# State Space models with Short Time Series

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:

https://stats.stackexchange.com/questions/14213/calculating-confidence-intervals-via-bootstrap-on-dependent-observations/14217#14217

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?

Thanks

Baz

• Without having a better sense of what you're trying to do, things I would try are 1) increasing frequency of data, 2) leave one out cross validation, 3) Bayesian methods. – John Aug 26 '14 at 20:29
• Thanks, the cross validation sounds like the simplest alternative. Problem with leave one out is that it's not possible to test a trading system on one observation? But I suppose I could make the hold out sample n (where n is enough to create a statistically signfificant number of trades say 15?). The other problem is that with this method I'd still need to use data points observed after the test period (in all but the last case) as part of the observation process would this not constitute data snooping? The very thing I am trying to avoid? Or have I misunderstood? – Bazman Aug 28 '14 at 16:13
• I was focusing on the estimation. Combining that with testing a trading strategy will introduce more complexity. No one right answer, I think. One thing I do sometimes is assume the model is true, then simulate a bunch of paths of data, and then run the trading strategy on simulated data and evaluate it way on the larger sample. Not sure if that makes sense in your case, because I'm really not sure what you're doing. – John Aug 28 '14 at 16:38
• I'm happy to supply more detail just let me know what you're not clear on. Basically though I have a state space model and it currently takes all of my available data to calibrate the model. However I need to be able to test it out of sample. Ideally I would test on empirical out of sample data. But I suppose failing that simulated out of sample data might be an option. – Bazman Aug 28 '14 at 17:34
• More to just get a sense if it's working the way that it should. – John Aug 28 '14 at 17:45