I have a graph which appears to be random but there seems to be a pattern hidden in it. How do I analyze it? The below graph seems to be random but I think the peaks seem to repeat after a certain period. Are there any statistical tools I can use to analyze this?

Edit:
I am adding the plot of its autocorrelation:


The plot that you made looks like using the function xcorr which computes an autocorrelation function without normalization.
$$R(l) = \sum_{\forall k:0\leq k \leq 800 \text{ and } 0\leq k+l \leq 800} R(k)\cdot R(k+l)$$
This is why you get this piramid shape. The number of terms in the sum changes/decline when the lag $l$ gets larger. This makes the sum become less.

If you normalize the function then you should get something like

This function can tell you whether there is a periodic behaviour. For instance there might be peaks repeating every 4 or 8/9 time points.
In my plot you see that the correlation is not very significant (the blue dotted lines point the boundary above/below which the correlations are significant). But, I sampled data from your image. If instead you do this with your raw data then the correlation might be stronger and the pattern could be more clear.
