Based on a microscopic approach we demonstrate that the unexpected ferromagnetic properties of BaTiO₃ (BTO) or PTO observed recently at room temperature are due to oxygen vacancies at the surface of the nanocrystalline materials. Such vacancies lead to the appearance of Ti³⁺ or Ti²⁺ ions with nonzero net spin. The resulting different valence states composed of Ti³⁺ or Ti²⁺ offer a nonzero magnetization which decreases with increasing particle size. The system shows a multiferroic behavior below a critical size of the nanoparticles and the related polarization tends to a saturation value when the particle size is enhanced.