Timeline for Simulating state space model with AR(1) dynamics
Current License: CC BY-SA 3.0
16 events
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| Jun 5, 2014 at 16:23 | comment | added | user12348 | As I mentioned in the update in my answer, you can use estimate() in ML for logL also, unless KF adds value then you can use it from there. But if you only have one empirical data set, then all you need to know from simulations is if the KF is working, then apply it to empirical data. Looks like you are getting mixed results from KF (?), then I would ditch it, do QRN MC, use antithetic variables, reduce error. This is all approximation. The low interest env may be change, then there goes the whole analysis-new dynamics. | |
| Jun 5, 2014 at 13:48 | comment | added | Bazman | also not working in HJM/LMM currently | |
| Jun 5, 2014 at 12:55 | comment | added | Bazman | The 3rd part should be OK given the suits of optimization tools in matlab (I hope) failing that I have good experience with differential evolution and other population based optimization techniques which are good for problems with multiple local minima (which these types of problem end to have.) | |
| Jun 5, 2014 at 12:55 | comment | added | Bazman | As the filter is obviously not able to estimate the process exactly but rather gives an optimal estimate (in the Kalman sense) based on the observed data, but I can obviously do the obvious things like check that the filtered results are closer to the signal than the noisy observations and that the estimated vol of the unobserved process converges (as it should for AR1/OU processes. Any further pointers you might have on how to test the KF part would be most welcome! | |
| Jun 5, 2014 at 12:50 | comment | added | Bazman | Thanks for the continued useful comments! I no longer think smoothing is the way to go, I will most likely use bootstrapping for the empirical part. The DNS/AFDNS models have been published in reputable journals and the mathematical basis for them is given there, I am assuming that is correct. To test them I generate simulated data based upon the assumed dynamics for the processes, think I'm getting there with this part. 2nd I need to apply the Kalman Filter and calculate the loglikelihood. This is implemented but it is a little difficult to test the implemtation. | |
| Jun 5, 2014 at 8:48 | comment | added | user12348 | you could also use Quasi RN with 100-300k MC runs with KF, you might see significantly better match up. Then you can use that process for empirical sets. However, empirical data set will have sample error, window selection errors etc. What you really want to do is forecast the parameters that you want to use. | |
| Jun 4, 2014 at 13:14 | history | edited | user12348 | CC BY-SA 3.0 |
modified the answer 3 to find the best simulated series
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| Jun 3, 2014 at 23:31 | comment | added | user12348 | can you summarize how you plan to implement the smoothing? Have you done HJM or LMM? How would you know if DNS or AFDNS is working? Have you documented your process and mathematical basis? | |
| Jun 3, 2014 at 12:18 | comment | added | Bazman | lse.ac.uk/statistics/documents/researchreport61.pdf | |
| Jun 3, 2014 at 12:17 | comment | added | Bazman | Ah nice idea! Let me check I understand you correctly for each simulated series I should apply the KF and calculate the LogL as in p 38 eq 3.19 of the paper I linked to in my second comment then apply AIC/BIC? Obviously by using the series which best matches the model parameters I give the optimizer the best chance to find the correct parameter values. That's fine for the testing but just thinking ahead I will only have one set of empirical data to work with would using a "simulation smoother" help in this case? | |
| Jun 3, 2014 at 10:57 | comment | added | user12348 | To find the best AR simulated series that best fits the parameters, check the LogL, or AIC/BIC (aicbic Matlab function) from estimate function in Matlab. KF will give you the best estimate implied in the simulated series. p-values wont help you here, you would get them from regression. | |
| Jun 3, 2014 at 10:06 | comment | added | Bazman | q3.) How do I calculate the p-value? | |
| Jun 3, 2014 at 10:05 | comment | added | Bazman | Q2 continued.) then compute the log-likelihood across all parameter values. As a final step the loglikelihood is used as the objective function for an optimization process to find the original variables. Right now I am simulating the AR(1) process and trying to apply the Kalman Filter/optimisation process but the results are not really that good even when i give the optimizer good initial guesses. Should this work? If not why not and how can I test the Kalman Filter/optimization scheme for this model set up? | |
| Jun 3, 2014 at 9:59 | comment | added | Bazman | Q2. The whole point of simulated the AR(1) process is so I can generate simluated data (i.e.) with known parameter values. Then fit the model shown at the bottom of p34 onwards here: pure.au.dk/portal-asb-student/files/48326397/…. As noted above I can check that the variance and means are correct across samples but any one individual sample will be subject to stochastic variation (and unfortunately in practice I can only use one sample). The idea is to estimate the mean and covariance of the state variable X using a Kalman filter, then to | |
| Jun 3, 2014 at 9:55 | comment | added | Bazman | Thanks!! 1 lag I will try it. Seems a little weird though> I can simulate the process 50 times (as shown in the first link) and then take the variance of the AR(1) process as different time steps for processes with a high auto-correlation value say 0.99 it cab take a few hundred steps before they settle to their steady state theoretical variance. It would seem that prior to this any estimation process is trying to hit a moving target? | |
| Jun 3, 2014 at 5:15 | history | answered | user12348 | CC BY-SA 3.0 |