MS_Regress - A Package for Markov Regime Switching Models in Matlab

Functions to Estimate, Simulate and Forecast Markov Regime Switching Models in Matlab

Description

This submission provides functions (and examples scripts) for estimation, simulation and forecasting of a general Markov Regime Switching Regression.
 
Features of the package:
- Support for univariate and multivariate models.
- Support of any number of states and any number of explanatory variables.
- Estimation, by maximum likelihood, of any type of switching setup for the model. This means that you can choose which coefficients in the model, including distribution parameters, are switching states over time.
- A wrapper function for the estimation of regime switching autoregressive models, including multivariate case (MS-VAR) is included in the package.
- The values of standard error for the estimated coefficients can be calculated with 4 different methods.
- Includes a C version of hamilton’s filter that may be used for speeding up the estimation function (see pdf for details).
- Possibility of three distinct distribution assumptions for residual vector (Normal, t or GED).
- Support for reduced/constrained estimation (see pdf document for details).
- Loads of example scripts.
 
Limitations of the Package (so far):
- The EM algorithm is not implemented (all models are estimated by direct maximization of log likelihood function).
- It doesn’t support state space models with markov switching effects.
- It cannot estimate a model with time varying transition probabilities (TVPT).
- It doesn’t support models with garch type of filters for conditional volatility.
 
Here a few references in Markov Switching models:
   
ALEXANDER, C. (2008) ‘Market Risk Analysis: Practical Financial Econometrics’ Wiley.
BROOKS, C. (2002) ‘Introduction to Econometrics’ Cambridge University Press.
HAMILTON, J., D. (2005) Regime Switching Models. Palgrave Dictionary of Economics, (available at http://dss.ucsd.edu/~jhamilto/palgrav1.pdf )
HAMILTON, J., D. (1994) ‘Time Series Analysis’ Princeton University Press.
KIM, C., J., NELSON, C., R. (1999) State Space Model with Regime Switching: Classical and Gibbs-Sampling Approaches with Applications. The MIT press.
   
Make sure you read the file About_the_MS_Regression_Models.pdf within the downloaded zip file. There you can find details regarding the structure of the package, along with instructions of how to use it.
   
I also wrote a R/S+ version of the package (fMarkovSwitching). It is available within the Rmetrics project: http://r-forge.r-project.org/projects/rmetrics/.
   
Fell free to send any comments/suggestions to my email.

• Required Products: Optimization Toolbox; Statistics Toolbox
• MATLAB release: MATLAB 7.2 (R2006a)

Other Files

license.txt,
MS_Regress_FEX/About_the_MS_Regression_Models.pdf,
MS_Regress_FEX/Example_MS_Regress_Fit.m,
MS_Regress_FEX/Example_MS_Regress_Fit_GED_Dist.m,
MS_Regress_FEX/Example_MS_Regress_Fit_MSVAR.m,
MS_Regress_FEX/Example_MS_Regress_Fit_MultiVar.m,
MS_Regress_FEX/Example_MS_Regress_Fit_t_Dist.m,
MS_Regress_FEX/Example_MS_Regress_Fit_using_constCoeff.m,
MS_Regress_FEX/Example_MS_Regress_Fit_with_MEX.m,
MS_Regress_FEX/Example_MS_Regress_Simul_2_States_Multivar.m,
MS_Regress_FEX/Example_MS_Regress_Simul_3_States.m,
MS_Regress_FEX/Example_MS_Regress_Simul_and_Fit_2_States.m,
MS_Regress_FEX/Example_MS_Regress_Simul_and_Fit_3_States.m,
MS_Regress_FEX/Example_MS_Regress_Simul_Fit_2_States_Multivar.m,
MS_Regress_FEX/m_Files/build_constCoeff.m,
MS_Regress_FEX/m_Files/check_constCoeff.m,
MS_Regress_FEX/m_Files/checkInputs.m,
MS_Regress_FEX/m_Files/checkSize_constCoeff.m,
MS_Regress_FEX/m_Files/confuneq_MS_Regress.m,
MS_Regress_FEX/m_Files/doOutScreen.m,
MS_Regress_FEX/m_Files/doOutScreen_MSVAR.m,
MS_Regress_FEX/m_Files/doPlots.m,
MS_Regress_FEX/m_Files/getvarMatrix_MS_Regress.m,
MS_Regress_FEX/m_Files/mex_MS_Filter.cpp,
MS_Regress_FEX/m_Files/mex_MS_Filter.mexw32,
MS_Regress_FEX/m_Files/MS_Regress_Fit.m,
MS_Regress_FEX/m_Files/MS_Regress_For.m,
MS_Regress_FEX/m_Files/MS_Regress_Lik.m,
MS_Regress_FEX/m_Files/MS_Regress_Sim.m,
MS_Regress_FEX/m_Files/MS_VAR_Fit.m,
MS_Regress_FEX/m_Files/mvnpdf_MSPERLIN.m,
MS_Regress_FEX/m_Files/myMVNPDF.m,
MS_Regress_FEX/m_Files/nr3matlab.h,
MS_Regress_FEX/m_Files/param2spec.m,
MS_Regress_FEX/m_Files/preCalc_MSModel.m,
MS_Regress_FEX/m_Files/spec2param.m,
MS_Regress_FEX/matFiles/Example_FEX.mat,
MS_Regress_FEX/matFiles/GNP_Hamilton.mat,
MS_Regress_FEX/Script_Hamilton_Comparison.m

[PAUL SHIWAMYA]

 

[Han A]

Thank you. Very useful to start my own model.

[rao xhui]

thank you! it is useful to me!

[tt fan]

thanks!

[LONG FEI]

Thanks!!!

[Anton Shishkin]

This is really great. Thank you very much. Have you tried models with endogenous switching?

[Marcelo Perlin]

Hi Anton,

I'm the author.
Thanks for your comments, I really apreciate it.

Regarding your question, no I haven't tried endogenous switching.

Cheers.
Marcelo.

[leo song]

great!thanks your

[knani ramzi]

 

[Jonathan]

Hi, what kind of parameter evaluation approach you are using in this package? is it the EM algorithm?

[Marcelo Perlin]

Hi Jonathan,
The parameters are estimated by standard maximum likelihood procedure so, currently, the EM algorithm is not implemented.
I'll keep it in mind for the future.

Regards.
Marcelo.

[Jonathan]

thanks for the quick response. Generally speaking, the code is already very useful, good work.

[Bongju]

your program is useful. How can I draw the picture which compare realized y and predicted y according to data sequence?

[Elena Dumitrescu]

Hi, I'm new in using matlab, but I would need to use a Markov switching model with time varying probabilities, evolving as logistic functions of the independent variables (as in Diebold and Weinbach 1994) . Can you, please, tell me how can I use your program in order to do that?
Thank you!

[Marcelo Perlin]

Hi Elena,

Currently the package can't handle TVTP models as the transition matrix is assumed constant.

You'll have to modify the original code for this setup.

Regards.
Marcelo.

[Salman]

 

[gajd]

Hi, Marcelo,

I've tried the R-package. It shows a mistake. Can we discull the mistake here or is there a special R-forum for that?

Regards, Gajd

[Marcelo Perlin]

Hi gajd, fell free to contact me in my email.
Cheers.

[MehdiHK Hosseinkouchack]

Nice file, thanks. Although, there are cases for which the algorithm does not work. You need to impose more structure on transition prob matrix Also if there are 2 states then there are only 2 prob's entering the search space not 4. Having more states increases the dimensions very fast.

[MehdiHK Hosseinkouchack]

Well, I decided to recode things from the beginning. I think that the p-values are wrong which is because of the problem I mentioned before with the way you enter the probabilities into the search space. This is not just a dimension problem. When you calculate a numerical gradient, for the probability param's for example (for k=2), you change p11 while p12 is constant! In this case even if p11+p12 was 1, it will not be one when feeding it to the likelihood function!!
Another point is that you need to make sure that sum of the probabilities for state j (j=1,2,...,k) is 1. This is not guaranteed in your program.

[Marcelo Perlin]

Dear MehdiHK, regarding your first comment, the way I coded the optimization problem was jsut a matter of simplicity in the algorithm. I'm fully aware that the search space could be decreased by one elemente by conducting it as a inequality optimization problem, as opposed to an equality one.

For your second comments, the p values of the coefficients are fine and so is the way I coded the transition matrix.
If you look closelly in MS_Regress_Fit, you'll see that I'm using constrained estimation so that the each column of Coeff.p is summing to 1, according to my choice of numerical convergence.

If you have any further question, feel free to drop me an email.
Marcelo.

[MehdiHK Hosseinkouchack]

Dear Marcelo,

A) I am pretty sure that the probabilities do not sum up to the correct value. As a check: for a k=2 case, try to check if sum of all the elements in Coeff.p always is equal to 1 in all the cases!

B) About the search space, for a case of k=2, not that ONE parameters are more than enough, but that TWO are more than enough b/c P=[p11 p12; p21 p22] is identified if from each ROW exactly ONE element is know so 2 element is enough not 3. (you mentioned that 4 can be decreased by 1!!!)

C) ROWS should sum up to ONE not columns.

I closely looked into all of your codes. They are neat, but you have some mistakes that should be fixed.

Thanks a lot
Mehdi

[Marcelo Perlin]

MehdiHK,

For A), from what you wrote it seems that the the transition matrix in the reference you used has a different notation than mine. In short, my transposed transition matrix will be equal to yours. Therefore, for my code, you should be looking at columns for the full process in each state (and not rows).

For B), I was not clear. I meant the decrease of one element in each state. So we agree.

Regards.

[MehdiHK Hosseinkouchack]

Dear Marcelo,

This still does not solve the problem. I had a check on the probabilities: for k=2 I was checking if sum of the elements of the transition matrix adds up to 2, and it was not! well transposed or not transposed, rows or columns, does not matter now ...

For comment B decreasing search space based on my comment is agreed then.

Best of Wishes
MehdiHK

[MehdiHK Hosseinkouchack]

Dear Marcelo,

I would like thank myself from your side for finding a little bug in your code. It is, however, excellent! I appreciate your efforts.

Best of Wishes
MehdiHK

[andrea182]

great job!

I need help ...

I would like to create a function that given a vector of price variation I restore the prediction of the next price change ...

How could I do?

I think it's a very simple thing to do but this thing is making me crazy ...

thanks for any help ...

[Marcelo Perlin]

Hi Andrea,

I used to have a function to calculate forecasts from a model but, with the new updates, the funcionality was lost. I shall write a compatible one once I have the free time.

In the meanwhile, have a look in the references writen in the pdf file. Its all there.

Regards.
Marcelo.

[Aaron]

Awesome code. I am really trying to do something absurdly simple here, which might be the problem. I want to generate a univariate two-state Markov regime switching process, where the series is only related to a regime-dependent mean (e.g. the only independent variable is a column of ones). Can MS_Regress_Sim.m be used for this purpose>

[Marcelo Perlin]

Hi Aron,

Thanks for your comments.

Yes, the code can handle your specification. For that, just set the indepMean=1 and indepStd=0. This will do the trick.

Regards.

[Aaron]

Hi Marcelo,

Thanks...This is exactly as I thought...The problem is that there are no non-switching independent parameters in this case. Setting nS_param to the null vector produces an error

[Marcelo Perlin]

Aaron, yes, I got the same error. It seems to a be a simple problem whitin the code. I'll fix it and include in the new update.

Thanks for the letting me know about this.

Regards,
M. P.

[Saad]

Hi,

I am currently working on the MS VAR and I was wondering if anyone of you who have been using the MS_regress_fit got a standard error of zero and a p value of zero (just below the estimation of the coeffcients). The estimations of the coefficients of the MSVAR seem intuitive to me but I am surprised to have a standard error and a pvalue of zero? Any thoughts about this issue? Thanks in advance

[Alexey Malashonok]

Hi Marcelo,

I've tried to run a couple of examples from your package and got following error:
Error using ==> fmincon
FMINCON cannot continue because...
Variable 'indep_nS' is used as a command/function.

There is probably a mistake in the code with vector of n-S independent parameters in the likelihood function. Unfortunately, I could not find where the problem is.
Could you help please.

PS: Thanks a lot for this package.

[Marcelo Perlin]

Hi Alexey,

I've seen this before and it is a version issue (I wrote the code in matlab 2008).

For fixing it for you version, you'll have to search for the lines where the error was found and replace with equivalent, version compatible, lines.

Cheers.
Marcelo.

[Ansgar Walther]

Hi Marcelo,

I've been trying to extend your code to include time-varying transition probabilities. I think I've got it to work, which mainly involved a few changes to the coefficient structure and the Hamilton filter in the MS_Regress_Lik file. The only odd thing is that fmincon converges to local maxima that don't make sense, so I've used fminsearch instead.

It would be great if you could have a look at it to see whether what I've done makes any sense. Drop me an email ([e-mail]) if you're up for it.

Cheers,

Ansgar Walther

[Marcelo Perlin]

Hi Ansgar,
My replies by email.

M. P.

[Jorge]

Excelent! I would like to combine TVP Models with Regime Switching as Kim y Nelson, have you any model like this?

[Marcelo Perlin]

Hi Jorge,

Sorry but no, I don't have the code for regime switching time varying parameter model.

Regards.