronautical Science and Engineering, Beihang University, Beijing 100191, China

Received 20 February 2014; Revised 28 April 2014; Accepted 30 April 2014; Published 9 June 2014

Academic Editor: M. I. Herreros

Copyright © 2014 Zhihua Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Reasonable prediction makes significant practical sense to stochastic and unstable time series analysis with small or limited sample size. Motivated by the rolling idea in grey theory and the practical relevance of very short-term forecasting or 1-step-ahead prediction, a novel autoregressive (AR) prediction approach with rolling mechanism is proposed. In the modeling procedure, a new developed AR equation, which can be used to model nonstationary time series, is constructed in each prediction step. Meanwhile, the data window, for the next step ahead forecasting, rolls on by adding the most recent derived prediction result while deleting the first value of the former used sample data set. This rolling mechanism is an efficient technique for its advantages of improved forecasting accuracy, applicability in the case of limited and unstable data situations, and requirement of little computational effort. The general performance, influence of sample size, nonlinearity dynamic mechanism, and significance of the observed trends, as well as innovation variance, are illustrated and verified with Monte Carlo simulations. The proposed methodology is then applied to several practical data sets, including multiple building settlement sequences and two economic series.