Time Series Name Notation

 

A large number of different time series can be analyzed, loaded from files, or generated by standardization, segmentation or resampled data generation. To keep track of the time series names unique notation is used in order to identify different time series that are generated on the basis of a time series or file. The full name of each time series is comprised by the file name upon loading followed by specific notation for the different operations on the time series.

Each parameter used in the time series operations is identified by a character, as shown in the first column in the table below.

The parameters may bear only a single value or a range of values given in standard matlab syntax, e.g. 1:10 or [1 5:10 20] (see second column in the table).

The parameters may be constrained to specific ranges, as given in the third column of the table.

 

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).