State-Space Model Convergence with Short Time Series

Summary

The document raises a practical estimation problem for a state-space model whose hidden state follows a pure AR(1) process. The author estimates it with the BHHH algorithm and reports that simulations suggest about 500 observations are needed for good convergence. The available empirical sample is shorter, and splitting it into in-sample and out-of-sample portions leaves roughly 188 observations for each part.

The author asks whether changing optimizers or bootstrapping dependent observations could help, and whether resampling might make a shorter sample behave like a longer one. The document gives no answer, comparative results, or specific alternative estimation procedure. Its central concern is the distinction between optimizer performance and the information available in a small sample: resampling can characterize sampling uncertainty, but it does not create new independent observations or guarantee better parameter-estimation convergence. The simulation result is specific to the stated model and setup, so it cannot establish a universal minimum sample size.

Key ideas

• The model’s hidden state is described as a pure AR(1) process.
• The author reports needing a longer simulated series for good BHHH convergence than the empirical data provide.
• An in-sample and out-of-sample split further reduces the observations available for estimation.
• The document asks whether optimizer choice or bootstrap methods could help, but provides no findings or recommendation.

Tags

# State Space models with Short Time Series


# 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

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.