This work presents a modelling approach to accurately predict the blood pressure (BP) waveform time series from a single input signal. A nonlinear autoregressive model with exogenous input (NARX) is implemented using artificial neural networks and trained on Electrocardiography (ECG) signals to predict the BP waveform. The efficacy of the model is demonstrated using the MIMIC II database. The proposed method can accurately estimate systolic and diastolic BP. The NARX model together with ECG measurement allows continuous monitoring of BP, enables the estimation of other physiological measurements, such as the cardiac output, and provides more insight on the patient health condition.