Fitting EXPAR Models Through the Extended Kalman Filter

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• 作者：Himadri Ghosh ; Bishal Gurung ; Prajneshu Gupta
• 关键词：Exponential autoregressive model ; extended Kalman filter ; forecast performance ; landings data ; out ; of ; sample forecast. ; Primary 62M10 ; Secondary 62M20.
• 刊名：Sankhya B
• 出版年：2015
• 出版时间：May 2015
• 年：2015
• 卷：77
• 期：1
• 页码：27-44
• 全文大小：361 KB
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• 作者单位：Himadri Ghosh (1)
  Bishal Gurung (1)
  Prajneshu Gupta (1)
  
  1. Indian Agricultural Statistics, Research Institute, New Delhi, 110012, India
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Statistics
  Statistical Theory and Methods
  Statistics Computing and Software
  
• 出版者：Springer India
• ISSN：0976-8394

文摘

Exponential autoregressive (EXPAR) family of parametric nonlinear time-series models, which is a discrete-time approximation of continuous-time nonlinear stochastic dynamical system, is considered. A heartening feature of this model is that it is capable of describing those data sets that depict cyclical variations. The estimation procedure for EXPAR models is developed using extended Kalman filter (EKF). Through simulation studies, it is shown that EKF is very efficient for fitting EXPAR models. Formulae for optimal one-step and two-step ahead out-of-sample forecasts are derived analytically by recursive use of conditional expectation. Conditions for the existence of limit cycle behaviour for EXPAR models are also established. Superiority of EKF method vis-a-vis Genetic algorithms (GA) method for fitting EXPAR models is shown through simulation studies. As an illustration, EXPAR models are employed for modelling and forecasting Oil sardine, Mackerel and Bombay duck time-series landings data in India. It is shown that all the three fitted models exhibit the desirable feature of existence of limit cycle behaviour. It is concluded that the EXPAR model performs better than ARIMA methodology for both modelling and forecasting purposes for the data sets under consideration.