Higher order auto‐spectra by maximum entropy method

Higher order auto‐spectra, in particular bispectra and perhaps trispectra, are being used increasingly for analyzing various nonlinear interactions in the ocean, e.g., Herring (1980) and McComas and Briscoe (1980). The resolution of these spectra, as with conventional energy spectra, is frequently limited because short data records must be used. The purpose of this note is to present a maximum entropy (MEM) representation for higher order auto‐spectra which has the advantage of the superior resolving power of the MEM technique under these circumstances. The derivation is a generalizaton of the power spectra derived for a linear process (Box and Jenkins, 1970). We derive an MEM representation for bispectra and show that this result can be generalized to auto‐spectra of any order.