Recurrence plots provide a unique way to visualize time-series data. In the right graph, we have the price of 3D Systems (DDD) from 2007 to now. On the left we have a recurrence plot (RP) of DDD’s price. RP’s are similar to a correlation heatmap:

- Each axis is time, the same time range as the price chart on the right
- The color of each point represents how similar the x time is to the y time in terms of price movement
- The plot is symmetric around a diagonal; Each time is most similar to itself by definition

**The darker the color the more similar the times**. **We can use a recurrence plot (RP) to visualize the effects of crashes over time**. Notice the cross pattern where x = 2011 and y = 2011? That is the fingerprint of the crash in DDD’s price in early 2011. There are crosses in 2013 and 2014 as well which correspond to severe declines during the same time periods.

The cross for each individual crash intersects those of other crashes. Notice how dark the patches are around the points **( x = 2011, y = 2013 )** and **(x = 2011, y = 2014)**? The RP is telling us that these periods were similar. Visual inspection of the stock chart can verify their similarity.

The first cross in the RP took about 4 years to occur. The next occurred 2 years later, then another in one year. **The time between successive boom-bust cycles is shortening.** We could be approaching what Didier Sornette would call a “phase-change.” This is a point where the price process fundamentally changes. You might also call it a crash.

Categories: Markets