Time Series Name
Notation |
Character |
Number
follows |
Operation |
Description (N=length of time series) |
C |
yes |
Load time series |
the index following 'C'
denotes the column of the data matrix when loading a file with multiple
columns. |
S |
yes |
Segment time series |
the index following 'S'
denotes the order of the time series segment in the series of segments
when splitting the original time series. |
n |
yes |
Segment time series |
length of each segment
when segmenting the time series. |
s |
yes |
Segment time series |
sliding step in the
generation of segments, when s=n there is no overlapping of segments,
when s<n there is overlapping, and when s>n
there are gaps in the time series not assigned to a segment. |
B |
no |
Segment time series |
when there are residuals
after splitting the original time series to segments of length n, the
unused residuals are taken from the beginning (B) of the original time
series. |
E |
no |
Segment time series |
when there are residuals
after splitting the original time series to segments of length n, the
unused residuals are taken from the beginning of the original time
series |
G |
no |
Transform time
series |
denotes the "Gaussian"
standardization of the time series, resulting in a time series with
Gaussian marginal distribution |
L |
no |
Transform time
series |
denotes the "Linear"
standardization of the time series, resulting in a time series with
minimum 0 and maximum 1 |
N |
no |
Transform time
series |
denotes the "Normalized"
or z-score standardization of the time series, resulting in a time
series with mean 0 and standard deviation 1 |
U |
no |
Transform time
series |
denotes the "Uniform"
standardization of the time series, resulting in a time series with
Uniform marginal distribution |
O |
no |
Transform time
series |
denotes the "Log-difference"-transform of the time series
taking first the natural logarithm of the data (setting first the minimum of the time
series to 1 if it contains negative values) and then the first
differences. |
D |
yes |
Transform time
series |
denotes the "Detrending"
of the time series. A polynomial of a given degree is fitted and the
detrended time series is the residual of the fit. |
T |
yes |
Transform time
series |
denotes the "Lag
difference"
of the time series for a given lag, so that the new component at time t
is x(t)-x(t-lag) |
X |
yes |
Transform time
series |
denotes the "Box-Cox"
power transform of the time series for a given parameter lambda (suitable for
normalizing the time series), which is denoted as integer lambda*100,
e.g. for lambda=1.71 the filename will have 'X171'. If lambda=0 the
transform is the natural logarithm (setting first the minimum of the time
series to 1 if it contains negative values) |
RP |
yes |
Resampled time series |
Randomly Permutated
(RP) resampled (surrogate) time series; only the marginal distribution is
preserved and the RP time series is otherwise random. |
FT |
no |
Resampled time series |
Fourier Transform
(FT) resampled (surrogate) time series; only the power spectrum or
equivalently the autocorrelation is preserved and the FT time series is
otherwise random. |
AAFT |
yes |
Resampled time series |
Amplitude Adjusted
Fourier Transform (AAFT) resampled (surrogate) time series; the power spectrum,
equivalently the autocorrelation, and the marginal distribution are
preserved (under conditions) and the AAFT time series is otherwise
random. |
IAAFT |
yes |
Resampled time series |
Iterated Amplitude
Adjusted Fourier Transform (IAAFT) resampled (surrogate) time series;
the the power
spectrum, equivalently the autocorrelation, and the marginal
distribution are preserved and the IAAFT time series is otherwise
random. |
STAP |
no |
Resampled time series |
Statically Transformed
Autoregressive Process (STAP) resampled (surrogate) time series; the power
spectrum, equivalently the autocorrelation, and the marginal
distribution are preserved and the STAP time series is otherwise random. The algorithm uses two parameters: the
degree of polynomial approximation (pol), and the order of
autoregressive model (arm). |
AMRB |
yes |
Resampled time series |
Autoregressive Model
Residual Bootstrap (AMRB) resampled (bootstrap) time series; the the power
spectrum, equivalently the autocorrelation, and the marginal
distribution are preserved (the later not exactly) and the AMRB time
series is otherwise random. The algorithm uses
one parameter: the order of autoregressive model (arm). |