astrochron (version 0.3.1)

lowspec: Robust Locally-Weighted Regression Spectral Background Estimation

Description

LOWSPEC: Robust Locally-Weighted Regression Spectral Background Estimation

Usage

lowspec(dat,decimate=NULL,tbw=3,padfac=5,detrend=F,siglevel=0.9,xmin,xmax,
        setrho,lowspan,b_tun,output=0,sigID=T,pl=1,genplot=T,verbose=T)

Arguments

dat

Stratigraphic series for LOWSPEC. First column should be location (e.g., depth), second column should be data value.

decimate

Decimate statigraphic series to have this sampling interval (via piecewise linear interpolation). By default, no decimation is performed.

tbw

MTM time-bandwidth product (2 or 3 permitted)

padfac

Pad with zeros to (padfac*npts) points, where npts is the original number of data points.

detrend

Remove linear trend from data series? This detrending is performed following AR1 prewhitening. (T or F)

siglevel

Significance level for peak identification.

xmin

Smallest frequency for plotting.

xmax

Largest frequency for plotting.

setrho

Define AR1 coefficient if desired (otherwise calculated).

lowspan

Span for LOWESS smoothing of prewhitened signal, usually fixed to 1. If using value

b_tun

Robustness weight parameter for LOWSPEC.

output

What should be returned as a data frame? (0=nothing; 1=spectrum + CLs; 2=sig peaks; 3=PDF image)

sigID

Identify signficant frequencies on power and probabilty plots? (T or F)

pl

Plot logarithm of spectral power (1) or linear spectral power (2)?

genplot

Generate summary plots? (T or F)

verbose

Verbose output? (T or F)

Value

• If option 1 is selected, a data frame containing the following is returned: Frequency, Prewhitened power, LOWSPEC background, LOWSPEC CL, F-test CL.

  If option 2 is selected, the 'significant' frequencies are returned (as described above).

  If option 3 is selected, the graphics are output to a PDF file.

Details

LOWSPEC is a 'robust' method for spectral background estimation, designed for the identification of potential astronomical signals that are imbedded in red noise (Meyers, 2012). The complete algoritm implemented here is as follows: (1) initial pre-whitening with AR1 filter (default) or other filter as appropriate (see function prewhiteAR), (2) power spectral estimation via the multitaper method (Thomson, 1982), (3) robust locally weighted estimation of the spectral background using the LOWESS-based (Cleveland, 1979) procedure of Ruckstuhl et al. (2001), (4) assignment of confidence levels using a Chi-square distribution.

Candidiate astronomical cycles are subsequently idenitified via isolation of those frequencies that achieve the required (e.g., 90 percent) LOWSPEC confidence level and MTM harmonic F test confidence level. Allowance is made for the smoothing inherent in the MTM power spectral estimate as compared to the MTM harmonic spectrum. That is, an F test peak is reported if it achieves the required MTM harmonic confidence level, while also achieving the required LOWSPEC confidence level within +/- half the power spectrum bandwidth resolution. One additional criterion is included to further reduce the false positive rate, a requirement that significant F tests must occur on a local power spectrum high, which is parameterized as occurring above the local LOWSPEC background estimate. See Meyers (2012) for futher information on the algorithm.

In this implementation, the 'robustness criterion' ('b' in EQ. 6 of Ruckstuhl et al., 2001) has been optimized for 2 and 3 pi DPSS, using a 'span' of 1. By default the robustness criterion will be estimated. Both 'b' and the 'span' can be expliclty set using parameters 'b_tun' and 'lowspan'. Note that it is permissible to decrease 'lowspan' from its default value, but this will result in an overly conservative false positive rate. However, it may be necessary to reduce 'lowspan' to provide an approporiate background fit for some stratigraphic data. Another option is to decimate the data series prior to spectral estimation.

References

W.S. Cleveland, 1979, Locally weighted regression and smoothing scatterplots: Journal of the American Statistical Association, v. 74, p. 829-836.

S.R. Meyers, 2012, Seeing Red in Cyclic Stratigraphy: Spectral Noise Estimation for Astrochronology: Paleoceanography, 27, PA3228, doi:10.1029/2012PA002307.

A.F. Ruckstuhl, M.P Jacobson, R.W. Field, and J.A. Dodd, 2001, Baseline subtraction using robust local regression estimation: Journal of Quantitative Spectroscopy & Radiative Transfer, v. 68, p. 179-193.

D.J. Thomson, 1982, Spectrum estimation and harmonic analysis: IEEE Proceedings, v. 70, p. 1055-1096.

See Also

spec.mtm, baseline, mtm, and periodogram

Examples

# generate example series with periods of 400 ka, 100 ka, 40 ka and 20 ka
ex = cycles(freqs=c(1/400,1/100,1/40,1/20),start=1,end=1000,dt=5)

# add AR1 noise
noise = ar1(npts=200,dt=5,sd=.5)
ex[2] = ex[2] + noise[2]

# LOWSPEC analysis
#lowspec(ex)