Applying wavelet analysis in the seasonal adjustment

X-12-ARIMA is a seasonal adjustment method based on different moving averages. Using these moving averages makes it robust, but on the other hand, distorts various components of a time series to some extent, which is its side effect. The frequencies of various components of a time series are different; multi resolution analysis (MRA) of the wavelet analysis may decompose a time series into different components according to the difference of the frequency. The paper tries to integrate the wavelet analysis into X-12-ARIMA to adjust the seasonality. Since the trend-cycle component is the lowest frequency band of a time series, the paper uses the approximation component of MRA decomposition as the estimate of the trend-cycle factor; it may reduce using moving averages. Examples of adjustments from X-12-ARIMA/MRA and X-12-ARIMA are shown.