This paper attempts to extract a fundamental trend, which we call a "trend-cycle component," from an economic time-series. The "trend-cycle component" consists of a medium-term business cycle component and a long-term trend component. The objective is to eliminate the short-term irregular and seasonal variations that hide a fundamental trend in an economic time-series. We test five different time-series methods. Among them, the Henderson moving average (which is incorporated in an X-12-ARIMA seasonal adjustment program), the Band-Pass filter (which utilizes a Fourier transformation), and the DECOMP are found to be effective in extracting a "trend-cycle component" with a cyclical period longer than 1.5 years. However, no method is found to be effective in extracting a "long-term trend component" with a cyclical period longer than that of a medium-term business cycle. Although the HP filter is somewhat successful, it still contains a component with a cyclical period of about three years that corresponds to a business cycle. These methods are useful for forecasting a wide variety of economic variables because they reveal a fundamental trend in the time series. In addition, statistical programs are available for easy application. They have, however, a few shortcomings. First, it is often difficult to provide a meaningful economic interpretation of the revealed characteristics of the "trend-cycle component." Second, the addition of new data can change the estimation results. In particular, an extracted component around the end of a sample period is likely to be revised with new data. Special caution is in order, therefore, in interpreting the estimation results and forecasting the time series when the data exhibit large variations. In this case, comparing the results of different methods provides a useful way to assess the reliability of an extracted "trend-cycle component."

Keywords: Fundamental trend; Time-series analysis; X-12-ARIMA; DECOMP; HP Filter; Fourier transformation; Beveridge and Nelson decomposition