基于频域的X-13ARIMA-SEATS季节调整过滤器诊断

本文从频域角度对X-13ARIMA-SEATS季节调整程序的对称和并行过滤器进行研究，考察不同的模型非季节和季节移动平均参数和不同过滤器长度对平方增益函数和相位延迟函数的影响，并以中国采购经理人指数（PMI）和居民消费价格指数（CPI）季节序列诊断为例，从频域角度比较X-11和以ARIMA为基础的（AMB）方法的平方增益函数和相位延迟函数来选择更优的季节调整方法。得出的结论：①非季节移动平均参数增大时，两种过滤器平方增益函数有下降趋势，季节移动平均参数增大时，平方增益函数有上升趋势。长度较短的过滤器波动更剧烈，季节频率上波谷宽度更宽；②季节移动平均参数越大时，相位延迟函数震荡越剧烈,非季节移动平均参数越大时，季节频率上的相位延迟增大。单个非季节频率区间内相位延迟函数与平方增益函数有反向关系；③AMB方法在非季节频率区间上的增益函数比X-11方法更趋于1，过滤器的凹槽比X-11方法更窄，且频率分量的相位失真更小，在PMI季节调整中更好；X-11方法对称过滤器的平方增益函数更小且更趋于1，在非频率区间上的相位延迟函数比AMB方法更小，更适用CPI的季节调整。④与传统季节调整质量诊断相比，频域诊断在估计季节成分的稳定性和过滤器的延迟特性方面具有优势，在季节调整方法选择时可综合两方面的结论。

Seasonal Adjustment Filters of X-13ARIMA-SEATS Program Diagnosis Analysis Based on Frequency Domain

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.