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.

中文翻译：

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平滑过渡移动平均模型：估计、测试和计算

本文介绍了非线性移动平均模型的一个新子类，称为平滑过渡移动平均 (STMA) 模型，并研究了其概率特性。结果表明，在一些温和的条件下，最小二乘估计（LSE）具有强一致性和渐近正态性。提出了 STMA 模型的强大的基于分数的拟合优度检验。应用与经典参数化不同的参数化来在数值上改进该模型的识别和估计。进行模拟研究是为了评估 LSE 的性能和有限样本中基于分数的测试。结果通过美元兑英镑的每周汇率的应用来说明。