# REDFIT spectral analysis

This module is an implementation of the REDFIT procedure of Schulz and Mudelsee (2002). It is a more advanced version of the simple Lomb periodogram described above. REDFIT includes an option for “Welch overlapped segment averaging”, which implies splitting the time series into a number of segments, overlapping by 50%, and averaging their spectra. This reduces noise but also reduces spectral resolution. In addition, the time series is fitted to an AR(1) red noise model which is usually a more appropriate null hypothesis than the white noise model described above. The given “false-alarm lines” are based on both parametric approximations (chi2) and Monte Carlo (using 1000 random realizations of an AR(1) process).

The input must be in the form of two columns with time and data values, or one column of equally-spaced data values. The data are automatically detrended. The fitting to AR(1) implies that the data must have the correct time direction (in contrast with the simple spectrogram above where the time direction is arbitrary). The time values are expected to be ages before present. If not, it will be necessary to give them negative signs.

The frequency oversampling value controls the number of points along the frequency axis (but having many points does not increase frequency resolution!). Increasing the number of segments will reduce noise, but also decrease the resolution. The window function influences the trade-off between spectral resolution and attenuation of side lobes.

The (average) tau value is the characteristic time scale (the parameter of the AR model). The bandwidth is the spectral resolution given as the width between the -6dB points.

The fit to an AR(1) model can be assessed using the runs value and its 5% acceptance interval. This test is only available with Monte Carlo on, oversampling=1, segments=1, window=rectangular.

In addition to a fixed set of false-alarm levels (80%, 90%, 95% and 99%), the program also reports a “critical” false-alarm level (False-al) that depends on the segment length (Thomson 1990).

*Important*: Because of long computation time, the Monte Carlo simulation is not run by default, and the Monte Carlo false-alarm levels are therefore not available. When the Monte Carlo option is enabled, the given spectrum may change slightly because the Monte Carlo results are then used to compute a “bias-corrected” version (see Schulz and Mudelsee 2002).

Missing values supported.

#### References

Schulz, M. & M. Mudelsee. 2002. REDFIT: estimating red-noise spectra directly from unevenly spaced paleoclimatic time series. *Computers & Geosciences* 28:421-426.

Thomson, D.J. 1990. Time series analysis of Holocene climate data. *Philosophical Transactions of the Royal Society of London, Series A* 330:601-616.