User’s Guide

To install the program is sufficient to create a directory C:/NTSA where you have to copy the file ntsa.exe and to create 2 subdirectory called data and output. This is not necessary for the functioning of the program but is easier to use because the load and saving of files is directed there.

When NTSA appears there are 3 window:

• Input Window
• Output Window
• Program Window

In the Input Window appears the list of the time series that have been loaded by the user; to select the time series to analyze is necessary to click once on the name of the time series (you can cross-check the time series selected verifying the title of the main window: for example, "Nonlinear time series analysis – Logistic[x]").

In the Output Window are listed all the outputs of the program: each time series has a corresponding node in the output tree and all the results will be listed as sub-node of the time series tree. Double clicking on the sub-node you get the plot of the relative output. Right clicking on the sub-node you get a menu composed by: Plot - Export Data - Delete. With Plot you plot the output (the same as double clicking), with Export Data you can save the output as a text file (and you get a Save Dialog Box); finally, with Delete you cancel the output from the output tree.

The Program Window is composed by the following menu:

• File: you can load the time series and save the output of the program. The additional submenu Toolbar you can open the signal and output window (if they are not open yet).
• View: you can plot the time series, the delay plot and the phase plot; in addition you can choose how to manage the plot windows (Tile and Cascade).
• Basic Operations: you can take the logarithm of the time series, differentiate and log-differentiate.
• Linear: you can calculate the main statistics for the time series (mean, absolute deviation, standard deviation, skew, kurtosis); in addition the submenu ACF and PACF compute the ACF-PACF functions.
• Nonlinear: compute correlation integrals, Lyapunov exponent and nonlinear prediction error (described below).
• Noise: add noise to the selected time series.

Linear Tools

You can compute the autocorrelation function and the partial autocorrelation function. On the box that appears you have to select the lag up to which calculate the ACF or PACF function.

NonLinear Tools

1. Correlation Integral: when selected appears a window similar to this in the right; the parameter to select are as follows:

• Max. Dim.: maximum embedding dimension for which are calculated the correlation integrals (the number must be not less than 2).
• Max. Radium: the maximum radium up to which computations are done. A valid input is a number between 0 and 1.
• Num. Ref. Points: number of points considered; this number cannot exceed the length of the time series (Default: 1/3 of the length of the time series).
• Tau: delay time.
• Theiler Correction: correction in order to exclude points neighbors both in time and in space.
• Number of Division per bin: setting this parameter you choose the level of coarseness; you can only choose between 2, 4, 6, 8 (default: 4).

Exercise: for the Henon time series you should get a plot like the one in the right (try to reproduce the same plot: you can get most of the information you need from it!).

 

 

 

When the correlation integrals are calculated automatically in the Output box are added also the Correlation Dimension and the KS entropy (as a function of epsilon). A double click is necessary to plot these quantities.

 

When the correlation integral has been plotted, in the Program Window there are 2 new menu: Dimension Estimation and KS Estimate. Clicking on one of this menu you get the box shown below where you have to select the region where you want to calculate the dimension and KS entropy (as a function of the embedding dimension).

 

1. Lyapunov Exponent: calculate the maximal Lyapunov Exponent. In the box that appears you have to set the following parameters:

• Min./Max. Embedding Dimension: the minimum embedding should be not less than 2 and the maximal should be not less than the minimum e.d. .
• Number of step: the number of step ahead for which are calculated the distances (at least 1).
• Min. Eps: the minimal size of the neighborhood (between 0 and 1).
• Step of Eps: calculate the distances for each embedding dimension and for different epsilon such that: eps(i) = min. Eps * 2ⁱ for i=1,…, step of eps.
• Delay Time: at least 1.
• Nmin: Theiler correction (see Correlation Integral).
• Nfmin: minimum number of neighbors to be found by the algorithm in a neighborhood of size epsilon.
• Ncmin: number of points for which are calculated the distances.

 Exercise: again for Henon try to reproduce thesame plot as. Most of the parameter can be infered by the plot.

 

 

 

 

1. Nonlinear Prediction: calculate the prediction error with the nearest neighbors method. The box that appears has the following parameters:

• Embedding dimension: the usual parameter (at least 2).
• Delay time: at least 1.
• Prediction Steps: number of step ahead for which is computed the error.
• Size of Eps: size of the neighborhood for which are selected the neighbors (between 0 and 1). A small number for epsilon imply that the prediction error extract the nonlinearity in the data (if any!). For a value near 1 you get the prediction error of an auto-regressive model.
• Number of prediction: from the length of the time series are taken out this number of elements on which will be calculated the error (smaller than the length of the time series).

Each of the output can be plotted by double clicking on it. When a plot is activated, on the main menu there is an additional Menu called 2D-Diagram and the submenu Copy to Clipboard, Save As… and Print.