Estimation of the AR order of an inhomogeneous AR model with input expanded by a set of basis

We proposed a new model for non-stationary time series analysis based on an inhomogeneous AR (autoregressive) equation [1]. Time series data is regard ed as white noise plus output of an AR system excited by non-stationary inp ut sequence represented in terms of a set of basis. A method of model param eter estimation was presented when the set of basis and the AR order are gi ven. In order to extend the method, we present a method of parameter estima tion when the AR order is unknown: we set two new criteria 1) minimize the root mean square error of the output sequence, and 2) minimize scattering o f estimated frequencies. Then, we derive a procedure for the estimation of the AR order and the other unknown parameters.