The detection of transient events related to slow earthquakes in GNSS positional time series is key to understanding seismogenic processes in subduction zones. Here, we present a novel Principal and Independent Components Correlation Analysis (PICCA) method that allows for the temporal and spatial detection of transient signals. The PICCA is based on an optimal combination of the principal (PCA) and independent component analysis (ICA) of positional time series of a GNSS network. We assume that the transient signal is mostly contained in one of the principal or independent components. To detect the transient, we applied a method where correlations between sliding windows of each PCA/ICA component and each time series are calculated, obtaining the stations affected by the slow slip event and the onset time from the resulting correlation peaks. We first tested and calibrated the method using synthetic signals from slow earthquakes of different magnitudes and durations and modelled their effect in the network of GNSS stations in Chile. Then, we analyzed three transient events related to slow earthquakes recorded in Chile, in the areas of Iquique, Copiapó, and Valparaíso. For synthetic data, a 150 days event was detected using the PCA-based method, while a 3 days event was detected using the ICA-based method. For the real data, a long-term transient was detected by PCA, while a 16 days transient was detected by ICA. It is concluded that simultaneous use of both signal separation methods (PICCA) is more effective when searching for transient events. The PCA method is more useful for long-term events, while the ICA method is better suited to recognize events of short duration. PICCA is a promising tool to detect transients of different characteristics in GNSS time series, which will be used in a next stage to generate a catalog of SSEs in Chile