Absolute value optimization to estimate phase properties of stochastic time series (Corresp.)

Most existing deconvolution techniques are incapable of determining phase properties of wavelets from time series data; to assure a unique solution, { minimum phase} is usually assumed. It is demonstrated, for moving average processes of order one, that deconvolution filtering using the absolute value norm provides an estimate of the wavelet shape that has the correct phase character when the random driving process is nonnormal. Numerical tests show that this result probably applies to more general processes.