Theory & Methods: Tree‐based wavelet regression for correlated data using the minimum description length principle

This paper considers the problem of non‐parametric regression using wavelet techniques. Its main contribution is the proposal of a new wavelet estimation procedure for recovering functions corrupted by correlated noise, although a similar procedure for independent noise is also presented. Two special features of the proposed procedure are that it imposes a so‐called ‘tree constraint’ on the wavelet coefficients and that it uses the minimum description length principle to define its ‘best’ estimate. The proposed procedure is empirically compared with some existing wavelet estimation procedures, for the cases of independent and correlated noise.