Two-dimensional wavelets for nonlinear autoregressive models with an application in dynamical system

In this note we introduce a new estimator for estimating autoregressive model function based on two-dimensional wavelet expansion of joint density function. We investigate some asymptotic properties of the proposed estimator. We also added the problem of estimating of derivative of autoregressive estimator through new approach. Finally, we apply our method in dynamical systems. In particular, we estimate a chaotic map from a noisy data and filter entropy of the chaotic map.