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Recurrence Analysis Output |
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The output of the Recurrence Analysis command is as follows:
| 1. | One recurrence plot for each of the selected series of up to 1024x1024 pixels. |
 | In the case where the number of points exceeds 1024, the given points are re-sampled equidistantly from the original series in state-space. |
| 2. | The following Recurrence Quantification Analysis (RQA) statistics: |
Series |
Epoch |
DIS |
REC |
DET |
ENT |
MAXLINE |
TREND |
<Series Number> |
<Epoch Number> |
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<Epoch Number> |
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"Entire Series:" |
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<Series Number> |
<Epoch Number> |
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"Entire Series:" |
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<Series Number> |
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Where epoch numbers correspond to each of the data windows that where constructed for the operation. The given statistics are interpreted as indicated by the related literature:
| DIS | Mean Distance between the embedded points. |
| REC | Recurrence -- quantifies the percentage of the plot occupied by recurrent points. It corresponds to the proportion of pair-wise distances below the chosen threshold among all the computed distances. |
| DET | Determinism -- is the percent of recurrent points that appear in sequence, forming diagonal line structures in the distance matrix. |
| ENT | Entropy, defined in terms of the Shannon formula for information entropy, computed over the distribution of the length of the lines of recurrent points and measures the richness of deterministic structure within the series. |
| MAXLINE | Is the length, in terms of consecutive points, of the longest recurrent line in the plot. This length was found to accurately predict the value of the largest Lyapunov exponent in a logistic map going from regular to chaotic regime (LYAP =  ). |
| TREND | Is the regression coefficient of the relation between time (in terms of the distance from the main diagonal) and the amount of recurrence. It is a least squares regression from the diagonal to the plot’s corner as a measure of stationarity. A flat slope indicates strong stationarity, whereas large slopes indicate poor stationarity due to changing values from one portion of the plot to another. |
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