关键词: 季节调整, X-13ARIMA-SEATS, 频域分析, 诊断

Abstract: This paper studies the symmetric filter and the concurrent filter of the X-13ARIMA-SEATS seasonal adjustment program in the frequency domain and analyzes the influence of non-seasonal and seasonal moving average parameters and filter length on the square gain function and phase delay function. Having diagnosis on the purchase managers' index (PMI) and consumer price index (CPI) seasonal sequences as an example, this paper tries to find out an optimal method for seasonal adjustment by comparing the X-11 and AMB methods based on the square gain function and the phase delay function in the frequency domain. It is found that: 1) when the non-seasonal moving average parameter increases, the square gain function of the two filters tends to decrease. When the seasonal moving average parameter increases, the square gain function has an upward trend. The filter with shorter length shocks more violently, and its trough of the seasonal frequency is wider; 2) when the seasonal moving average parameter increases, the phase delay function shocks more violently. When the non-seasonal moving average parameter increases, the phase delay of the seasonal frequency is larger. There is a negative relationship between the phase delay function and the square gain function in the single non-seasonal frequency range. 3) the gain function of AMB method is more closed to 1 in the non-seasonal frequency range, compare to that of X-11 method. The groove of the AMB filter is narrower and its phase distortion of the frequency component is smaller. These imply that AMB method performs better in the PMI seasonal adjustment. Compared to AMB method, X-11 method has smaller square gain function of the symmetric filter, which tends obviously to 1 and its phase delay function on the non-frequency interval is smaller. So X-11 method is more suitable for the seasonal adjustment of the CPI; 4) compared with the traditional diagnosis on seasonal adjustment quality, the frequency domain diagnosis has advantages in estimating the stability of the seasonal components and the delay characteristics of the filter. In choosing seasonal adjustment methods, the above-mentioned conclusions can be compromised.

Key words: Seasonal Adjustment, X-13ARIMA-SEATS, Frequency Domain Analysis, Diagnosis