The author introduces the parabolic analogue to Muckenhoupt's \(A_p\) weights. Given a cube \(Q=\prod_{i=1}^n [a_i, a_i+h]\) and \(r>0\), the author denotes by \[ Q^{+,r}= \prod_{i=1}^{n-1} \big[a_i,a_i+h\big]\times \big[a_n+rh,a_n+(r+1)h\big] \] the forward in time \(r\)-translation of the cube. Similarly, the backward \(r\)-translation is denoted by \(Q^{-,r}\). With this notation out of the way a weight function in \(\mathbb R^n\) is a forward parabolic \(A_p\)-weight for \(10\) so that \[ \bigg(\frac{1}{|Q|}\int_Q w^{1+\delta} \,dx\bigg)^{1/1+\delta}\leq C\bigg(\frac{1}{|Q^{+,r}|}\int_{Q^{+,r}} w \,dx\bigg). \] This result extends the version appearing in [\textit{D. Cruz-Uribe, C. J. Neugebauer} and \textit{V. Olesen}, Stud. Math. 116, No.3, 255--270 (1995; Zbl 0851.42017)]. Also, the connection with maximal operators is given, showing that if \(w\in PA_p^+(\mathbb R^n)\) then the maximal operator \(N_r^{+}\) defines a bounded operator on \(L^p(w)\) for \(10} \frac{1}{|Q_{x,h}^r|} \int_{Q_{x,h}^r} |f(y)| \,dy \] for \(0