Parameter Estimation of Inhomogeneous AR Model Expanded with Unknown Basis

We proposed a new model for non-stationary time series analysis based on the IAR (inhomogeneous autoregressive) model, and a method for model parameter estimation when the set of basis is given [1], [2]. In this paper, we further propose a method for parameter estimation including that of basis set: we set a new condition that power of the input sequence is concentrated in low-frequency domain, and developed an iterative estimation method. We firstly select an initial set of basis, from which new sets are created in order to minimize the difference between the model and data. Among new sets of basis, we select a good one that gives minimum standard deviation of estimated frequencies. key words: AR model, inhomogeneous AR model, statistical modeling, non-stationary time series analysis, Sompi method