Smooth transition moving average models: Estimation, testing, and computation

The article introduces a new subclass of nonlinear moving average model, called the smooth transition moving average (STMA) model, and studies its probabilistic properties. It is shown that, under some mild conditions, the least squares estimation (LSE) is strongly consistent and asymptotically normal. A powerful score-based goodness-of-fit test for the STMA model is presented. A different parametrization from the classical one is applied to numerically improve the identification and estimation of this model. Simulation studies are conducted to assess the performance of the LSE and the score-based test in finite samples. The results are illustrated with an application to the weekly exchange rate of the USA Dollar to the British Pound.

Automated summary

This article introduces a new subclass of nonlinear moving average model, called the smooth transition moving average (STMA) model, and investigates its probabilistic properties. It demonstrates that, under certain conditions, the least squares estimation (LSE) is strongly consistent and asymptotically normal. Additionally, a score-based goodness-of-fit test for the STMA model is proposed. The study applies a different parametrization to numerically enhance the identification and estimation of the model. Simulation studies are conducted to evaluate the performance of LSE and the score-based test in finite samples, with an application to the weekly exchange rate of USD to GBP illustrating the results.