Detrending

Methods of analysis Fourier periodograms calculated in the range between 0 and 20 d 1. Automatic search for periodicities with the application of prewhitening and detrending. The photometry of selected objects was examined visually. 

Fig. 9.1. The NIR spectra from strained and freeze-dried whole rumen liquor from sheep fed on ryegrass (solid line), and the bacterial (dotted line) and protozoal (dashed line) fractions. The standard normal variate and detrended data (SNV-DT) Is plotted vs. wavelength. Log 1/R = - log (Reflectance) and Is equivalent to absorbance.

Standard normal variate transformation and detrending of near infrared diffuse reflectance spectra. Applied Spectroscopy 43, 112-111. 

Hill, M. O. DEC ORAN A A FORTRAN Program for Detrended Correspondence Analysis and Reciprocal Averaging Section of Ecology and Systematics, Cornell University Ithaca, NY, 1979. 

Wavelet techniques (Koscielny-Bunde et al., 1998) and detrended fluctuation analysis (DFA) (Peng et al., 1994) are among the most recently used tools along these lines. Recently, much attention has been paid to DFA, because it has already proved its usefulness in a wide variety of complex systems (e.g., Stanley, 1999 Talkner and Weber, 2000 Varotsos et al., 2003a, b, 2005 Chen et al., 2005 Varotsos and Kirk-Davidoff, 2006). More information about the DFA method is given in Section 3.6.3.2. 

According to the DFA method, the time series y t) is first integrated and then divided into boxes of equal length, At. In each box, a least squares line (or polynomial curve of order /, DFA-/) is then fitted, in order to detrend the integrated time series by subtracting the locally fitted trend in each box. The root-mean-square (rms) fluctuation Fd(At) of this integrated and detrended time series is calculated over all timescales (box sizes). 

More specifically, the detrended fluctuation function F(t) is calculated as follows ... 

Figure 3.14. Log-log plot of the DFA function vs. the temporal interval At (in months) for detrended and deseasonalized C02 concentrations, during 1958-2004.

Chen Z. Hu K. Carpena P. Bernaola-Galvan P. Stanley H.E. and Ivanov P. (2005). Effect of nonlinearities on detrended fluctuation analysis. Physical Review, E71, art. no. 011104. 

Kantelhardt J.W. Zschiegner S.A. Koscielny-Bunde E. Havlin S. Bunde A. and Stanley H.E. (2002). Multifractal detrended fluctuation analysis of nonstationary time series. Physica, A316(14), 87-114. 

Talkner P. and Weber R.O. (2000). Power spectrum and detrended fluctuation analysis Application to daily temperatures. Physical Review, Part A, E62(l), 150-160. 

FdM detrended local fluctuations within a window of length X... 

Fig. 18 Detrended fluctuation function for the copolymer sequences of length N = 1024, which were generated via surface-induced computer-aided design. Solid line shows the analytical (PM) result at

Barnes, R.J., Dhanoa, M.S., and Lister, S.J., Standard normal variate transformation and detrending of near infrared diffuse reflectance, Appl. Spectrosc., 43, 772-777, 1989. 

Ramp-function space series were initially divided into two segments ramp data and nonramp data. The ramp data show the presence of a linear trend. This trend was removed, and the residual data series was retained. Virtually all the ramp data in this study are representative of inshore (i.e., coastal) data. The offshore (i.e., nonramp) data also were tested for trends. The detrended segments were tested for stationarity with the procedures just cited. 

A trend in the data is defined (46) as any frequency component whose period is longer than the sample record. Failure to remove these trends often produces large distortions in correlation functions (and spectra), especially at low frequencies. A least-squares detrending procedure (46) was used to remove linear trends in the data. This method differs from the endpoint technique 49, 50). The end-point technique was not used here because it is recommended for use on data in which a large deterministic com-... 

Figure 7. Spatial segments of silicate nitrate, dissolved O2, pH, and chlorophyll a from Line E of the southern region (Figure 6), Key left, data and mean spatial trend and ri t, the detrended series.

There have been attempts to deal with the issue of nonlinearity in data sets. Detrended principal components (DPC) use a polynomial expression to remove the nonlinear relationships from the PCA axes. DPC are useful for data sets of moderate nonlinearity. Detrended correspondence analysis uses a more complex algorithm to eliminate the nonlinearity but requires a more complex computation. Nonmetric multidimensional scaling (NMDS) is a robust method that deals with nonlinearities by using ranks. 

FIGURE 5.10 Detrended, standardized (mean —0, standard deviation (STD) = 1) winter series (JFM) of the Arctic Oscillation (AO) (NOAA, 2006d) and of the North Atlantic Oscillation (NAO), expressed by the air pressure difference between Gibraltar in the south and Reykjavik in the north according to Hagen and Feistel (2005). 

FIGURE 5.16 Seven years running means of detrended, standardized series [mean = 0, STD = 1, given in standard deviations (STD)] of the WIBIX (bold line), the winter frequency (JFM) of eastward traveling cyclones with core pressures lower than 950 hPa (FEC, thin line) over the North Atlantic-European sector (30-90°N, 60 W-60 E) compiled by Schinke (1993), and the averaged sea surface temperature anomaly (SSTA, broken line) in the area between 47.5 82.5 N and 22.5 W- 47.5 E the SSTA series results from the well-known Kaplan series, (NOAA, 2006c). 

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