An artificial neural network approach for stochastic process power spectrum estimation subject to missing data

• Artificial neural networks may ‘learn’ spectral properties of stochastic processes.
• Power spectra can be drawn from trained network outputs.
• Network training is shown to be relatively insensitive to missing data.
• Power spectra may be drawn for evolutionary, non-separable processes.

An artificial neural network (ANN) based approach is developed for estimating the power spectrum of stochastic processes subject to missing/limited data. In this regard, an appropriately defined ANN is utilized to capture the stochastic pattern in the available data in an average sense. Next, the extrapolation capabilities of the ANN are exploited for generating realizations of the underlying stochastic process. Finally, power spectrum estimates are derived based on established frequency (e.g. Fourier analysis), or versatile joint time–frequency analysis techniques (e.g. wavelets) for the cases of stationary and non-stationary stochastic processes, respectively. One of the significant advantages of the approach relates to the fact that no a priori knowledge about the data is assumed, while the approach is applicable for treating non-stationary processes not only with separable but non-separable in time and frequency evolutionary power spectra as well. Comparisons of several target power spectra with Monte Carlo simulation based power spectrum estimates demonstrate the versatility and reliability of the approach for up to 50% missing data.