Fitting of self-exciting threshold autoregressive moving average nonlinear time-series model through genetic algorithm and development of out-of-sample forecasts

Abstract

Self-exciting threshold autoregressive moving average (SETARMA) nonlinear time-series model is considered here. Sufficient conditions for invertibility and stationarity are derived. Parameter estimation algorithm is developed by employing real-coded genetic algorithm stochastic optimization procedure. A significant feature of the work done is that optimal out-of-sample forecasts up to three-step ahead and their forecast error variances are derived analytically. Relevant computer programs are written in statistical analysis system (SAS) and C. As an illustration, annual mackerel catch time-series data are considered. Forecast performance of the fitted model for hold-out data is evaluated by using Naive and Monte Carlo approaches. It is found that optimal out-of-sample forecast values are quite close to actual values and estimated variances are quite close to theoretical values. Superiority of the SETARMA model over the SETAR model for equal predictive ability through Diebold–Mariano test is also established.

Keywords:

• SETARMA nonlinear time-series model
• real-coded genetic algorithm
• mackerel catch data
• mean square forecasting error
• optimal out-of-sample forecast

2010 Mathematics Subject Classification::

• 37M10

View correction statement:

Corrigendum

Acknowledgements

The authors are grateful to the referee for valuable comments. Doctors Himadri Ghosh and Prajneshu thank the Department of Science and Technology, New Delhi, India, for providing financial assistance during the course of this research work.