How did you add the noise? The chart you showed does not look like it has enough noise.
In this case was the data perfect or did it have some random variations?
I think you are running into the repeating inputs problem for the TM. HTM does not predict that well, that’s why we used it primarily in anomaly detection applications. Making the data more random should help, I would think. You could also manually reset the TM at a preferred temporal cycle, which will hard-code the period into the system.