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Enveloping spectral surfaces: covariate dependent spectral analysis of categorical time series
Author(s) -
Krafty Robert T.,
Xiong Shuangyan,
Stoffer David S.,
Buysse Daniel J.,
Hall Martica
Publication year - 2012
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.1467-9892.2011.00773.x
Subject(s) - covariate , mathematics , categorical variable , series (stratigraphy) , statistics , time series , spectral analysis , econometrics , paleontology , biology , physics , quantum mechanics , spectroscopy
Motivated by problems in Sleep Medicine and Circadian Biology, we present a method for the analysis of cross‐sectional categorical time series collected from multiple subjects where the effect of static continuous‐valued covariates is of interest. Towards this goal, we extend the spectral envelope methodology for the frequency domain analysis of a single categorical process to cross‐sectional categorical processes that are possibly covariate dependent. The analysis introduces an enveloping spectral surface for describing the association between the frequency domain properties of qualitative time series and covariates. The resulting surface offers an intuitively interpretable measure of association between covariates and a qualitative time series by finding the maximum possible conditional power at a given frequency from scalings of the qualitative time series conditional on the covariates. The optimal scalings that maximize the power provide scientific insight by identifying the aspects of the qualitative series which have the most pronounced periodic features at a given frequency conditional on the value of the covariates. To facilitate the assessment of the dependence of the enveloping spectral surface on the covariates, we include a theory for analysing the partial derivatives of the surface. Our approach is entirely non‐parametric, and we present estimation and asymptotics in the setting of local polynomial smoothing.