MSVARSetup—Markov switching support procedures

[TomDoan]

@MSVARSetup pulls in the Markov switching support procedures for VAR's. This is mainly designed to deal with the more complicated "Hamilton" type model, where the switch is in the mean. All other types of switches can also be handled by the @MSSYSRegression procedures, which have the additional flexibility of allowing variables other than just the lagged dependent variables into the model.

Detailed description

[hungufm]

Dear Tom,
May I ask you a question related to MS-VAR.

According to paper Walid & Duc (2014) http://www.ipagcn.com/wp-content/upload ... 14_388.pdf

Two variables, stock and exchange returns. I do not know how to estimate correlation coefficients between two regimes. And the rest of the number of the Table 4.

Please take a little time to help me. I have a look at some replication example in connection with MS-VAR. But I cannot see these coeffients.

I am looking forward to hearing from you,

Ngo

[TomDoan]

That's not the correlation "between" regimes, it's the residual correlation within each regime. With regime-dependent covariance matrices, you estimate two separate covariance matrices, sigmav(1) and sigmav(2). All those are are the correlations implied by those two covariance matrices. Similarly, the standard deviations are just the square roots of the variances in those.

[hungufm]

Hi Tom,

Your instruction would be appreciated,

I would attach simple data consisted of 2 variables. Please give me an example code to estimate the similar outcome of above paper. MS(2)-VAR(2)

Please help me. The sample paper of Krolzig is different.

I am looking forward to hearing from you,

Ngo

[TomDoan]

You have to use a "heteroscedastic" MS-VAR in order to get those as in the WBC_MULTIVARIATE_PT2.RPF in the Krolzig examples.

[hungufm]

Dear Tom,

May you send me the paper: "International business cycles : regime shifts in the stochastic process of economic growth"

I cannot find it, so i have not understood the coding.

Please send the paper to email: hung.ngothai@gmail.com

Thank for your kind assistance,

Ngo

[hungufm]

Hi Tom,

According to your guide, I have run the MS-VAR model with two variables.
r1 = c +Phi r1(-1) +Phi r1(-2) +Phi r11(-1)+ Phi r11(-2) + e
I see from the output. There are two regimes, but according to the above paper, they reported only one regime. Which one can i choose?
Correlation coefficient between r1 and r11 in tow regimes? Please tell me how can i estimate these?

I cannot see probability P11, p22 as well, And average duration?

I find the text: http://fmwww.bc.edu/ec-p/software/ox/Msvardoc.pdf

I run the sample example. But the outputs are too different.

Here is my coding for the case r1, r11

Code: Select all

OPEN DATA "C:\Users\Ngo Hung\Desktop\Arab\data.xls"
DATA(FORMAT=XLS,ORG=COLUMNS) 2000:11 2018:3 R1 r11 
source msvarsetup.src
calendar(q) 2000
compute gstart=2000:11,gend=2018:3
@msvarsetup(lags=1,states=2,switch=mh)
# r1 r11
@msvarinitial gstart gend
@msvarEMgeneralsetup
do emits=1,50
   @msvaremstep gstart gend
   disp "Iteration" emits "Log Likelihood" %logl
end do emits
set smoothp1 gstart gend = pstar=%MSVARMarginal(msvarptsm(t),0),pstar(1)
graph(footer="Recession/Expansion Mode")
# smoothp1
@msvarinitial gstart gend
input mu(1)
 1.0791 2.2775 1.1262 0.8986 1.4590 1.4466
input mu(2)
 0.4754 0.9462 0.4926 0.3707 0.6757 0.6141
@msvarEMgeneralsetup
do emits=1,100
   @msvaremstep gstart gend
   disp "Iteration" emits "Log Likelihood" %logl
end do emits
set smoothp1 gstart gend = pstar=%MSVARMarginal(msvarptsm(t),0),pstar(1)
graph(footer="End of Golden Age")
# smoothp1
*
* Full sample ML which finds that same "End of Golden Age mode".
*
nonlin(parmset=varparms) mu phi sigmav
nonlin(parmset=msparms) theta
gset pt_t  gstart gend = %zeros(nexpand,1)
gset pt_t1 gstart gend = %zeros(nexpand,1)
frml msvarf = log(%MSVARProb(t))
@msvarinitial gstart gend
maximize(parmset=varparms+msparms,$
  start=%(p=%mslogisticp(theta),pstar=%MSVARInit()),$
  reject=%minvalue(MSVARTransProbs)<0.0,method=bfgs,iters=400) msvarf gstart gend
*
* Clean up the ML results by using the EM likelihood
*
@msvarEMgeneralsetup
do emits=1,10
   @msvaremstep gstart gend
   disp "Iteration" emits "Log Likelihood" %logl
end do emits
set smoothp1 gstart gend = pstar=%MSVARMarginal(msvarptsm(t),0),pstar(1)
Iteration 1 Log Likelihood     -50.99242
Iteration 2 Log Likelihood     -26.91860
Iteration 3 Log Likelihood     -22.83758
Iteration 4 Log Likelihood     -19.58104
Iteration 5 Log Likelihood     -17.82397
Iteration 6 Log Likelihood     -16.62990
Iteration 7 Log Likelihood     -15.25152
Iteration 8 Log Likelihood     -14.46483
Iteration 9 Log Likelihood     -14.11782
Iteration 10 Log Likelihood     -13.85962
Iteration 11 Log Likelihood     -13.69781
Iteration 12 Log Likelihood     -13.64178
Iteration 13 Log Likelihood     -13.62990
Iteration 14 Log Likelihood     -13.62783
Iteration 15 Log Likelihood     -13.62748
Iteration 16 Log Likelihood     -13.62741
Iteration 17 Log Likelihood     -13.62740
Iteration 18 Log Likelihood     -13.62739
Iteration 19 Log Likelihood     -13.62739
Iteration 20 Log Likelihood     -13.62739
Iteration 21 Log Likelihood     -13.62739
Iteration 22 Log Likelihood     -13.62739
Iteration 23 Log Likelihood     -13.62739
Iteration 24 Log Likelihood     -13.62739
Iteration 25 Log Likelihood     -13.62739
Iteration 26 Log Likelihood     -13.62739
Iteration 27 Log Likelihood     -13.62739
Iteration 28 Log Likelihood     -13.62739
Iteration 29 Log Likelihood     -13.62739
Iteration 30 Log Likelihood     -13.62739
Iteration 31 Log Likelihood     -13.62739
Iteration 32 Log Likelihood     -13.62739
Iteration 33 Log Likelihood     -13.62739
Iteration 34 Log Likelihood     -13.62739
Iteration 35 Log Likelihood     -13.62739
Iteration 36 Log Likelihood     -13.62739
Iteration 37 Log Likelihood     -13.62739
Iteration 38 Log Likelihood     -13.62739
Iteration 39 Log Likelihood     -13.62739
Iteration 40 Log Likelihood     -13.62739
Iteration 41 Log Likelihood     -13.62739
Iteration 42 Log Likelihood     -13.62739
Iteration 43 Log Likelihood     -13.62739
Iteration 44 Log Likelihood     -13.62739
Iteration 45 Log Likelihood     -13.62739
Iteration 46 Log Likelihood     -13.62739
Iteration 47 Log Likelihood     -13.62739
Iteration 48 Log Likelihood     -13.62739
Iteration 49 Log Likelihood     -13.62739
Iteration 50 Log Likelihood     -13.62739
Iteration 1 Log Likelihood   -1854.42867
Iteration 2 Log Likelihood     -31.81295
Iteration 3 Log Likelihood     -31.81274
Iteration 4 Log Likelihood     -31.81273
Iteration 5 Log Likelihood     -31.81273
Iteration 6 Log Likelihood     -31.81273
Iteration 7 Log Likelihood     -31.81273
Iteration 8 Log Likelihood     -31.81273
Iteration 9 Log Likelihood     -31.81273
Iteration 10 Log Likelihood     -31.81273
Iteration 11 Log Likelihood     -31.81273
Iteration 12 Log Likelihood     -31.81273
Iteration 13 Log Likelihood     -31.81273
Iteration 14 Log Likelihood     -31.81273
Iteration 15 Log Likelihood     -31.81273
Iteration 16 Log Likelihood     -31.81273
Iteration 17 Log Likelihood     -31.81273
Iteration 18 Log Likelihood     -31.81273
Iteration 19 Log Likelihood     -31.81273
Iteration 20 Log Likelihood     -31.81269
Iteration 21 Log Likelihood     -31.69565
Iteration 22 Log Likelihood     -25.84197
Iteration 23 Log Likelihood     -23.31138
Iteration 24 Log Likelihood     -22.92901
Iteration 25 Log Likelihood     -22.84728
Iteration 26 Log Likelihood     -22.83739
Iteration 27 Log Likelihood     -22.83646
Iteration 28 Log Likelihood     -22.83638
Iteration 29 Log Likelihood     -22.83637
Iteration 30 Log Likelihood     -22.83637
Iteration 31 Log Likelihood     -22.83637
Iteration 32 Log Likelihood     -22.83637
Iteration 33 Log Likelihood     -22.83637
Iteration 34 Log Likelihood     -22.83637
Iteration 35 Log Likelihood     -22.83637
Iteration 36 Log Likelihood     -22.83637
Iteration 37 Log Likelihood     -22.83637
Iteration 38 Log Likelihood     -22.83637
Iteration 39 Log Likelihood     -22.83637
Iteration 40 Log Likelihood     -22.83637
Iteration 41 Log Likelihood     -22.83637
Iteration 42 Log Likelihood     -22.83637
Iteration 43 Log Likelihood     -22.83637
Iteration 44 Log Likelihood     -22.83637
Iteration 45 Log Likelihood     -22.83637
Iteration 46 Log Likelihood     -22.83637
Iteration 47 Log Likelihood     -22.83637
Iteration 48 Log Likelihood     -22.83637
Iteration 49 Log Likelihood     -22.83637
Iteration 50 Log Likelihood     -22.83637
Iteration 51 Log Likelihood     -22.83637
Iteration 52 Log Likelihood     -22.83637
Iteration 53 Log Likelihood     -22.83637
Iteration 54 Log Likelihood     -22.83637
Iteration 55 Log Likelihood     -22.83637
Iteration 56 Log Likelihood     -22.83637
Iteration 57 Log Likelihood     -22.83637
Iteration 58 Log Likelihood     -22.83637
Iteration 59 Log Likelihood     -22.83637
Iteration 60 Log Likelihood     -22.83637
Iteration 61 Log Likelihood     -22.83637
Iteration 62 Log Likelihood     -22.83637
Iteration 63 Log Likelihood     -22.83637
Iteration 64 Log Likelihood     -22.83637
Iteration 65 Log Likelihood     -22.83637
Iteration 66 Log Likelihood     -22.83637
Iteration 67 Log Likelihood     -22.83637
Iteration 68 Log Likelihood     -22.83637
Iteration 69 Log Likelihood     -22.83637
Iteration 70 Log Likelihood     -22.83637
Iteration 71 Log Likelihood     -22.83637
Iteration 72 Log Likelihood     -22.83637
Iteration 73 Log Likelihood     -22.83637
Iteration 74 Log Likelihood     -22.83637
Iteration 75 Log Likelihood     -22.83637
Iteration 76 Log Likelihood     -22.83637
Iteration 77 Log Likelihood     -22.83637
Iteration 78 Log Likelihood     -22.83637
Iteration 79 Log Likelihood     -22.83637
Iteration 80 Log Likelihood     -22.83637
Iteration 81 Log Likelihood     -22.83637
Iteration 82 Log Likelihood     -22.83637
Iteration 83 Log Likelihood     -22.83637
Iteration 84 Log Likelihood     -22.83637
Iteration 85 Log Likelihood     -22.83637
Iteration 86 Log Likelihood     -22.83637
Iteration 87 Log Likelihood     -22.83637
Iteration 88 Log Likelihood     -22.83637
Iteration 89 Log Likelihood     -22.83637
Iteration 90 Log Likelihood     -22.83637
Iteration 91 Log Likelihood     -22.83637
Iteration 92 Log Likelihood     -22.83637
Iteration 93 Log Likelihood     -22.83637
Iteration 94 Log Likelihood     -22.83637
Iteration 95 Log Likelihood     -22.83637
Iteration 96 Log Likelihood     -22.83637
Iteration 97 Log Likelihood     -22.83637
Iteration 98 Log Likelihood     -22.83637
Iteration 99 Log Likelihood     -22.83637
Iteration 100 Log Likelihood     -22.83637

MAXIMIZE - Estimation by BFGS
Convergence in    34 Iterations. Final criterion was  0.0000036 <=  0.0000100

Quarterly Data From 2002:03 To 2018:03
Usable Observations                        65
Function Value                       -13.2735

    Variable                        Coeff      Std Error      T-Stat      Signif
************************************************************************************
1.  MU(1)(1)                     -0.177468454  0.382220736     -0.46431  0.64242652
2.  MU(1)(2)                     -0.007123944  0.033935022     -0.20993  0.83372312
3.  MU(2)(1)                      0.425749305  0.192034387      2.21705  0.02661986
4.  MU(2)(2)                     -0.000382178  0.008439696     -0.04528  0.96388144
5.  PHI(1)(1,1)                   0.388793480  0.128952146      3.01502  0.00256961
6.  PHI(1)(2,1)                   0.002485919  0.010521583      0.23627  0.81322432
7.  PHI(1)(1,2)                   0.426116513  1.054140707      0.40423  0.68604275
8.  PHI(1)(2,2)                   0.023142041  0.113906457      0.20317  0.83900445
9.  SIGMAV(1)(1,1)                1.305255135  0.424961571      3.07147  0.00213010
10. SIGMAV(1)(2,1)               -0.039342009  0.040675421     -0.96722  0.33343494
11. SIGMAV(1)(2,2)                0.028444657  0.008369630      3.39856  0.00067743
12. SIGMAV(2)(1,1)                0.536546587  0.140894346      3.80815  0.00014001
13. SIGMAV(2)(2,1)                0.010385164  0.006355302      1.63409  0.10223902
14. SIGMAV(2)(2,2)                0.002305342  0.000549614      4.19447  0.00002735
15. THETA(1,1)                    2.032411063  0.696489886      2.91808  0.00352197
16. THETA(1,2)                   -2.859502897  0.729210147     -3.92137  0.00008805

Please give me comments

[TomDoan]

Dear Tom,

May you send me the paper: "International business cycles : regime shifts in the stochastic process of economic growth"

I cannot find it, so i have not understood the coding.

Please send the paper to email: hung.ngothai@gmail.com

Thank for your kind assistance,

Ngo

I don't seem to have a PDF of that any longer (just a hard copy), and it looks like it was never published (none of Krolzig's subsequent papers look like they would be a renamed version of that). I would try contacting Prof. Krolzig if you want that.

[TomDoan]

Hi Tom,

According to your guide, I have run the MS-VAR model with two variables.
r1 = c +Phi r1(-1) +Phi r1(-2) +Phi r11(-1)+ Phi r11(-2) + e
I see from the output. There are two regimes, but according to the above paper, they reported only one regime. Which one can i choose?
Correlation coefficient between r1 and r11 in tow regimes? Please tell me how can i estimate these?

I cannot see probability P11, p22 as well, And average duration?

I find the text: http://fmwww.bc.edu/ec-p/software/ox/Msvardoc.pdf

I run the sample example. But the outputs are too different.

Could you be more specific about what you mean---you seem to be talking about two different papers plus your own model so it's not clear to what some of your comments apply.

The paper that you posted does two regimes---I'm not sure why you think it doesn't. The theta's in your output are the logistic coding for the transition probabilities---that's described in Section 11.7.2 of the User's Guide. p(2,2) is just 1-p(1,2); we don't use p11 and p22 for the two transition probabilities because that doesn't generalize to more than two regimes. Expected durations are simple functions of the transition probabilities---the expected duration of a stay in regime 1 is 1/(1-p11).

[hungufm]

Hi Tom,
According to this paper: (https://www.sciencedirect.com/science/a ... 1913000792).

With the output here:
Variable Coeff Std Error T-Stat Signif
************************************************************************************
1. MU(1)(1) -0.177468454 0.382220736 -0.46431 0.64242652
2. MU(1)(2) -0.007123944 0.033935022 -0.20993 0.83372312
3. MU(2)(1) 0.425749305 0.192034387 2.21705 0.02661986
4. MU(2)(2) -0.000382178 0.008439696 -0.04528 0.96388144
5. PHI(1)(1,1) 0.388793480 0.128952146 3.01502 0.00256961
6. PHI(1)(2,1) 0.002485919 0.010521583 0.23627 0.81322432
7. PHI(1)(1,2) 0.426116513 1.054140707 0.40423 0.68604275
8. PHI(1)(2,2) 0.023142041 0.113906457 0.20317 0.83900445
9. SIGMAV(1)(1,1) 1.305255135 0.424961571 3.07147 0.00213010
10. SIGMAV(1)(2,1) -0.039342009 0.040675421 -0.96722 0.33343494
11. SIGMAV(1)(2,2) 0.028444657 0.008369630 3.39856 0.00067743
12. SIGMAV(2)(1,1) 0.536546587 0.140894346 3.80815 0.00014001
13. SIGMAV(2)(2,1) 0.010385164 0.006355302 1.63409 0.10223902
14. SIGMAV(2)(2,2) 0.002305342 0.000549614 4.19447 0.00002735
15. THETA(1,1) 2.032411063 0.696489886 2.91808 0.00352197
16. THETA(1,2) -2.859502897 0.729210147 -3.92137 0.00008805

1. How can I calculate the correlation coefficient between r1 and r11 in each regime?
2. As your comment, theta's coefficient is transaction probability, why these value are greater than 1?

Your guide would be appreciated,
Ngo

[TomDoan]

1. How can I calculate the correlation coefficient between r1 and r11 in each regime?

Again, it's not the correlation between r1 and r11, but between their residuals in the two regimes. sigmav(1) is the covariance matrix in regime 1 (which would be the high volatility regime) and sigmav(2) is the covariance matrix in regime 2. Just convert the information in that to the implied correlation. (They presumably estimated the model using the two standard deviations and the correlation rather than using the equivalent covariance matrix).

2. As your comment, theta's coefficient is transaction probability, why these value are greater than 1?

Those are not the transitition probabilities themselves, but the logistic parameterization of the transition probabilities. p(1,1)=exp(theta(1,1))/(1+exp(theta(1,1)), similarly for theta(1,2). Again, that's described in the User's Guide.

[hungufm]

Hi Tom,
I understand.

Thank you so much for your kind help.

[TomDoan]

Note that the paper you are citing describes a MS-VAR with switching lag coefficients but fixed intercepts (which is not a good idea) then apparently actually estimates a model with fixed lag coefficients and only switching variances---I didn't read it word for word, but it's not clear to me where they explained why they did that. It's not that that's necessarily a bad choice (with @MSVARSETUP you would do that with the SWITCH=H option), as their emphasis is on volatility switching anyway. However, you need to realize that the model they describe in the paper does not seem to be the model they actually estimate.

[ManfredE]

Dear Mr. Doan. I am trying to estimate a Hamilton Switching Model by using the Hamilton.RPF example and procedures included in chapter 11 of the RATS User’s Guide (version 9.0). I’ve got some results for the probabilities of recession of my GDP series (quarterly Costa Rican, 1977Q1-2019Q1). In general parameter estimates are not reasonable, which leads to probabilities of recessions and booms that are not completely in line with the periods of recession and booms usually accepted for that data series.

I’ve come to suspect that might be due to a different average growth rate during booms and recession in the first part of my sample (1977 – 1990). Whatever the reason for that, I think that if I modify the equation that describes the evolution of the state dependent mean growth (“mu” in the User’s Guide) to explicitly allow for that difference, I would be able to get better results.

As I understand, “mu” is modeled in Hamilton.RPF as:
mu_st = mu_0 (1 - S_t) + mu_1 (S_t). Where S_t might be 0 or 1 depending on the state of the model.

What I want to do is to define a dummy variable (D_t), which equals zero for the first part of my sample (1977-1990) and one otherwise. Then set:
mu_st = (mu_0 + mu*_0 D_t) (1 - S_t) + (mu_1 + mu*_1 D_t) (S_t).

You can notice that this would allow the model to have a different mean growth rate during booms and recessions in the first part of my sample.
My question is, what part of the procedure described in the Hamilton example of chapter 11 should I change to be able to make such modification?

[TomDoan]

You might want to look at @MSRegression instead. The "Hamilton" model isn't as flexible when it comes to any change to the mean function. With @MSRegression, you can have CONSTANT D and lags as your regressors and fix the first two (or not, depending upon whether you think the dynamics might be different as well). It's not quite the same---in the Hamilton model, the mu is the process mean so when the regime changes, the mean changes immediately, while with a MS regression, the change to the intercept causes a gradual change. However, in most cases, the change to the intercept actually fits better (and the model is simpler on top of that).