In this paper we study the positivity of an estimated time series (or impulse response) described by a sum of real exponentials. Such a problem, i.e. fitting a time series as a sum of exponential functions, is a longstanding one and has been studied by a very large number of authors. Positivity of the time series is often required in many diverse fields of application where it is a direct consequence of the physics underlying the process, under study. In this paper we suggest a possible way to incorporate the positivity constraints in the parameters estimation process.