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THE COMPARISON OF LEAST SQUARES AND THIRD‐ORDER PERIODOGRAM PROCEDURES IN THE ESTIMATION OF BIFREQUENCY
Author(s) -
Brillinger David R.
Publication year - 1980
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/j.1467-9892.1980.tb00303.x
Subject(s) - mathematics , periodogram , third order , least squares function approximation , generalized least squares , estimation , order (exchange) , statistics , series (stratigraphy) , ordinary least squares , estimator , paleontology , philosophy , theology , finance , economics , biology , management
. Given a stretch of time series values, the third‐order periodogram is investigated as a criterion for use in the estimation of bifrequencies, that is of frequency triples (ω 1 ω 2 , ω 3 ) with ω 3 = 2ω ‐ω 1 ω 2 . The least squares estimates of such frequencies are compared with estimates derived by maximizing the modulus of the third‐order periodogram. It is found that neither estimation procedure is uniformly better than the other.