Biology Reference
In-Depth Information
1. The value of a filter window (FWINDOW) to apply; and
2. Whether the detrended data are to be presented in original
y-value space or in terms of standard normal deviates (SND)
space, with the latter being used to address variance
nonstationarities.
The DTRNDANL software also allows users to specify one of several
ways of reporting the pointwise uncertainties with the detrended data,
such as uniform weighting, the arithmetic standard error of the mean
(SEM) of calculated detrended values, and others.
Here, again, we should point out that many commercially available
software packages provide detrending options. MINITAB and Microsoft
Excel, for example, allow for trend removal of known shapes, such as
linear, exponential, S-shaped, and others. The functional form of the
trend, however, is often not obvious.
The DTRNDANL algorithm does not assume any specific
functional form for the trend. It begins by considering a data
sequence of length FWINDOW beginning with the first data point.
A linear regression detrending is performed on this subseries data
sequence. Subsequently, the values of the detrended subsequence
are stored in their original units, or one additional step is performed
on the detrended subseries values: each value is divided by the
standard deviation of the subseries prior to storing. In the latter case,
we say that the result is stored in standard normal deviate space
(SND-space). The algorithm then repeats this process by starting
its second pass with the second point in the original time series, its
third pass with the third point, and so on, until terminating the
detrending process when the filter window requests a subseries
analysis that extends beyond the last point of the original time series
data. All values stored at x-value locations are then averaged to
produce the final, detrended time series sequence of values. When
the method is applied, the averaging of the sequential linearly
detrended subseries acts to remove the trend from the data.
Further, if the data are divided by the SD, then variance
nonstationarity is also reduced.
The selection of an appropriate value for a filter window is critical
for successful application of this algorithm. For example, to
detrend circadian rhythms data that are recorded in units of hours,
a value for the filter window of 24 hours would be an appropriate
choice (assuming that the dominant rhythm exhibited by the data has
a period near 24 hours). Figures 11-18 and 11-19 visualize the output
of DTRNDANAL with input provided by the data sets from
Figures 11-14 and 11-15, respectively.
