Patient respiratory motion during PET image acquisition leads to blurring in the reconstructed images and may cause significant artifacts, resulting in decreased lesion detectability, inaccurate standard uptake value calculation and incorrect treatment planning in radiation therapy. To reduce these effects data can be regrouped into (nearly) 'motion-free' gates prior to reconstruction by selecting the events with respect to the breathing phase. This gating procedure therefore needs a respiratory signal: on current scanners it is obtained from an external device, whereas with data driven (DD) methods it can be directly obtained from the raw PET data. DD methods thus eliminate the use of external equipment, which is often expensive, needs prior setup and can cause patient discomfort, and they could also potentially provide increased fidelity to the internal movement. DD methods have been recently applied on PET data showing promising results. However, many methods provide signals whose direction with respect to the physical motion is uncertain (i.e. their sign is arbitrary), therefore a maximum in the signal could refer either to the end-inspiration or end-expiration phase, possibly causing inaccurate motion correction. In this work we propose two novel methods, CorrWeights and CorrSino, to detect the correct direction of the motion represented by the DD signal, that is obtained by applying principal component analysis (PCA) on the acquired data. They only require the PET raw data, and they rely on the assumption that one of the major causes of change in the acquired data related to the chest is respiratory motion in the axial direction, that generates a cranio-caudal motion of the internal organs. We also implemented two versions of a published registration-based method, that require image reconstruction. The methods were first applied on XCAT simulations, and later evaluated on cancer patient datasets monitored by the Varian Real-time Position ManagementTM (RPM) device, selecting the lower chest bed positions. For each patient different time intervals were evaluated ranging from 50 to 300 s in duration. The novel methods proved to be generally more accurate than the registration-based ones in detecting the correct sign of the respiratory signal, and their failure rates are lower than 3% when the DD signal is highly correlated with the RPM. They also have the advantage of faster computation time, avoiding reconstruction. Moreover, CorrWeights is not specifically related to PCA and considering its simple implementation, it could easily be applied together with any DD method in clinical practice.