Order Selection for General Expression of Nonlinear Autoregressive Model Based on Multivariate Stepwise Regression

Abstract

Abstract. An order selection method based on multiple stepwise regressions is proposed for General Expression of Nonlinear Autoregressive model which converts the model order problem into the variable selection of multiple linear regression equation. The partial autocorrelation function is adopted to define the linear term in GNAR model. The result is set as the initial model, and then the nonlinear terms are introduced gradually. Statistics are chosen to study the improvements of both the new introduced and originally existed variables for the model characteristics, which are adopted to determine the model variables to retain or eliminate. So the optimal model is obtained through data fitting effect measurement or significance test. The simulation and classic time-series data experiment results show that the method proposed is simple, reliable and can be applied to practical engineering. IntroductionTime series analysis technology is a kind of system identification method which can establish models based on the inherent law of data with no need for system inputs, so it has important applications in natural and social science field of industrial process control, economy and biomedical engineering, etc.[1]- [5]. Determining model's order plays a very important role in time series analysis process. Insufficient order of the model tends to the losing of valuable information to decrease model's tracking and prediction ability of data sequence. Meanwhile, excessive order makes a complex model and huge computing quantity. At present, order determination for the linear models based on the stationary assumptions have many research and lots of classic criterions are applied in engineering such as AIC criterion, residual test, minimization of residual sum of squares or final prediction error and other information criterions[6] [7]. But for nonlinear systems, due to their multifarious characteristics, there are no universal order determinations or goodness judgment strategies. The General Expression of Nonlinear Autoregressive (GNAR) model is a novel time-series model, which can be applied to system identification, data tracking and system prediction, etc.[8] [9]. In this paper, an order selection method based on multiple stepwise regressions is proposed for GNAR model which converts the model order selection into variable selection for multiple linear regression equation. Firstly, the partial autocorrelation function is adopted to define the linear term in GNAR model. And the linear result is set as the initial model, and then the nonlinear terms are added gradually. Statistics are chosen to study all the variables and their improvements are adopted to determine the model variables to retain or eliminate. Finally, the optimal model is obtained through data fitting effect measurement or significance test.