Masking of volatility by seasonal adjustment methods

We report that the X-12 ARIMA and TRAMO-SEATS seasonal adjustment methods consistently underestimate the variability of the differenced seasonally adjusted series. We show that underestimation is due to a non-zero estimation error in estimating the seasonal component at each time period, which is the result of the use of low order seasonal filter in X12-ARIMA for estimating the seasonal component. Hence, we propose the use of high order seasonal filter for estimating the seasonal component, which helps reducing the estimation error noticeably, helps amending the underestimation problem, and helps improving the forecasting accuracy of the series. In TRAMO-SEATS, Airline model is found to deliver the best seasonal filter among other ARIMA models.