Segmented Regression
The segmented regression method determines the linear dependence of an output time series on an input time series for intervals defined by breakpoints. The method interpolates the point cloud of the input and output time series juxtaposed in an X-Y diagram using linear equations defined by the breakpoints.
You can select the number of breakpoints in the range from 1 to 1000 or calculate the optimal number in the range from 1 to 10.
The starting points for the breakpoint calculation are first determined and tested according to a given formula. After that, iterations are performed with random numbers within the intervals.
Apply Method
To start the method, select the Analyze split button in the Analyze group in the Method ribbon and there the entry Segmented Regression (see following figure).
Alternatively, you can start the method via the context menu of the time series in the project explorer.
In the window that opens (see the following figure), select the time series for the model output and the model input from the drop-down lists respectively.
You can specify the number of breakpoints under settings or let them select automatically.
You can change the suffix for the file name of the newly created time series.
Click Apply to start the method.
After finishing the method, a new time series with the selected suffix is stored in the project explorer under temporary time series (see following figure).
This newly generated time series contains the function values calculated with the regression function from the input time series, in the example shown: the heat output resulting from the function determined by the regression in which the fuel output was inserted, this is an approximation of the heat time series used in the regression.
Result
As a result, the names of the selected input and output time series and as formulas the linear functions for the respective sections are displayed (see the following figure).
In addition, the coordinates for the breakpoints are given. The first and the last row in the table show the boundary points. For n breakpoints, n+1 equations and n+2 rows for the coordinates are displayed in the table.
In the field statistic characteristics, the statistic values R2, AIC, and BIC are displayed.
An error message (see following figure) appears if there is an invalid input (for example in case of constant or identical input and output time series) or the result does not converge (for example due to unfavorable randomly chosen starting points for the calculation).
Due to the random choice of the starting points for the calculation, the results can be different when running the method several times under the same conditions. For example, with a higher number of selected breakpoints, the first attempt may be successful while the second attempt may indicate an error because the result may not converge. This tends to occur with a comparatively high number of breakpoints and is related to the fact that convergence depends, among other things, on how well the random start positions are chosen during the iterations. Accordingly, the number of breakpoints calculated in automatic mode is often not a global result, but only the best possible within this trial.
