Yule-Walker Equations Using Higher Order Statistics for Nonlinear Autoregressive Model

The paper presents the derivation of Yule-Walker equations for the nonlinear autoregressive model NAR(p) of a time-series. The proposed method allows for easy calculation of parameters of the model. In the determined equations, higher order statistics are used, instead of autocovariances. For the linear autoregressive model AR(p), the standard Yule-Walker equations are directly based on autocovariances of time-series, or equivalently autocorrelations if the equations are rescaled. Unfortunately, it does not apply for nonlinear model. The authors show a compact matrix notation of Yule-Walker equations for the nonlinear autoregressive model with the nonlinearity of polynomial type of degree 2, with the use of higher order statistics up to 4th order, and numerical examples for electromyography signals for different hand movements.