In this paper we propose a stochastic model of PPG (photoplethysmographic) signals that is able to synthesize an arbitrary number of other statistically equivalent signals to the one under analysis. To that end, we first preprocess the pulse signal to normalize and time-aling pulses. In a second stage we design a single-pulse model, which consists of 10 parameters. In the third stage, the time-evolution of this 10-parameter vector is approximated by means of two ARMA (autoregressive moving average) models, one for the trend and one for the residue; this model is applied after a decorrelation step which let us process each vector component in parallel. The experiments carried out show that the model we here propose is able to maintain the main features of the original signal; this is accomplished by means of both a linear spectral analysis and also by comparing two measures obtained from a non-linear analysis. Finally, we explore the capability of the model to: 1) track physical activity; 2) obtain statistics of clinical parameters by model sampling; 3) recover corrupted or missing signal epochs by synthesis.