以均方誤差為準則比較X-12-ARIMA和以模型基礎推導的季節調整濾器

AMean Squared Error Criterion for Comparing X-12-ARIMA and Model-Based Seasonal Adjustment Filters

許多文獻如Cleveland and Tiao （1976）， Burridge and Wallis （1984），和Depoutot and Planas （1998） 已比較X-11 和以模型基礎推導的季節調整濾器的權數函數， 本文則建議另一個以計算均方誤差為準則的比較方法。對於一個ARIMA 模型所產生的時間數列， 本文分別計算以X12-ARIMA 估算的季節成分， 及以模型為基礎所估算最適的季節成分， 並比較兩者的均方誤差。以挑選較低均方誤差為圭臬， 本文的方法提供了如何選擇最佳X-12 季節調整濾器的準則， 以及尚可改進的幅度。當以航空公司月資料模型做模擬實驗，我們發現如果估計標準季節成分，選擇最佳X-12 季節調整濾器只會造成些許均方誤差值的增加； 但如果是在白噪音為均一先驗分配假設下估計季節成分， 最佳X-12 季節調整濾器會造成均方誤差值大幅的增加， 所以並不是一個好的選擇。模擬實驗分析發現X-12-ARIMA程式經常會選擇較短的季節調整濾器。

Various authors – Cleveland and Tiao (1976), Burridge and Wallis (1984), and Depoutot and Planas (1998) – have compared weight functions from X-11 versusmodel-based seasonal adjustment filters. We suggest a different approach to comparing filters by computing the mean squared error (MSE) when using an X-12-ARIMA filter for estimating the underlying seasonal component from an ARIMA model-based decomposition, and comparing this to the MSE of the optimal model-based estimator. This provides a criterion for choosing an X-12 filter for a given series (model the series and pick the X-12 filter with lowest MSE), and also provides results on how much MSE increases when using an X-12 filter rather than the optimal model-based filter. Calculations for monthly time series following the airlinemodel with various parameter values showgenerally small increases in MSE for estimating the canonical seasonal component by using the best X-12 filter instead of the optimal model-based filter. The results are much less favorable to the X-12 filters with a uniform prior distribution on the white noise allocation in the seasonal model decomposition. Examinations of simulated series showthat, for the canonical decomposition, automatic filter choices of the X-12-ARIMA program sometimes use shorter seasonal moving averages than are desirable.