Abstract: A non-stationary time series model using a likelihood function as a function of input data, base demand parameters, and time dependent parameter. The likelihood function may represent any statistical distribution. The likelihood function uses a prior probability distribution to provide information external to the input data and is used to control the model. In one embodiment the prior is a function of adjacent time periods of the demand profile. The base demand parameters and time dependent parameter are solved using a multi-diagonal band matrix. The solution of base demand parameters and time dependent parameter involves making estimates thereof in an iterative manner until the base demand parameters and time dependent parameter each converge. A non-stationary time series model is provided from an expression using the solution of the base demand parameters and time dependent parameter. The non-stationary time series model provides a demand forecast as a function of time.