Aims: We derive the vertical velocities of disk stars in the range of Galactocentric radii of R = 5 - 16 kpc within 2 kpc in height from the Galactic plane. This kinematic information is connected to dynamical aspects in the formation and evolution of the Milky Way, such as the passage of satellites and vertical resonance and determines whether the warp is a long-lived or a transient feature. Methods: We used the PPMXL survey, which contains the USNO-B1 proper motions catalog cross-correlated with the astrometry and near-infrared photometry of the 2MASS point source catalog. To improve the accuracy of the proper motions, the systematic shifts from zero were calculated by using the average proper motions of quasars in this PPMXL survey, and we applied the corresponding correction to the proper motions of the whole survey, which reduces the systematic error. From the color-magnitude diagram K versus (J - K) we selected the standard candles corresponding to red clump giants and used the information of their proper motions to build a map of the vertical motions of our Galaxy. We derived the kinematics of the warp both analytically and through a particle simulation to fit these data. Complementarily, we also carried out the same analysis with red clump giants spectroscopically selected with APOGEE data, and we predict the improvements in accuracy that will be reached with future Gaia data. Results: A simple model of warp with the height of the disk zw(R,φ) = γ(R - R⊙)sin(φ - φw) fits the vertical motions if dot {γ }/γ = -34±17 Gyr-1; the contribution to dot {γ } comes from the southern warp and is negligible in the north. If we assume this 2σ detection to be real, the period of this oscillation is shorter than 0.43 Gyr at 68.3% C.L. and shorter than 4.64 Gyr at 95.4% C.L., which excludes with high confidence the slow variations (periods longer than 5 Gyr) that correspond to long-lived features. Our particle simulation also indicates a probable abrupt decrease of the warp amplitude in a time of about one hundred Myr. Conclusions: The vertical motion in the warp apparently indicates that the main S-shaped structure of the warp is a long-lived feature, whereas the perturbation that produces an irregularity in the southern part is most likely a transient phenomenon. But we need higher accuracy in the systematic errors of proper motions to confirm this tentative detection of vertical motion in the outer disk. With the use of the Gaia end-of-mission products together with spectroscopically classified red clump giants, the precision in vertical motions can be increased by an order of magnitude at least.