| In Markov examples, often seen in chaotic dynamics, the forbidden pairs tell the whole story: |
| any forbidden string must contain a forbidden pair. |
| This can be interpreted as placing a limit on the effects of history: only the immediately previous step is important. |
| Here is a simple combinatorial example of how addresses can be used to approach this problem. |
| We sketch two approaches to quantifying this notion. |
| First, we count the number of data points in each of the four bins. Next we create a surrogate data set having the same number of points in each bin as the original data set. Then we compare the length 2 addresses of the driven IFSs. |
| The second approach is to use the bin occupancy data to estimate the likelihood that longer addresses are empty. This involves a Markov chain calculation, so is a bit more mathematically demanding. |
| More detailed analyses can estimate the length of memory of a system, thus placing bounds on how far into the future we can predict. |
Return to Data-Driven IFS.