Butterworth-Induced Autoregressive Model

This work proposes a novel autoregressive (AR) modeling framework in which the model structure and coefficients are induced from the analytical properties of Butterworth filters. By exploiting the equivalence between AR models and all-pole discrete-time filters, the proposed approach derives the AR coefficients directly from the pole locations of a continuous-time Butterworth prototype mapped to the discrete-time domain. In this formulation, the filter order and stopband attenuation act as hyperparameters controlling the complexity and frequency-selective behavior of the resulting predictor, while a scalar gain parameter is estimated from data using a maximum likelihood criterion. Model selection is carried out through a nested cross-validation strategy tailored to time series data, employing a rolling-origin scheme to prevent look-ahead bias. The predictive performance of the resulting Butterworth-induced AR models is evaluated using one-step-ahead forecasts and compared against classical ARIMA models on simulated data. Experimental results show that the proposed approach achieves competitive predictive accuracy, while offering a structured and interpretable link between frequency-domain filter design and time-domain autoregressive modeling.