Multiscale autoregressive models and the stochastic realization problem

We provide a linear-time algorithm for the solution of the multiscale autoregressive (MAR) stochastic realization problem. The MAR framework is a powerful generalization of the classical state-space one. As in the state-space case, to apply the framework, one must first build an appropriate model (i.e., find model parameters). Our focus is on a computationally efficient model realization and, after introducing our approach, we compare it to that of Frakt and Willsky (see International Conference on Acoustics, Speech, and Signal Processing, Seattle, WA, 1998) which is quadratic in problem size.