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Keywords:

  • Ergodicity;
  • feedback;
  • multiple-regime TMA models;
  • piecewise linear process;
  • strict stationarity
  • C51;
  • C62

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.