Transform
Time Series
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Multiple time series
can be selected and each selected time series is standardized or
transformed. For standardization the user can use any of the following four standardization types:
1. Gaussian: The rank ordering function from the sample
marginal distribution to marginal Gaussian distribution is applied.
For transformation, there are four types: The first of the four transforms attempts to make the magnitudes of the time series Gaussian while the other three transforms aim to reduce non-stationarity of the time series. First differences or logarithm of first differences, as well as polynomial detrending, aims at removing the slow drifts in the time series. Lag differences may be used to reduce the effect of periodicity if the selected lag matches the period of the cycle in the data. |
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Select one or more time series ... |
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Multiple time series names can be selected from this list. This can be done by standard use of the mouse: a click on the first name and Shift^click on the last name selects all names between the first and the last name; a click on the first name and subsequent Ctrl^clicks on other names select these names including the first name; Ctrl^a selects the whole list. | |
Standardization types |
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Any of the four
standardization types, or even all standardization types (along with
selected transformation types) can be
selected. The standardization types are briefly explained below. Gaussian : A rank ordering function from the sample marginal distribution to marginal Gaussian distribution is applied. Let x(i), i = 1,...,N, the selected time series. The position plotting transform estimates the marginal cumulative density function (cdf) as F(x(i)) = ((i)-0.326)/(N+0.348), where (i) is the order of x(i) in the N sample of the time series. Then the Gaussian standardization transform reads y(i) = Ö-1(F(x(i)), where Ö-1 is the inverse marginal Gaussian cdf. Uniform : A rank ordering function from the sample marginal distribution to marginal Uniform distribution is applied. Let x(i), i = 1,...,N, the selected time series. The position plotting transform estimates the marginal cumulative density function (cdf) as F(x(i)) = ((i)-0.326)/(N+0.348), where (i) is the order of x(i) in the N sample of the time series. Then the Unifrom standardization transform reads y(i) = F(x(i). Linear [0,1] : The samples of the time series are linearly transformed so that the minimum is transformed to 0 and the maximum to 1. Let xmin and xmax the minimum and maximum of the time series x(i), i = 1,...,N. Then the Linear standardization transform reads y(i) = (x(i) - xmin) / (xmax - xmin). Normalized (or z-score) : The samples of the time series are transformed linearly so that they have mean zero and standard deviation 1. Let m and SD the mean and standard deviation of the samples of the time series x(i), i = 1,...,N. Then the Normalized standardization transform reads y(i) = (x(i) - m) / SD. |
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Transformation types |
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Any of the four
transformation types, or even all transformation types (along with
selected standardization types) can be
selected. The transformation types are briefly explained below. Log-difference: This transform takes the first differences of the natural logarithms of the time series. If the time series contains negative value(s) then the logarithm transform is applied as y(i)=log(x(i)-xmin+1), for each value x(i) of a given time series, where xmin is the minimum value of the time series. Then the transform reads y(i)-y(i-1). Box Cox : This is the Box Cox power transform and requires a parameter lambda. The transform is (x(i)^lambda-1)/lambda if lambda is not zero, and log(x(i)-xmin+1) if lambda is zero, where xmin is the minimum value of the time series. For the lambda parameter the user can give multiple values (according to the standard matlab format for forming arrays) and then the time series is transformed with the Box Cox formula for each lambda value. Differencing : The transform of differencing for a given order (lag) t is defined as x(i)-x(i-t) (for t=1 this is the common first difference). For the order parameter the user can give multiple values (according to the standard matlab format for forming arrays) and then equally many differenced time series are obtained for each order. Detrend : This is the detrending of the time series with a polynomial. First a polynomial of a given degree is fitted to the time series and then the fitted values are subtracted from the corresponding values of the time series. For the polynomial degree parameter the user can give multiple values (according to the standard matlab format for forming arrays) and then equally many detrended time series are obtained for each polynomial degree. |
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OK |
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By pressing this button, the standardizations of the selected time series starts and when it is completed the window is closed. | |
Cancel |
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The window is closed without segmenting any time series. | |
Help |
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This page is displayed. |