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A UNIFIED APPROACH TO CONFIDENCE BOUNDS FOR THE AUTOREGRESSIVE SPECTRAL ESTIMATOR
Author(s) -
Koslov Judith W.,
Jones Richard H.
Publication year - 1985
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.1467-9892.1985.tb00405.x
Subject(s) - mathematics , autoregressive model , estimator , confidence interval , a priori and a posteriori , confidence and prediction bands , confidence region , statistics , series (stratigraphy) , statistic , quadratic equation , paleontology , philosophy , geometry , epistemology , biology
. Confidence bounds for the spectral density of a stationary time series are derived. A unified method begins with the autoregressive spectral estimate and produces both confidence intervals at single frequencies chosen a priori and a simultaneous confidence band for multiple a posteriori comparisons. The crux is optimization of a quadratic form subject to the constraint imposed by the F ‐statistic. An approximate method that may produce tighter bounds is described. The former methods are demonstrated on the Waldmeier annual mean sunspot numbers.