A Note on Overdifferencing and the Equivalence of Seasonal Time Series Models With Monthly Means and Models With (0, 1, 1)12Seasonal Parts When ⊖ = 1
证明，当季节移动平均参数⊖=1且对初始观测值做相同假设时，含月度均值的季节模型与含(0,1,1)12结构的ARIMA模型等价，并讨论了初始观测值假设的作用。
Abstract 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 practical purposes the two models can be regarded as equivalent when ⊖ = 1. It is observed that the result extends easily to more general models involving overdifferencing. KEY WORDS: Seasonal ARIMA modelStarting values