# Spectral density and wold decomposition

1. May 25, 2009

### pezze

Hello, I would greatly appreciate any comment on the following problem:

Suppose that I estimate the spectral density of a weakly stationary series, say, nonparametrically by smoothing the periodogram. Is there a simple way to recover the coefficients of the wold decomposition of the process? (i.e. the infinite moving average representation of the process?) And the best of the world would the finding these coefficients and being able to obtain their asymptotic standard errors based on those of the spectral density.

This is a real problem that I have to solve in my research, so any comment would be greatly appreciated.

Thanks!

Pezze