My problem is that I have a state space model that I estimate using the Berndt–Hall–Hall–Hausman (BHHH) algorithm. The state space model is relatively simple in that the hidden part follows a pure AR(1) process.

From tests on simulated data I know I need a time series of 500 observations to get good convergence. However my empirical data set is only 375 observations, worse I need to be able to test the model in and out of sample so I have more like 188 observations!!

Just wondered what my best options are?

1.) Use a different optimization method and hope that it is more efficient (seems labor intensive to try and find the right optimizer)

2.) Use bootstrapping similar to what they have done in the question below:

Calculating confidence intervals via bootstrap on dependent observations

Will the bootstrapping allow me to get better convergence with smaller data sets? If so how much shorter data set can I use? If 500 are required for good convergence will bootstrapping give me similar convergence with 350 observations or even 188 observations?

Are there any other options I can try?



  • $\begingroup$ Do you mean that you need 500 observations in order to get convergence of the BHHH algorithm? I don't have experience with this algorithm but considering it is similar to a Gauss-Newton algorithm it sounds strange to me. Bootstrapping is not intended to improve the convergence of optimization algorithms, but maybe I misunderstood you question. $\endgroup$ – javlacalle Sep 29 '14 at 18:06

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