Climate data often provides a periodically stationary time series, due to seasonal variations in the mean and covariance structure. Periodic ARMA models, where the parameters vary with the season, capture the nonstationary behavior. High frequency data collected weekly or daily results in a large number of model parameters. In this paper, we apply discrete Fourier transforms to the parameter vectors, and develop a test for the statistically significant harmonics. An example of daily high temperatures illustrates the method, whereby a periodic autoregressive model with 1095 parameters is reduced to a parsimonious 12 parameter version without any apparent loss of fidelity.

中文翻译：

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高频气候数据的简约时间序列建模

由于均值和协方差结构的季节性变化，气候数据通常提供周期性平稳的时间序列。参数随季节变化的周期性 ARMA 模型捕捉非平稳行为。每周或每天收集的高频数据会产生大量模型参数。在本文中，我们将离散傅立叶变换应用于参数向量，并开发了对具有统计意义的谐波的测试。每日高温的示例说明了该方法，其中具有 1095 个参数的周期性自回归模型被简化为简约的 12 个参数版本，而没有任何明显的保真度损失。