A note on moving-average models with feedback


Dong Li, Department of Statistics and Actuarial Science, The University of Iowa, Iowa City, IA 52242, USA


This note generalizes the results in Li et al. (2012) to threshold moving-average (TMA) models with more than two regimes. Under some mild conditions, it is shown that multiple-regime TMA models are always strictly stationary and ergodic without any restriction on the coefficients. This is very different from threshold AR models. An explicit/closed form of the solution to the multiple-regime TMA model is derived as well. A three-regime TMA model is illustrated with an application to monthly data of the exchange rate of the Japanese yen against the USA dollar from January 1971 to December 2000.