The frequency regression and smoothing method, or the SIML frequency method, is developed based on the non-stationary errors-in-variables model. Many macroeconomic time series contain not only trend, cycle, seasonal, and measurement error components, but also factors such as abrupt changes, trading-day effects, and institutional changes. The frequency regression and smoothing method is an effective tool for such factors in non-stationary time series. The proposed method is simple and applicable to analyzing non-stationary economic time series and to handle seasonal adjustments. Our formulation leads to the asymptotic results on the low-frequency method proposed by M \(\ddot{u}\) ller and Watson (Econometrica 86-3:775–804, 2018) as a consequence. To illustrate the method, we present empirical example.