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I am working on calibrating a Heston model from simulated historical stock data.

After obtaining an accurate estimate of the model parameters I found very large 95% confidence intervals for these estimations if the sample size is about 10-15 years.

In view of the graph below, how would you choose the ideal sample size?

kappa vs. time

A 5-10 years period seems small since a large confidence interval means that there is a large uncertainty about the estimation. On the other hand, it appears useless to accept a sample size for which the confidence interval is small (50 years) since shorter periods provides good enough estimates.

I am a little confused as to how to interpret these results.

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1 Answer

Unless it is due to random chance, there seems to be a bias in your estimation method for $\kappa$, and this bias appears to depend on the size of the sample. This may be revealing a deeper underlying problem with your technique that will ultimately make it clearer what the tradeoff is between accuracy and sample size. I do not believe it should be the case that a shorter sample-size yields a more accurate estimate in a simulation where you can be certain the data generating process has not changed.

In practice, though, you will want to use as long a sample as possible over which you can be reasonably sure the underlying DGP has not changed. I would also suggest trying to obtain higher frequency data. Unless your time scale here is arbitrary, it will be difficult to justify an estimate based on 20+ actual years of stock market data.

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Thank you very much sheegaon for your helpful answer. Actually, there is no error on the above graph, the confidence bounds are built with the aid of a CLT for weakly dependent processess so the convergence is very very slow –  Beer4All Sep 8 '11 at 7:03
    
The suspected error is in the calibrated parameter (red line), not the CI. –  Tal Fishman Sep 8 '11 at 12:03
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