Algorithm for adaptively smoothing the log-periodogram

We use the principle of minimum cross entropy (MCE) to build a non-parametric adaptive algorithm for smoothing the log-transformed periodogram, and construct an optimal estimate for the spectral density function of a process. We show that this estimate minimizes the cross-entropy with the log-transformed spectral density function of the process. The method is non-parametric and performs very well for the case of processes having rapidly changing spectra that exhibits a variable order of smoothness. The algorithm is locally based on linearly approximating the information present in the process, and uses this approximation to allow the bandwidth of the spectral window in the smoothed log-periodogram to vary. We extend the algorithm empirically for better application to processes having mixed, narrow-band spectra. Comparisons with other currently used procedures are performed through the means of simulated examples.