Re: [Scilab-users] Grocer - Markov Switching model estimation

[Éric Dubois]

Hello Christian.

The fact that your data are annuel does not have any influence except for the 
definition of the bounds if your data are Grocer Time series and you do not 
want to use the maximum time span.

If your data are called mydata and whethrer they are Grocer Time series or a 
vector, then you may run:
--> r=ms_var('all',1,mydata,2,2,1)

(Run : Help ms_var for détails)

Éric

Envoyé de mon iPhone

> Le 13 juin 2015 à 01:53, Cristian  a écrit :
> 
> Hello everyone, I try to estimate a MS with Grocer . I have *annual data*. I
> have read the chapter 23 (manual), where I found an perfect example for
> quartely data. Even though, I have alredy a doubt. 
> 
> The chapter 23 gives us an example to etimate a MS-AR(3). The specification
> is the following:
> 
> r=ms_reg('100*(lpbi-lagts(2,lpbi))',['100*(lagts(1,lpbi)-lagts(3,lpbi))';...
> -->'100*(lagts(2,lpbi)-lagts(4,lpbi))';'100*(lagts(3,lpbi)-lagts(5,lpbi))'],'cte',nb_states,switch_var,var_opt,'transf=stud',...
> -->'prt=initial;final')
> 
> So, the question is: How should I modify that expression in order to
> estimate a MS-AR(1) with anual data? 
> 
> Thanks in advance
> 
> Cristian
> 
> 
> 
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[Scilab-users] Grocer - Markov Switching model estimation

[Cristian]

Hello everyone, I try to estimate a MS with Grocer . I have *annual data*. I
have read the chapter 23 (manual), where I found an perfect example for
quartely data. Even though, I have alredy a doubt. 

The chapter 23 gives us an example to etimate a MS-AR(3). The specification
is the following:

r=ms_reg('100*(lpbi-lagts(2,lpbi))',['100*(lagts(1,lpbi)-lagts(3,lpbi))';...
-->'100*(lagts(2,lpbi)-lagts(4,lpbi))';'100*(lagts(3,lpbi)-lagts(5,lpbi))'],'cte',nb_states,switch_var,var_opt,'transf=stud',...
-->'prt=initial;final')

So, the question is: How should I modify that expression in order to
estimate a MS-AR(1) with anual data? 

Thanks in advance

Cristian



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Re: [Scilab-users] Grocer / Markov Switching Model

[ericdoblas]

Thank you very much Éric!!

Best regards 
Eric



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Re: [Scilab-users] Grocer / Markov Switching Model

[Eric Dubois]

Correction: what I propose is correct from a syntaxical point a view but
nonsensical from an economic one. Run rather:

-->
r=ms_reg('100*(lpbi-lagts(2,lpbi))',['100*(lagts(1,lpbi)-lagts(3,lpbi))';'100*(lagts(2,lpbi)-lagts(4,lpbi))';'100*(lagts(3,lpbi)-lagts(5,lpbi))'],'cte',nb_states,switch_var,var_opt,'transf=stud','prt=initial;final')

Éric.

2013/1/11 Eric Dubois 

> try:
>
> -->r=ms_reg('100*lpbi-lagts(2,lpbi)',['100*(lagts(1,lpbi)-lagts(3,lpbi))';'100*(lagts(2,lpbi)-lagts(4,lpbi))';'100*(lagts(3,lpbi)-lagts(5,lpbi))'],'cte',nb_states,switch_var,var_opt,'transf=stud','prt=initial;final')
>
> (you had 2 typos in your command)
>
> Éric.
>
> 2013/1/11 ericdoblas 
>
>>
>> r=ms_reg('100*lpbi-lagts(2,lpbi))','['100*(lagts(1,lpbi)-lagts(3,lpbi))';'100*(lagts(2,lpbi)-lagts(4,lpbi))';'100*(lagts(3,lpbi)-lagts(5,lpbi))'],'cte',nb_states,switch_var,var_opt,'transf=stud','prt=initial;final')
>>
>
>
>
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Re: [Scilab-users] Grocer / Markov Switching Model

[Eric Dubois]

try:
-->r=ms_reg('100*lpbi-lagts(2,lpbi)',['100*(lagts(1,lpbi)-lagts(3,lpbi))';'100*(lagts(2,lpbi)-lagts(4,lpbi))';'100*(lagts(3,lpbi)-lagts(5,lpbi))'],'cte',nb_states,switch_var,var_opt,'transf=stud','prt=initial;final')

(you had 2 typos in your command)

Éric.

2013/1/11 ericdoblas 

>
> r=ms_reg('100*lpbi-lagts(2,lpbi))','['100*(lagts(1,lpbi)-lagts(3,lpbi))';'100*(lagts(2,lpbi)-lagts(4,lpbi))';'100*(lagts(3,lpbi)-lagts(5,lpbi))'],'cte',nb_states,switch_var,var_opt,'transf=stud','prt=initial;final')
>
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Re: [Scilab-users] Grocer / Markov Switching Model

[ericdoblas]

Dear Éric,

I can solve all

Thank you so much for your help, and thank you for Grocer!!! It´s a
fantastic toolbox!!

Best regards from Argentina

Eric Doblas



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Re: [Scilab-users] Grocer / Markov Switching Model

[ericdoblas]

Dear Éric, 
I appreciate your great help.

I can load the data!!

I just need the last step. When I run

r=ms_reg('100*lpbi-lagts(2,lpbi))','['100*(lagts(1,lpbi)-lagts(3,lpbi))';'100*(lagts(2,lpbi)-lagts(4,lpbi))';'100*(lagts(3,lpbi)-lagts(5,lpbi))'],'cte',nb_states,switch_var,var_opt,'transf=stud','prt=initial;final')


I have

  !--error 276 
Falta operador, coma o punto y coma. (English: missing operator, comma or
dot and comma)

Thank you!

Best regards 
Eric




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Re: [Scilab-users] Grocer / Markov Switching Model

[Eric Dubois]

What if you change the comma in your file into a dot (the dot is the
decimal separator in Scilab)?

Éric.

PS:
1) if you use the file I have sent to you, then LPIB is equivalent to LnPBI
you want to load into Scilab
2) and log(GDP) too!

2013/1/11 ericdoblas 

> Hello Éric,
>
> I need only one step, because I was able to replicate your example.
>
> I can load the data:
>
> "Dates;LnPBI"
> "1993q1;12,2847456986185"
> "1993q2;12,3961633542544"
> "1993q3;12,3993569016157" .. so on.
>
> Then, I used impexc2bd, and after that, I loaded .dat file. But, I can´t
> run
> LnPBI.
>
> Thank you!
>
> Eric
>
>
>
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Re: [Scilab-users] Grocer / Markov Switching Model

[ericdoblas]

Hello Éric, 

I need only one step, because I was able to replicate your example.

I can load the data:

"Dates;LnPBI"
"1993q1;12,2847456986185"
"1993q2;12,3961633542544"
"1993q3;12,3993569016157" .. so on.

Then, I used impexc2bd, and after that, I loaded .dat file. But, I can´t run
LnPBI.

Thank you!

Eric



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Re: [Scilab-users] Grocer / Markov Switching Model

[Eric Dubois]

Take the file transformed as joined, store it say in folder c:/gdp and run
unde scilab
-->impexc2bd('c:\gdp\exemple.txt',';','c:\gdp\exemple.dat')

and do not forget to load the database:
--> load('c:\gdp\exemple.dat')

and run:
-->GDP

Éric.





2013/1/11 ericdoblas 

> Thank you Éric!
>
> Tha last consulting: Could you give me a example (or routine) to load my
> data (the first mail)?
>
> Best Regards
>
> Eric Doblas
>
>
>
>
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dates;GDP;LGDP
1993Q1;216370.1113;12.2847457
1993Q2;241871.8584;12.39616335
1993Q3;242645.5224;12.3993569
1993Q4;245132.4288;12.40955387
1994Q1;232945.3257;12.35855905
1994Q2;257476.8946;12.45868527
1994Q3;253467.7781;12.44299199
1994Q4;257341.5437;12.45815945
1995Q1;237968.1031;12.37989192
1995Q2;248093.6393;12.42156153
1995Q3;242214.6991;12.3975798
1995Q4;244467.9646;12.40683956
1996Q1;236566.0366;12.37398267
1996Q2;260751.9252;12.47132476
1996Q3;262166.9638;12.47673685
1996Q4;267020.0467;12.49507902
1997Q1;256387.8567;12.45444664
1997Q2;281769.8008;12.54884571
1997Q3;284092.2675;12.55705435
1997Q4;287515.3456;12.56903151
1998Q1;271702.3677;12.51246251
1998Q2;301207.5978;12.61
1998Q3;293315.4036;12.58900377
1998Q4;286267.8493;12.56468319
1999Q1;265024.6359;12.48757807
1999Q2;286412.3269;12.56518775
1999Q3;278472.6935;12.53707528
1999Q4;283566.3992;12.55520159
2000Q1;264555.9181;12.48580792
2000Q2;285275.1759;12.56120952
2000Q3;276767.971;12.53093478
2000Q4;278091.6764;12.53570611
2001Q1;259199.8739;12.46535476
2001Q2;284795.7629;12.55952758
2001Q3;263126.5054;12.4803902
2001Q4;248864.5552;12.42466407
2002Q1;216849.495;12.28695882
2002Q2;246314.6332;12.41436499
2002Q3;237416.8668;12.37757281
2002Q4;240361.3921;12.38989887
2003Q1;228595.8824;12.33971102
2003Q2;265402.4777;12.48900274
2003Q3;261534.5226;12.47432157
2003Q4;268560.9668;12.50083323
2004Q1;254330.4234;12.44638958
2004Q2;284375.6106;12.55805122
2004Q3;284392.0599;12.55810906
2004Q4;293467.0606;12.58952068
2005Q1;274594.5026;12.52305075
2005Q2;313927.2903;12.65691668
2005Q3;310593.0805;12.64623891
2005Q4;319939.2408;12.67588638
2006Q1;298695.5617;12.60718015
2006Q2;338243.7275;12.731522
2006Q3;337741.8852;12.73003723
2006Q4;347578.7074;12.75874641
2007Q1;322448.8712;12.68369986
2007Q2;367492.3517;12.81445779
2007Q3;367538.7276;12.81458397
2007Q4;379199.6613;12.84581816
2008Q1;349945.3229;12.7655322
2008Q2;396227.2401;12.88974316
2008Q3;393039.23;12.88166471
2008Q4;394564.9401;12.88553902
2009Q1;357096.4155;12.7857611
2009Q2;393181.2789;12.88202605
2009Q3;391678.8883;12.87819762
2009Q4;404860.9562;12.91129897
2010Q1;381221.6341;12.8511362
2010Q2;439766.5937;12.9939994
2010Q3;425323.1724;12.96060456
2010Q4;442208.8085;12.99953747
2011Q1;419023.1666;12.94568149
2011Q2;479963.6782;13.08146571
2011Q3;464882.753;13.04954051
2011Q4;474414.821;13.06983737
2012Q1;440884.2806;12.99653772
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Re: [Scilab-users] Grocer / Markov Switching Model

[ericdoblas]

Thank you Éric!

Tha last consulting: Could you give me a example (or routine) to load my
data (the first mail)?

Best Regards

Eric Doblas




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Re: [Scilab-users] Grocer / Markov Switching Model

[Eric Dubois]

To load data, you have many solutions. For time series I recommend to store
your data in a .txt file, transform the dates in a suitable format (that is
1993q1, 1993q2, etc.), set the name of the corresponding column to "dates"
and use impexc2bd (see impexc2bd). And have a look at chapter 5 of the
manual (as well as chapters 1, 2 and 3  which can also be helpful before
starting any econometric estimation).

For the second question, using one of the functions ms_var, ms_reg or
ms_mean indicates that you are estimating a Markov-switching model: there
rare not other steps inovolved!

Lastly, I do not understand what you mean by "conditioning the var-cov
matrix"; if by this, you mean that the var-cov matrix is different
according to the state of the economy, then give as 3rd argument of
function ms_mean of 5th argument of function ms_reg the number of states
you assumes the economy can experience (this is what is done in the example
provided in ms_reg_d() with the instruction :"switch_var=2 // variances are
switching").

Éric.


PS : turnpoints is a subroutine used by the brybos program, therefore not
relevant for Markov-switching estimation

2013/1/10 ericdoblas 

> Dear Éric,
>
> The following information is  in you example, but I have a lot of doubts,
> for exmple:
>
>
> - How to load the data?
> - How indicate it is MSM?
>
>
> I hope you can help me!!
>
> Thank you very much!
>
> Eric Doblas
>
>
> function [bcp,bct] = turnpoints(y,k)
>
> // PURPOSE: rough selection of peaks and troughs indexes
> //-
> // INPUT:
> // . y = vector of data
> // . k = x(t-i)>x(t) & x(t+i)>x(t), i=1:k defines a trough at t
> //   x(t-i) //-
> // OUTPUTS :
> // . bcp = vector of peak indexes
> // . bct = vector of trough indexes
> //-
> // Translated to Scilab by E. Michaux (2005)
> // from Julien Matheron
> // Banque de France, centre de recherche, sept. 2002
>
> [T,n] = size(y);
> if Ty = y';
>[T,n] = size(y);
> end;
> v = zeros(T,n);
>
> // --
> // I. Defines the k-dependent logical
> // argument of the following "if-loops"
> // --
>
> s_up = "(y(i)>y(i-1))";
> s_do = "(y(i)
> for step = 2:k;
>s_up = joinstr(s_up,msprintf("&(y(i)>y(i-%d))",step),'+');
>s_do = joinstr(s_do,msprintf("&(y(i) end;
>
> for step=1:k
>s_up = joinstr(s_up,msprintf("&(y(i)>y(i+%d))",step),'+');
>s_do = joinstr(s_do,msprintf("&(y(i) end;
>
>
> // --
> // II. Defines peaks
> // --
>
> for i = k+1:T-k ;
>if evstr(s_up) then
>   v(i) = 1;
>end;
> end
> bcp = find(v>0)'; // selects indexes such that a peak occurs
>
> // --
> // III. Defines troughs
> // --
>
> v = zeros(T,n); // reinitializes v
>
> for i = k+1:T-k
>if evstr(s_do) then
>   v(i) = 1 ;
>end;
> end;
> bct = find(v>0)'; // selects indexes such that a trough occurs
> endfunction
>
>
>
>
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Re: [Scilab-users] Grocer / Markov Switching Model

[ericdoblas]

function r=ms_reg_d()
 
global GROCERDIR;
 
// demo of ms_reg

I sorry Éric, this is the routine.

How I can conditioning the var-cov matrix??

Thank you!!
Eric 


load(GROCERDIR+'\data\us_revu.dat')
 
bounds('1967m4','2004m2')
 
nb_states=2
switch_var=2 // variances are switching
var_opt=3 // unrestricted var-cov matrix
 
r=ms_reg('100*(log(us_revu)-lagts(2,log(us_revu)))',['100*(lagts(1,log(us_revu))-lagts(3,log(us_revu)))';...
'100*(lagts(2,log(us_revu))-lagts(4,log(us_revu)))';'100*(lagts(3,log(us_revu))-lagts(5,log(us_revu)))'],'cte',nb_states,switch_var,var_opt,'transf=stud',...
'prt=initial;final')
endfunction




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Re: [Scilab-users] Grocer / Markov Switching Model

[ericdoblas]

Dear Éric,

The following information is  in you example, but I have a lot of doubts,
for exmple:


- How to load the data?
- How indicate it is MSM?


I hope you can help me!!

Thank you very much!

Eric Doblas


function [bcp,bct] = turnpoints(y,k)
 
// PURPOSE: rough selection of peaks and troughs indexes
//-
// INPUT:
// . y = vector of data
// . k = x(t-i)>x(t) & x(t+i)>x(t), i=1:k defines a trough at t
//   x(t-i)y(i-1))";
s_do = "(y(i)y(i-%d))",step),'+');
   s_do = joinstr(s_do,msprintf("&(y(i)y(i+%d))",step),'+');
   s_do = joinstr(s_do,msprintf("&(y(i)0)'; // selects indexes such that a peak occurs
 
// --
// III. Defines troughs
// --
 
v = zeros(T,n); // reinitializes v
 
for i = k+1:T-k
   if evstr(s_do) then
  v(i) = 1 ;
   end;
end;
bct = find(v>0)'; // selects indexes such that a trough occurs
endfunction




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Re: [Scilab-users] Grocer / Markov Switching Model

[ericdoblas]

Dear Éric,

Thank you so much!

Any doubts, I will write again.

Best regards

Eric Doblas 



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Re: [Scilab-users] Grocer / Markov Switching Model

[Eric Dubois]

Dear Eric.

I have done my best to make Grocer ms programs use easy (help files, manual
and demos: did you have a look at the ms_reg_d.sci, ms_var_d.sci demos?).

So tell me what you do not understand?

Éric.

2013/1/10 ericdoblas 

> That´s ok Éric. Thank you!
>
> I will try to be more specific. In the chapter 23 (Grocer´s Manual) you
> wrote about MSM. I need estimate the most general model (ms_reg) and the
> two
> particulars cases: ms_mean and ms_var, for data sent in the first mail...
>
> Excuse me if the consultation is very elemental, but recently I am starting
> with Grocer MSM. I think that is a excellent tool for Scilab. Rigth now, I
> am investing time to learn .
>
> Thank you very much!
>
> Eric Doblas
> CONICET - Argentina
>
>
>
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Re: [Scilab-users] Grocer / Markov Switching Model

[ericdoblas]

That´s ok Éric. Thank you!

I will try to be more specific. In the chapter 23 (Grocer´s Manual) you
wrote about MSM. I need estimate the most general model (ms_reg) and the two
particulars cases: ms_mean and ms_var, for data sent in the first mail...

Excuse me if the consultation is very elemental, but recently I am starting
with Grocer MSM. I think that is a excellent tool for Scilab. Rigth now, I
am investing time to learn .

Thank you very much!

Eric Doblas
CONICET - Argentina



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Re: [Scilab-users] Grocer / Markov Switching Model

[Eric Dubois]

Sorry, but maybe you could be a little bit more explicit: I have not the
paper immediately available and Hamilton (1989) page 7 does not as such
speak very much...

Éric.

2013/1/10 ericdoblas 

> Dear Éric,
>
> Thank you for your answer. Specifically, I need estimate a MSM as in
> Hamilton (1989), as follows:
>
>   (page 7).
>
> Thank you very much!
>
> Greetings from Argentina!
>
> Eric Doblas 
>
>
>
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> http://mailinglists.scilab.org/Grocer-Markov-Switching-Model-tp4025635p4025642.html
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Re: [Scilab-users] Grocer / Markov Switching Model

[ericdoblas]

Dear Éric,

Thank you for your answer. Specifically, I need estimate a MSM as in
Hamilton (1989), as follows:

  (page 7).

Thank you very much!

Greetings from Argentina!

Eric Doblas  



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Re: [Scilab-users] Grocer / Markov Switching Model

[Eric Dubois]

Dear Eric.

Could be more precise on the model you want to estimate? (The term
"Markov-switching model" is a generic one: you have to define the law of
your data under the regimes as well as the number of regimes you want to
estimate).

Anyway, there is another Scilab toolbox performing Markov-switching models
(HMM), but it does not seem to be maintained. And I think you will not find
other Scilab ressources corresponding to this kind of models.

Éric.

2013/1/9 ericdoblas 

> Hello all,
>
> I am using Markov Switching Model (MSM) to detect turning points. I can´t
> use Bry Boschan or Harding Pagan. I must use MSM. I don´t understand the
> manual´s instructions for Grocer. Specifically, I don´t understand all
> steps
> of the routine on grocer. So, I need a routine for MSM on Grocer.
>
> Thank you very much who can help me
> Eric Doblas
> Argentina
>
>
> This is the data:
>
> DateGDP LGDP
> I 93216370,1113 12,2847457
> II 93   241871,8584 12,39616335
> III 93  242645,5224 12,3993569
> IV 93   245132,4288 12,40955387
> I 94232945,3257 12,35855905
> II 94   257476,8946 12,45868527
> III 94  253467,7781 12,44299199
> IV 94   257341,5437 12,45815945
> I 95237968,1031 12,37989192
> II 95   248093,6393 12,42156153
> III 95  242214,6991 12,3975798
> IV 95   244467,9646 12,40683956
> I 96236566,0366 12,37398267
> II 96   260751,9252 12,47132476
> III 96  262166,9638 12,47673685
> IV 96   267020,0467 12,49507902
> I 97256387,8567 12,45444664
> II 97   281769,8008 12,54884571
> III 97  284092,2675 12,55705435
> IV 97   287515,3456 12,56903151
> I 98271702,3677 12,51246251
> II 98   301207,5978 12,61
> III 98  293315,4036 12,58900377
> IV 98   286267,8493 12,56468319
> I 99265024,6359 12,48757807
> II 99   286412,3269 12,56518775
> III 99  278472,6935 12,53707528
> IV 99   283566,3992 12,55520159
> I 00264555,9181 12,48580792
> II 00   285275,1759 12,56120952
> III 00  276767,971  12,53093478
> IV 00   278091,6764 12,53570611
> I 01259199,8739 12,46535476
> II 01   284795,7629 12,55952758
> III 01  263126,5054 12,4803902
> IV 01   248864,5552 12,42466407
> I 02216849,495  12,28695882
> II 02   246314,6332 12,41436499
> III 02  237416,8668 12,37757281
> IV 02   240361,3921 12,38989887
> I 03228595,8824 12,33971102
> II 03   265402,4777 12,48900274
> III 03  261534,5226 12,47432157
> IV 03   268560,9668 12,50083323
> I 04254330,4234 12,44638958
> II 04   284375,6106 12,55805122
> III 04  284392,0599 12,55810906
> IV 04   293467,0606 12,58952068
> I 05274594,5026 12,52305075
> II 05   313927,2903 12,65691668
> III 05  310593,0805 12,64623891
> IV 05   319939,2408 12,67588638
> I 06298695,5617 12,60718015
> II 06   338243,7275 12,731522
> III 06  337741,8852 12,73003723
> IV 06   347578,7074 12,75874641
> I 07322448,8712 12,68369986
> II 07   367492,3517 12,81445779
> III 07  367538,7276 12,81458397
> IV 07   379199,6613 12,84581816
> I 08349945,3229 12,7655322
> II 08   396227,2401 12,88974316
> III 08  393039,23   12,88166471
> IV 08   394564,9401 12,88553902
> I 09357096,4155 12,7857611
> II 09   393181,2789 12,88202605
> III 09  391678,8883 12,87819762
> IV 09   404860,9562 12,91129897
> I 10381221,6341 12,8511362
> II 10   439766,5937 12,9939994
> III 10  425323,1724 12,96060456
> IV 10   442208,8085 12,99953747
> I 11419023,1666 12,94568149
> II 11   479963,6782 13,08146571
> III 11  464882,753  13,04954051
> IV 11   474414,821  13,06983737
> I 12440884,2806 12,99653772
>
>
>
> --
> View this message in context:
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[Scilab-users] Grocer / Markov Switching Model

[ericdoblas]

Hello all,

I am using Markov Switching Model (MSM) to detect turning points. I can´t
use Bry Boschan or Harding Pagan. I must use MSM. I don´t understand the
manual´s instructions for Grocer. Specifically, I don´t understand all steps
of the routine on grocer. So, I need a routine for MSM on Grocer.

Thank you very much who can help me
Eric Doblas
Argentina


This is the data:

DateGDP LGDP
I 93216370,1113 12,2847457
II 93   241871,8584 12,39616335
III 93  242645,5224 12,3993569
IV 93   245132,4288 12,40955387
I 94232945,3257 12,35855905
II 94   257476,8946 12,45868527
III 94  253467,7781 12,44299199
IV 94   257341,5437 12,45815945
I 95237968,1031 12,37989192
II 95   248093,6393 12,42156153
III 95  242214,6991 12,3975798
IV 95   244467,9646 12,40683956
I 96236566,0366 12,37398267
II 96   260751,9252 12,47132476
III 96  262166,9638 12,47673685
IV 96   267020,0467 12,49507902
I 97256387,8567 12,45444664
II 97   281769,8008 12,54884571
III 97  284092,2675 12,55705435
IV 97   287515,3456 12,56903151
I 98271702,3677 12,51246251
II 98   301207,5978 12,61
III 98  293315,4036 12,58900377
IV 98   286267,8493 12,56468319
I 99265024,6359 12,48757807
II 99   286412,3269 12,56518775
III 99  278472,6935 12,53707528
IV 99   283566,3992 12,55520159
I 00264555,9181 12,48580792
II 00   285275,1759 12,56120952
III 00  276767,971  12,53093478
IV 00   278091,6764 12,53570611
I 01259199,8739 12,46535476
II 01   284795,7629 12,55952758
III 01  263126,5054 12,4803902
IV 01   248864,5552 12,42466407
I 02216849,495  12,28695882
II 02   246314,6332 12,41436499
III 02  237416,8668 12,37757281
IV 02   240361,3921 12,38989887
I 03228595,8824 12,33971102
II 03   265402,4777 12,48900274
III 03  261534,5226 12,47432157
IV 03   268560,9668 12,50083323
I 04254330,4234 12,44638958
II 04   284375,6106 12,55805122
III 04  284392,0599 12,55810906
IV 04   293467,0606 12,58952068
I 05274594,5026 12,52305075
II 05   313927,2903 12,65691668
III 05  310593,0805 12,64623891
IV 05   319939,2408 12,67588638
I 06298695,5617 12,60718015
II 06   338243,7275 12,731522
III 06  337741,8852 12,73003723
IV 06   347578,7074 12,75874641
I 07322448,8712 12,68369986
II 07   367492,3517 12,81445779
III 07  367538,7276 12,81458397
IV 07   379199,6613 12,84581816
I 08349945,3229 12,7655322
II 08   396227,2401 12,88974316
III 08  393039,23   12,88166471
IV 08   394564,9401 12,88553902
I 09357096,4155 12,7857611
II 09   393181,2789 12,88202605
III 09  391678,8883 12,87819762
IV 09   404860,9562 12,91129897
I 10381221,6341 12,8511362
II 10   439766,5937 12,9939994
III 10  425323,1724 12,96060456
IV 10   442208,8085 12,99953747
I 11419023,1666 12,94568149
II 11   479963,6782 13,08146571
III 11  464882,753  13,04954051
IV 11   474414,821  13,06983737
I 12440884,2806 12,99653772



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