In this paper we addressed the problem of backcasting and forecasting non-stationary time series. Given that traditional backcasting are based on the classical cross-correlation function assuming two stationary time series, assumptions based on two non-stationary time series need a new approach. Thus, Detrended Cross-Correlation Analysis (DCCA) provides a fanned estimator for a correlation between two non-stationary time series, providing then the stationary time series. Therefore, we developed a backcaster estimator and a predictor for the obtained stationary time series. The practical example of a Chilean cement production time series (1991–2015) illustrates our results.