I am working on a process which produces time series similar to the one shown in the graph below:
I calculated Fractal dimension $D$ and Generalised Hurst Exponent $H$, to confirm that equality $D=n+1-H$ holds for $n=1$.
I followed the line of reasoning in this paper, to conclude that this is indeed a self similar signal (with an $H \approx 0.8$ and $D \approx 1.2$).
Now, assuming that I have access to only a final portion of the signal, bounded in red box on the graph, the question is: How I can reconstruct the signal from $t=0$ to the beginning of the red box?