Some methods of spectral analysis: Comparison with MEM-MRA combination

Rigozo et al. [N.R. Rigozo, E. Echer, D.J.R. Nordemann, L.E.A. Vieira, H.H. de Faria, Comparative study between four classical spectral analysis methods, Applied Mathematics and Computation 168 (2005) 411-430] presented a comparative study of spectral analysis by four classical methods: Fourier, multitaper, iterative regression (ARIST), and maximum entropy (MEM). For the first three methods, periodicities and amplitudes were compared but for maximum entropy method (MEM), only periodicities were calculated as the power estimates are unreliable. Kane [R.P. Kane, Power spectrum analysis of solar and geophysical parameters, Journal of Geomagnetism and Geoelectricity 29 (1977) 471-495] has shown that when MEM is supplemented by a multiple regression analysis (MRA [P.R. Bevington, Data Reduction and Error Analysis for the Physical Sciences, McGraw-Hill, New York, 1969, pp. 164-176]), the MEM/MRA combination gives excellent, accurate results for periodicities and their amplitudes. In the present communication, the samples used by Rigozo et al. [N.R. Rigozo, E. Echer, D.J.R. Nordemann, L.E.A. Vieira, H.H. de Faria, Comparative study between four classical spectral analysis methods, Applied Mathematics and Computation 168 (2005) 411-430] were reexamined by the MEM/MRA combination and results compared. The Fourier and multitaper methods give erroneous estimates of periodicities, more so of their amplitudes. The results of the methods of iterative regression (ARIST) and MEM/MRA combination were almost similar and very accurate, with errors less than 1% in estimates of periodicities and amplitudes for periodicities less than about 1/3rd of the data length. For higher periodicities, the errors could be larger and larger but still less than 10%.