Invertibility of non-linear time series models

Abstract

Sufficient conditions for invertibility of non-linear time series models are available in the literature only for a few special cases. In this paper a practical and general method for checking invertibility is presented. Briefly stated, it consists of feeding independent and identically distributed innovations into the non-linear model and then observing whether the model blows up or not. Using this idea invertibility conditions are derived for several recently proposed non-linear moving average models. Finally, the method is applied to a number of bilinear models fitted to economic time series.

Keywords:

• Additive smooth transition moving average model
• asymmetric moving average model
• bilinear model
• self-exciting threshold moving average model
• forecasting