Lomb-Scargle Periodogram
Computes the Lomb-Scargle periodogram for a time series with irregular (or regular) sampling intervals. Allows selecting a frequency range to be inspected, as well as the spacing of frequencies scanned.
lsp(x, times = NULL, from = NULL, to = NULL, type = c("frequency", "period"),
ofac = 1, alpha = 0.01, plot = TRUE, ...)x |
The data to be analysed. x can be either a two-column numerical dataframe or matrix, with sampling times in columnn 1 and measurements in column 2, a single numerical vector containing measurements, or a single vector |
times |
If x is a single vector, times can be provided as a numerical vector of equal length containing sampling times. If x is a vector and times is NULL, the data are assumed to be equally sampled and times is set to 1:length(x). |
from |
The starting frequency (or period, depending on type) to begin scanning for periodic components. |
to |
The highest frequency (or period, depending on type) to scan. |
type |
Either “frequency” (the default) or “period”. Determines the type of the periodogram x-axis. |
ofac |
The oversampling factor. Must be an integer>=1. Larger values of ofac lead to finer scanning of frequencies but may be time-consuming for large datasets and/or large frequency ranges (from...to). |
alpha |
The significance level. The periodogram plot shows a horizontal dashed line. Periodogram peaks exceeding this line can be considered significant at alpha. Defaults to 0.01. Only used if plot=TRUE. |
plot |
Logical. If plot=TRUE the periodogram is plotted. |
... |
Further graphical parameters affecting the periodogram plot. |
The p-value for the significance of the largest peak in the periodogram is computed from the exponential distribution, as outlined in Press et al. (1994), see below. For a more robust - but potentially time-consuming estimation of p-values see randlsp.
Significance levels in both lsp and randlsp increase with the number of frequencies inspected. Therefore, if the frequency-range of interest can be narrowed down a priori, use arguments “from” and “to” to do so.
A named list with the following components:
scanned |
A vector containing the frequencies/periods scanned. |
power |
A vector containing the normalised power corresponding to scanned frequencies/periods. |
data |
Names of the data vectors analysed. |
n |
The length of the data vector. |
type |
The periodogram type used, either "frequency" or "period". |
ofac |
The oversampling factor used. |
n.out |
The length of the output (powers). This can be >n if ofac >1. |
alpha |
The false alarm probability used. |
sig.level |
Powers > sig.level can be considered significant peaks at p=alpha. |
peak |
The maximum power in the frequency/period interval inspected. |
peak.at |
The frequency/period at which the maximum peak occurred. |
p.value |
The probability that the maximum peak occurred by chance. |
For a description of the properties of the Lomb-Scargle Periodogram, its computation and comparsion with other methods see Ruf, T. (1999). Function lsp uses the algorithm given by Press et al (1994). The Lomb-Scargle Periodogram was originaly proposed by Lomb N.R. (1976) and furher extended by Scargle J.D. (1982).
Thomas Ruf thomas.ruf@vetmeduni.ac.at based on code by Press et al (1994).
Lomb N.R. (1976) Least-squares frequency analysis of unequally spaced data. Astrophysics and Space Science 39:447–462
Press W.H., Teukolsky S.A., Vetterling S.T., Flannery, B.P. (1994) Numerical recipes in C: the art of scientific computing.2nd edition. Cambridge University Press, Cambridge, 994pp.
Ruf, T. (1999) The Lomb-Scargle Periodogram in Biological Rhythm Research: Analysis of Incomplete and Unequally Spaced Time-Series. Biological Rhythm Research 30: 178–201.
Scargle J.D. (1982) Studies in astronomical time series. II. Statistical aspects of spectral analysis of unevenly spaced data. The Astrophysical Journal 302: 757–763.
# ibex contains an unevenly sampled time series data(ibex) lsp(ibex[2:3],) lsp(ibex$temp,times=ibex$hours,type='period',ofac=5) # lynx contains evenly sampled data lsp(lynx) lynx.spec <- lsp(lynx,type='period',from=2,to=20,ofac=5) summary(lynx.spec)
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