theta & Hss

Warning:
1) There is no typo in the title. Post is no way related to any snake or any snaky-Mallika.
2) Post is too clumsy; you shouldn't enter, if you don't want to get lost in notations. One reason I am writing this is just to note down my repeated absent-mindedness (RAM), and make a record of it.


All it is related to is, estimation of parameter in a process driven by fBM, which is certain kind of H-ss process... and then my stupidness.. which lead to mere waste of more than 15 days of CPU time.


So here goes a detailed account :
We are working on,  to be very precise, on estimation of two parameters of a process driven by Hss (H-self similar) process. So the two parameters we were interested in were theta and the Hurst parameter, H. We were studying two different procedure simultaneously; and at this stage a simulation study is being carried out for both of them.

Some 20 odd days back, we were almost through the procedure for estimation of theta. It involved the calculation of a function in some grid for theta. Since I simulated the process from a known theta, at the first place, so I choose the closer grid. I thought, if original theta is 7 why not take grid of values in  [6, 8]. So I made the R program on the run, keeping the other parameter, H, constant.

In the meanwhile we got almost certain with the steps for estimation of H. Now for this parameter the range is (0,1). I was checking things out, sometimes for 0.6 sometimes 0.7. So far so good.

So when the program for theta turned up, it gave the estimate as 6.47. All of a sudden I felt like slapping myself. I thought the original theta is 0.6. What a fool I am to estimate in range [6, 8]; should have been [0.6, 0.8]. (Note: I hope by now reader must have already noted first instance of my RAM.)  So, now the only thing that could be done was to ask the R to redo it. As an obedient assistant, it started the work.

Now today morning, when I came to the department, I saw R smiling at me with the result. This time it was something 0.637. Well, it took 2 mins for me to realize that the original theta is 7. So the program which I did on first place was correct; and it was the parallel estimation of H (running in my mind) that confused me. to select the wrong grid later. OK, so up till now it looks like I was not at much of a loss, since I still had the previous simulation's result; which was supposedly correct. Now the big surprise is yet to come, which will be the 2nd and final instance of my RAM.

It took me some 10 minutes to realize that the original theta which I was using in simulation was 5 which could neither be in [6, 8] nor in [0.6, 0.8]. At least as far as we go by the norms of Real Analysis.



PS: Well, in case, despite of the warning, someone still dared to enter the irritating territory of this post, I am no way responsible for any kind of mental damage you suffered. Still, on humanitarian grounds, I express my deep sympathy for you.