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过度差分与季节模型等价性：⊖=1 时的月度均值与季节 ARIMA 模型AI 解读

Two general models for monthly seasonal time series are considered, one in which seasonality is modeled with monthly means and another in which seasonality is modeled with a (0, 1, 1)12 ARIMA structure. The models are shown to be equivalent if the seasonal moving average parameter (⊖) is 1 and if the same assumptions about the 12 initial observations are made for both models. The role of the assumptions about the initial observations is analyzed, and it is argued that for…

非平稳时间序列的信号提取AI 解读

The nonstationary signal extraction problem is to estimate $s_t$ given observations on $z_t = s_t + n_t$ (signal plus noise) when either $s_t$ or $n_t$ or both is nonstationary. Homogeneous or explosive nonstationary time series described by models of the form $\delta(B)z_t = w_t$ where $\delta(B)$ has zeroes on or inside the unit circle and $w_t$ is stationary are considered. For certain cases, approximate solutions to the nonstationary signal extraction problem have been…