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 parameter's standard errors can be calculated with 2 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.
   
Before using the package, make sure you read the pdf file (About the MS_Regress_Package.pdf) in the downloaded zip file. A copy of this paper can be found in http://ssrn.com/abstract=1714016.
   
I also wrote a R/S+ version of the package (fMarkovSwitching). It is public available in the Rmetrics project: http://r-forge.r-project.org/projects/rmetrics/. Please be aware that the R version in no longer being maintained so it is actually an older version of the package with only the basic features.
   
Fell free to send any comments/suggestions to my email.

• Required Products: Optimization Toolbox; Statistics Toolbox
• MATLAB release: MATLAB 7.10 (2010a)

[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 M]

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.

[Flavio]

Marcelo, congratulations for your job in this package, it's the best markov switching program I saw so far!

However, I just can't find the package "fMarkovSwitching" you mentioned, it seems that it isn't available anymore in Rmetrics and in CRAN. I think it's a great lost for the R community.

Could you remake the package for the new R version and make it available ???

Thank you very much, It would be a great thing to have your package available for R.

[Marcelo Perlin]

Hi Flavio,
Tahnks for your comments, really apreciate it.

The fMarkovSwitching is still there, but the command:

install.packages("fMarkovSwitching", repos="http://R-Forge.R-project.org")

is somehow not working for any of the packages in rmetrics.
For instanlling it, dowload the source file from:

https://r-forge.r-project.org/R/?group_id=156

and go to R and install it from local source (the file you download).

Regarding making it available for new version of R, this is not from lack of will, but because the optimizer I use in the estimation (rdnlop2) is not compatible with R>2.8.

Regards,
Marcelo.

[Flavio]

Thank you for your reply!

But I install R 2.7.1 and try to install the package "fmarkovswitching" from the zip file you gave a link of, however i couldn't install it. It appears the following message:
"Warning in install.packages(choose.files("", filters = Filters[c("zip", : 'lib = "C:/PROGRA~2/R_2.7/R-27~1.1/library"' is not writable"

Is there any chance you change the optimizer you utilize in order to make it compatible with the new version?

At last, do you know any package or software that can do a 3 BAND-SETAR ?

Thanks again.

[Marcelo Perlin]

Hi Flavio,

Somethign is wrogn with your installation of R. I tried it here and it worked fine for R 2.8.1:

> utils:::menuInstallLocal()
package 'fMarkovSwitching' successfully unpacked and MD5 sums checked
updating HTML package descriptions

Regarding making it compatible for newer versions, I tried it in the past by working in the optimization fucntion, but the problem is that it is not writen in R native code, so this makes it difficult.

Regarding setar models, no, I'm not aware of any available package.

Regards,
Marcelo.

[Flavio]

Now I tried with R 2.8.1 version and it works.
Thank you very much.
I hope you keep making so useful and smart packages like this!
Regards.

[Muneer]

Hi,

Thanks for the package, it looks grreat! Is it possible to do a simple MS-ARMA or ARIMA with this? I'm a little new to matlab so sorry if the answer is obvious!

Also, are there any nice simple clean commands to do forecasting, or do I need to forecast manually? I couldnt see any examples using forecasting in the pdf.

Thanks again for a great package!

[Marcelo Perlin]

Hi Munner,

No, MS ARMA models are not supported, but MS AR models are.
I'll keep it in mind for introducing MA terms in upcoming new version.

Regarding forecasting, I'm working on a new forecasting function as we speak. Should be up in a few days.

Regards,
Marcelo.

[Muneer]

Hi Marcelo,

Thanks for the prompt reply! Glad to hear it is still being worked on and look forward to the update!

You wouldn't happen to know of any MS models that can handle MA terms would you? :)

Thanks for the great work!
Muneer

[Marcelo Perlin]

Hi Muneer,
No, I'm not aware of any software that can handle this type of specifications.
Perhaps you should contact the authors of the paper on MS-ARMA models. They might give you the code if you're convincing enough..

Cheers.

[Salman]

Excellent package...indeed a great service to matlab users

[Salman]

Would you be going foe VECM as well?

[Marcelo Perlin]

Hi Salman,

I have a greater plan of designing a proper interface for time series MS models which should include support for VECM specificatinos.

But, this is not in my short term agenda. Time is scarse this days and I don't know when I'll have the time for developing it.

Marcelo.

[Wei]

Thanks for providing this excellent package. It has been a starting point of my research.

[Alex Nikolov]

Marcelo, I would like first to thank you for the incredible package. I have a few questions though. I'm trying to generate a univariate two-state Markov regime switching process, where the series has a regime-dependent mean and regime-dependent variance. I set stock market returns in the first column of the input file (dependent variable), but I am not sure what should I set in the other columns of the input file? And can you tell me what should I give as input to the S in order to get what I have described above. Probably S = [1 1 1 1]? Thank you in advance for your help.

[Alex Nikolov]

Hi Marcelo. I'm sorry for the stupid questions, I figured them out myself. I just wanted to express my gratitude once again. The package just rocks!!!

[Marcelo Perlin]

Hi Alex.

I'm glad it all worked out.

All the best,
Marcelo.

[luching]

Hi Marcelo,

I am trying to estimate a structural VAR where both the coefficients and Var-Cov matrix are regime dependent. It looks like MS_VAR_fit always assumes that the reduced form error terms are independent of each other. Are there options that relax this assumption to allow for a more general Var-Cov matrix with non-zeros for the off-diagonal elements?

Luching.

[Marcelo Perlin]

Hi Luching,

There is a option in the algorithm for using a full covariance matrix in the estimation. Just use:

advOpt.diagCovMat=0;

meaning that you dont want a diagonal covariance matrix.

Cheers.
Marcelo.

[ss4johnny Hall]

In my experience the full covariance matrix estimation was quite slow, especially as the covariance matrix got bigger.

Anyway, is there any way to do a weighted markov regime-switching regression? For instance, if I have S&P500 data going back to 1929 and want to exponentially weight it so that the earlier data is less important.

Thanks

[Marcelo Perlin]

Hi Johnny,

Yes, it is natural that the algorithm is slower for a high number of equations in the system.

Regarding the smoothing, no, the package does not have a support for such procedure.

Regards,
Marcelo.

[luching]

Hi Marcelo,

I think with large no. of variables and/or lags, "MS_Regress_Fit_MSVAR" as expected does not really give precise estimates. I am trying to circumvent this problem by imposing certain restrictions on the coefficients, but NOT on the variance covariance matrix of the VAR. I see that "MS_Regress_Fit_MultiVar" on the other hand always imposes a diagonal variance covariance matrix. Is there a straightforward approach to resolve this?

Luching.

[Marcelo Perlin]

Hi Luching,

There is an option in MS_VAR_Fit for estimating the non diagonal elements of the covariance matrix. For the mentioned script, change line 15 to :

advOpt.diagCovMat=0;

Regards,
Marcelo.

[luching]

So, I was wondering if there is any way either using "MS_Regress_Fit_MultiVar" OR "MS_VAR_Fit" where I can have both features:
(1) non-diagonal elements on the var-cov
(2) restrictions on the coefficients, say for instance I want some coefficients not to be regime dependent.

[Marcelo Perlin]

Yes, it is possible because the main function MS_Regress_Fit has support for such. Have a look inside MS_VAR_Fit and you'll see that it just builds the lagged variables and pass the options and data to MS_Regress_Fit.

In order to place the constraints, which by way, have to be scalar values (e.g. beta_1=0) and not intervals (e.g. beta_1>0), you'll just have to implement the option structure inside MS_VAR_Fit.

Regards,
Marcelo.

[Ajax]

Hi Macelo,

I'm wondering why in "MS_Regress_Fit_MultiVar.m" when I impose a diagonal matrix (advOpt.diagCovMat=0) I'm receiving errors like:"input to SVD must not contain NaN or Inf".

Many Thanks
Apostolos

[Djibril TOGOLA]

Hi Marcelo,
I was very happy to see your code is referenced by hamilton (http://dss.ucsd.edu/~jhamilto/software.htm). So you have my best congratulations !
nevertheless it would be good to provide more details about your implementation process. It is easy to use your programs but difficult to know why you have created some functions and why you use them into some loops. So according to me more comments is all you need to be perfect.

Thank you so much !!!

Best regards,

Djibril

[Marcelo Perlin]

Hi Djibril,

Thanks for the rating.

Regarding the programming, the package became quite complex with the additional functionalities I implemented such as constrained estimation and multivariate models.

There are comments in the code, but I understand that these are not exactly helpful. I'll keep it in mind for the next update.

Regards,
Marcelo.

[Zack]

Thanks for the code,

could you please tell me what the conditionnal Std from the output graph is supposed to be
is that from a GARCH model?

[Marcelo Perlin]

Hi Zack,

The output in the plot is the standard deviation conditional on the states of the world. No, it is not from a garch model.

Marcelo.

[Shichang]

 

[Fuzhi Cheng]

Thank you very much for the code. Would you please advise (through an example) how to use this model to set up a trading rule and show how the trading results are (in terms of P/L, Sharpe ratio, etc) as compared to a random walk or other models?
Regards,
Fuzhi

[Marcelo Perlin]

Hi Fuzhi,

Thanks for the rating. You can find information about using ms models in a trading enviroment in the web. For example, have a look in this paper:

http://ideas.repec.org/a/eee/jbfina/v31y2007i2p279-296.html

Cheers,
Marcelo.

[Zack]

Hi Marcelo

Could you please give me the methode to calculate this conditionnal std deviation

Thanks a lot

[Marcelo Perlin]

Hi Zack, you can find this information in the references (see pdf file).

Cheers.
Marcelo.

[Zack]

thanks

[Fuzhi Cheng]

Obrigado Marcelo!

[Grigoras Veaceslav]

Hi Marcelo.
I was wondering if it is possible to do an impulse response analysis with MSVAR in this package.

[Marcelo Perlin]

Hi Grigoras,

Yes, it is possible since all estimated parameters are available to the user.

But this as well as others diagnostic procedures are not included in the package.

Marcelo.

[Sverrir]

Dear Marcelo

Thank you for pstoing your code, it is working really well!

I'm however having a slight problem regarding the covariance matrix.
Why in "MS_Regress_Fit_MultiVar.m" when I impose "advOpt.diagCovMat=0" I receive the following error:"input to SVD must not contain NaN or Inf".

Best regards
Sverrir

[Marcelo Perlin]

Hi Sverrir,

Sorry for the (very) late reply. I have been working on different things and time is scarse these days...

The error you got can be the combination of many thigns. Basically it says that the optimizer got stuck in a part of the log likelihood function and could not get out on its own. This can be the result of:

- bad starting coefficients
- data badly shaped (e.g. outliers)

So, my suggestion for you would be to check the data you are running the code.

Regards,
Marcelo.

[Giancarlo]

Thanks!

[Marie Bunckenburg]

Dear Marcelo,

First of all, thank you for posting your code.

I am very new in Matlab so I hope the question is ok.

I am trying to estimate a markov switching model to detect shift-contagion in financial markets.
Using your framework, is it possible to:
a) Decompose the errors into common and idiosyncratic structural shocks in order to test for cantagion
b) ensure that the timing of changes in volatility is endogenously estimated

My model draws on Gravelle, Kichian and Morley (2006).

Best regards,
Marie Louise

[Marcelo Perlin]

Hi Marie,

Sorry for the late reply.

I'm not familiar with the methodology, but if you can send me the equations of the model in pdf by email, I promiss to have a look.

Regards,
Marcelo.

[Thorsten Schmidt]

Marcelo,
I'm very excited about the prospect of using fMarkovSwitching for R.

I have installed it for R 2.8.1, unfortunately I can't run the package as I get "Error: package 'Rdonlp2' could not be loaded."

It seems that Rdonlp2 is no longer available for download at http://arumat.net/Rdonlp2/
due to some licensing issues between Rdonlp2 and DONLP2.

Do you have any recommendations as to what to do in this case...would fMarkovSwitching work with any other optimizers?
Rgds,
Thorsten Schmidt

[Marcelo Perlin]

Replied by email.

Cheers.

[Maria Sole]

Hi Marcelo.
Thanks for this code, it is very useful. By the way, I would like to know if it is possible to introduce some identification assumption concerning the errors (hence if I can run an MS SVAR).
Moreover, I would like to ask you why, whenever I try to use a full VarCov Matrix, I get this error for every type of data I may use:"input to SVD must not contain NaN or Inf".
Thanks,
Best
Maria Sole Pagliari

[Marcelo Perlin]

Hi Maria,

From the pdf file you can find a section on this error. Basically the problem is with the optimizaer. One simple solution I have seen to work is to divide the dependent variable by 100.

Regarding imposing identification, it is not possible unless you know the values beforehand.

Regards,
Marcelo.

[Maria Sole]

I tried to adopt that solution, but it keeps on giving me the same error. I think that this depends upon the type of data I'm using actually. Furthermore I noticed that if I use 4 variables in the model, the process simply gets stuck at a certain point and the optimization process simply stops without producing any output or error...

[Rendi Prasetya]

I tried to adopth this code for regime switching with chartist and fundamental model. like as at stefan reitz paper titled "central bank intervention and exchange rate expectations - evidence from the daily DM/US Dollar exchange rate". can you help me to use your code in that problem.

[Jiaqi Zhu]

It is of great help to me! Thank you a lot!

[Gilbert]

Hi Marcelo,
I am using your package to estimate a bivariate model. However, I use returns which are not normally distributed so I think I need to use t-distribution. Do you plan an update for the multivariate case with non-normal errors soon? Is there a modification I could make to use a different distribution for the multivariate case?
Thanks,
Gilbert.

[Marcelo Perlin]

Hi Gilbert,

Sorry but no plans for a multivariate t distribution so far.

If you are going to implement it, all you need to do place the new likelihood function for the mv t distribution in the code and also add the new parameters in the estimation process. The first part is trivial, the second will require some good coding skills.

Marcelo.

[Gilbert]

Hi Marcelo,
Thanks, will attempt to make the changes and see what happens. If I succeed, I will let you know so you can check if I did it correctly.
Once again thanks. Great program.
Gilbert.

[Marcelo Perlin]

Glad to help"

Btw, you can always check if the new code is working by comparing the results against simulated data. That is, simulate a bivariate process with t-dist innovations, fit with with the new function and check whether the parameters from the simulation and estimation match.

Regards,
Marcelo.

[ss4johnny Hall]

Marcelo,
I just ran across a paper by Gatumel and Ielpo called "The Number of Regimes Across Asset Returns: Identification and Economic Value". They use a rather simple test statistic to identify the number of regimes. Might be something simple to add to the program.

[Marcelo Perlin]

Thanks Johnny, I'll keep it in mind for future releases.

Cheers.

[yuxia zhang]

 

[Tim Kenyon]

Hi,

I have the same problem as Thorsten Schmidt above regarding DONLP2 for the fMarkovSwitching program in R. Is there any way around this problem?

Thanks,

Tim

[Marcelo Perlin]

Hi Tim,

I made an update to the package a while ago. I just tested it with R 2.14.2 and it is working fine.

Best,
Marcelo.