The nonlinear transformation used in reservoir computing can be effectively replaced by nonlinear vector autoregression (NVAR) for data prediction. In such a method, also known as next generation reservoir computing (NGRC), the input signal consists of a linear part, including several previous data points, and their nonlinear combinations. Here we show that the application of this method to a network with memristive weights (memristors) can be used to predict signals, depending on the nature of the nonlinear functions and the number of memristors. The network allows an accurate prediction of chaotic time series of Mackey-Glass and Duffing oscillators.