Abstract
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.
Highlights
Many planning activities require prediction of the behavior of variables, such as economic, financial, traffic, and physical ones [1, 2]
Since we focus on the rationality and validity of ARPRM approach in small sample forecasting problems, we consider conducting l = 5 step ahead prediction based on a observational data set with sample size n = 10
This study presents a novel approach to settle the small sample time series prediction problem in the presence of unstable
Summary
Many planning activities require prediction of the behavior of variables, such as economic, financial, traffic, and physical ones [1, 2]. Mass work on model structural change has been conducted [23, 24] To settle this problem, similar with the basic idea of K-nearest neighbor and local prediction approaches, many scholars have recommended using only recent data to increase future forecasting accuracy if chaotic data exist. Similar with the basic idea of K-nearest neighbor and local prediction approaches, many scholars have recommended using only recent data to increase future forecasting accuracy if chaotic data exist Based on this point of view, grey model GM(1,1) rolling model, called rolling check, was proposed by Wen [25]. Motivated by the GPRM approach and the practical relevance of very short-term forecasting or 1-step-ahead prediction elucidated above, the first objective of this study is to construct a novel prediction model with the rolling mechanism to improve the forecasting precision.
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