We theoretically investigate the effects of electronic correlations (including spin and Coulomb correlations) on the magnetotransport through a parallel double quantum dot (DQD) coupled to ferromagnetic leads. Two dots couple coherently through electron correlations, rather than tunneling directly between two dots, and each dot is coupled to two semi-infinite ferromagnetic leads. We assume that the intradot Coulomb repulsion is much larger than the interdot Coulomb repulsion U. Thus, only the zero, one and two-particle DQD states are relevant to transport. Because of interdot electron correlation, the I-V characteristics of each dot is sensitive to the change in the state of the other dot. This work focuses on the effects of electron spin correlation and electron Coulomb correlation on magnetotransport through this system. In order to determine the transport properties of the system, we use the generalized master equation method. This method is based on the reduced density operator defined by averaging the statistical operator of the total system over the states of all leads. With the framework of the generalized master equation and the sequential tunneling approximation, we calculate the current, differential conductance and tunnel magnetoresistance (TMR) in the dot 1 as a function of bias for different spin correlations and Coulomb correlations. Our results reveal that the magnetotransport through this system is more sensitive to Coulomb correlation than to spin correlation; when Coulomb correlation equals zero, the spin correlation can induce a giant tunnel magnetoresistance, which is further larger than the Jullieres value of TMR; when Coulomb correlation occurs, the giant tunnel magnetoresistance disappears; when Coulomb correlation is equal to or larger than spin correlation, Coulomb correlation can suppress spin correlation; while the coexistence of Coulomb correlation and asymmetry of the DQD system can result in dynamical channel blockade, which can lead to the occurrence of negative tunnel magetoresistance and negative differential conductance. These novel properties lead to the potential applications in nanoelectronics, and relevant underlying physics of this problem is discussed.