Modelling and Forecasting Based on Recurrent Pseudoinverse Matrices

Time series modelling and forecasting techniques have a wide spectrum of applications in several fields including economics, finance, engineering and computer science. Most available modelling and forecasting techniques are applicable to a specific underlying phenomenon and its properties and lack generality of application, while more general forecasting techniques require substantial computational time for training and application. Herewith, we present a general modelling framework based on a recursive Schur - complement technique, that utilizes a set of basis functions, either linear or non-linear, to form a model for a general time series. The basis functions need not be orthogonal and their number is determined adaptively based on fitting accuracy. Moreover, no assumptions are required for the input data. The coefficients for the basis functions are computed using a recursive pseudoinverse matrix, thus they can be recomputed for different input data. The case of sinusoidal basis functions is presented. Discussions around stability of the resulting model and choice of basis functions is also provided. Numerical results depicting the applicability and effectiveness of the proposed technique are given.