Periodic autoregressive moving average (PARMA) models are indicated for time series whose mean, variance, and covariance function vary with the season. In this paper, we develop and implement forecasting procedures for PARMA models. Forecasts are developed using the innovations algorithm, along with an idea of Ansley. A formula for the asymptotic error variance is provided, so that Gaussian prediction intervals can be computed. Finally, an application to monthly river flow forecasting is given, to illustrate the method.

中文翻译：

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周期性自回归移动平均模型的预测区间预测

周期自回归移动平均 (PARMA) 模型适用于均值、方差和协方差函数随季节变化的时间序列。在本文中，我们为 PARMA 模型开发和实施预测程序。预测是使用创新算法以及 Ansley 的想法开发的。提供了渐近误差方差的公式，以便可以计算高斯预测区间。最后，给出了在每月河流流量预测中的应用，以说明该方法。