Auxiliary utilities

The following commands implement auxiliary utilities for time series analysis:

BAND/TSA -

Frequency grid: The frequency grid suitable for the analysis of evenly sampled observations is well determined. However, for uneven sampling no simple rules exist in general. BAND/TSA may be used to find a reasonable guess for the frequency grid. The results are returned in the keywords START, STEP and NSTEPS. BAND/TSA may err, as usual in guessing; its results must be checked for consistency.

COVAR/TSA -

Correlation length: The statistical evaluation of TSA results rests on the assumption that the noise in the data is white noise. However, quite often this assumption is wrong. One way to test its justification is to compute the residuals from the model fit (e.g. by using SINEFIT/TSA) and to examine the correlation length in the residuals from the autocorrelation function (ACF; computed with COVAR/TSA). The average number of observations per correlation length is the average number of correlated observations n_corr. For white noise this number should be of order 1.

NORMALIZE/TSA -

Normalize mean & variance: Normalize mean and (optionally) variance of a column to 0 and 1, respectively. Subtraction of the average value from the data is always recommended for numerical reasons. Certain commands will not work correctly for large mean values. Normalization of the variances to the same unit value is required for DELAY/TSA.

SINEFIT/TSA -

Filtering of the series: This versatile command may be used not only for parameter estimation but also for data massaging. SINEFIT/TSA may also be used to remove a trend from data (high pass filtering). For this purpose choose a low value for frequency, so that only few cycles cover the time interval spanned by the observations. Specify just 1 iteration, so that the routine does not attempt a frequency correction. Subtraction of such data from the raw data returns the fitted trend (low pass filtering). The results are in a format suitable for renewed input to the other frequency domain TSA commands.

WIDTH/TSA -

Width of spectral lines: Profiles of spectral lines appearing in test statistics may be used to refine signal parameters and their errors. In its present primitive form, this command analyses the strongest maximum (an 'emission' line) in the specified sub-spectrum. The window should not be too narrow as it is also used for the determination of the continuum level. A comparison of the continuum level with the expected value of the statistic for a pure noise signal may reveal interference and/or noise correlation. The width of the line may be used to estimate confidence interval of the frequency associated with the line. However, note that the width at half intensity is generally not a good estimate. For Scargle's statistic and power spectra use the width at the level corresponding to the peak level minus the average noise level P-N (Schwarzenberg-Czerny, 1991). For this purpose, this command returns a small table of widths on the screen and in keyword OUTPUTR. In power spectra, the peak height of the line is a good measure of the square of the amplitude of the oscillation. - An 'absorption' line can be converted into a 'emission' line by simply changing the sign with COMPUTE/TABLE.