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# Resources

# Error G0008

While running the code "MAXSEEK" (downloaded from Hamilton's website), I get the following error. Hamilton said he did not face the following errors. Can someone please advise? Is there any option of attaching a file?

Line 153 in C:\gauss10\mrs\procs

Syntax error G0008 : 'endp'

Line 182 in C:\gauss10\mrs\MAXSEEK

Nested procedure definition G0155

Line 182 in C:\gauss10\mrs\MAXSEEK

Syntax error G0008 : 'proc matpm(xth)'

## 2 Answers

**MAXSEEK and PROCS codes are given below **

MAXSEEK

@ This GAUSS file reads in data, sets options, and calls numerical

optimization routine for numerical estimation of switching model @

output file=junk reset;

/* ======================================================================= */

@ Replace this first section with a section to read in your data

Example 1 reproduces the GNP results from Hamilton, "A New

Approach to the Economic Analysis of Nonstationary Time Series

and the Business Cycle," Econometrica, March 1989

Example 2 reproduces the interest rate results from Hamilton,

"Rational Expectations Econometric Analysis of Changes in Regime:

An Investigation of the Term Structure of Interest Rates," Journal

of Economic Dynamics and Control, June 1988

Example 3 reproduces the results for the French exchange rate in "Long

Swings in the Exchange Rate: Are They in the Data and Do Markets

Know It?" by Charles Engel and James D. Hamilton (AER, Sept. 1990).

Example 4 fits a three-state model to US real GNP data; estimation

algorithm bogs down due to bumping against corners with nonnegative

definite hessian; Example 5 reestimates with zeros imposed @

/*===============================================

EXAMPLE 1:*/

@ The following lines read in the raw data, and convert to

100 times the first difference of the log @

capt = 135; @ capt is the sample size @

load bbbb[capt+1,1] = C:\gauss10\swarch\gnp82.dat;

bbbb = bbbb[1:capt,1]~bbbb[2:capt+1,1];

y = 100*ln(bbbb[.,2]./bbbb[.,1]);

@ Adjust any of the following to control specification desired @

ns = 2; @ ns is the number of primitive states @

ps = 4; @ ps is the number of lagged states that matter

for y; use ps = 0 if only the current state

matters @

pphi = 4; @ pphi is the number of lags in autoregression

for y; pphi should be greater than or equal

to ps @

isig = 1; @ isig = 1 for constant variances,

isig =ns for changing variances @

ipm = 1; @ ipm specifies way in which transition probs

are parameterized

ipm = 1 implies p11 and p22 estimated

ipm = 2 implies pij for i=1,..,n j=1,..,n-1

ipm = 3 user input code @

a=0;b=0;c=0; @ These parameters control the Bayesian prior

as suggested in Hamilton, "A Quasi-Bayesian

Approach to Estimating Parameters for Mixtures

of Normal Distributions", Journal of Business

and Economic Statistics, January 1991. If

no Bayesian adjustment is desired, set all

parameters to zero @

/* Input initial values for parameters

The order in which variables are represented is as follows

first ns elements: means for states

next pphi elements: autoregressive coefficients

next isig elements: variances for states when izz =1

std. deviations for states when izz =2

next elements: when izz =1 these are the transition probs

when izz =2 these are params v(i,j) such that

p(i,j) = v(i,j)^2 / sum j v(i,j)^2

elements are ordered as p11, p22 when ns =2

ordered as p(1,1),p(2,1),...,p(ns,1),

p(2,1),...,p(ns-1,ns) when ns > 2 */

nth = 9; @ nth is the number of params to be estimated@

mu1 = 1; mu2 = 0; phi1 = .1; phi2 = 0; phi3 = 0; phi4 = 0;

sig = 1; p11 = 1.5; p22 = 1.5;

th = mu1|mu2|phi1|phi2|phi3|phi4|sig|p11|p22;

/* =============================================

EXAMPLE 2:

capt = 103;

load y[capt,1] = rradj.dat;

ns = 2;

ps = 4;

pphi = 4;

isig = 2;

ipm = 1;

a=0;b=0;c=0;

nth = 10;

mu1 = 2; mu2 = 1; phi1 = .9; phi2 = 0.; phi3 = 0.;

phi4 = 0; sig1 = .8; sig2 = .2; p11 = 1; p22 = 1;

th = mu1|mu2|phi1|phi2|phi3|phi4|sig1|sig2|p11|p22; */

/*==============================================

EXAMPLE 3

capt = 58;

load y[capt,3] = exdata.txt; @ this loads exchange rate data

for France, U.K. and Germany @

y = y[.,1]; @ this selects French data @

ns = 2;

ps = 0;

pphi = 0;

isig = 2;

ipm = 1;

a = .2; b = 1.0; c = .1;

nth = 6;

mu1 = 3; mu2 = -3; sig1 = 3; sig2 = 6; p11 = 2; p22 = 2;

th = mu1|mu2|sig1|sig2|p11|p22; */

/* ============================================================

EXAMPLE 4

capt = 135; @ capt is the sample size @

load bbbb[capt+1,1] = gnp82.dat;

bbbb = bbbb[1:capt,1]~bbbb[2:capt+1,1];

y = 100*ln(bbbb[.,2]./bbbb[.,1]);

a=.1;b=.1;c=.1;

ns = 3; ps = 1; pphi = 1; isig = 1; ipm = 2;

nth = 11;

mu1 = -1; mu2 = .2; mu3 = 1.2; phi1 = .1; sig = .8;

p11 = 1.1; p21 = 1.8; p31 = .1; p12 = .15; p22 = 3; p23 = .33;

th = mu1|mu2|mu3|phi1|sig|p11|p21|p31|p12|p22|p23; */

/* ============================================================

EXAMPLE 5

capt = 135; @ capt is the sample size @

load bbbb[capt+1,1] = gnp82.dat;

bbbb = bbbb[1:capt,1]~bbbb[2:capt+1,1];

y = 100*ln(bbbb[.,2]./bbbb[.,1]);

a=.1;b=.1;c=.1;

ns = 3; ps = 1; pphi = 1; isig = 1; ipm = 3;

nth = 8;

mu1 = -1; mu2 = .2; mu3 = 1.2; phi1 = .1; sig = .8;

p11 = 1; p21 = 1; p23 = 1;

th = mu1|mu2|mu3|phi1|sig|p11|p21|p23; */

/* ======================================================================= */

/* ======================================================================= */

@ In general no parts of this section should be changed @

proc startval; @ This defines starting value for iteration to be th @

retp(th); endp;

nk = pphi+1; @ nk is the first observation for which the

likelihood will be evaluated @

izz = 1; @ izz = 1 when params read in so as to assure inequality

constraints; izz = 2 for final reporting of results @

n = ns^(ps+1); @ n is the dimension of the state vector @

kc = 1; @ kc = 2 to echo parameter values @

ks = 1; @ ks = 2 if smoothed probs are to be calculated @

captst = capt - nk +1; @ captst is the effective sample size @

skif = zeros(captst,n); @ skif is the matrix of filtered probs @

skis = zeros(captst,n); @ skis is the matrix of smoothed probs @

id = eye(ns); @ used in certain calculations below @

"Bayesian prior used";

"a=";;a;;"b=";;b;;"c=";;c;

proc pattern1; @ This proc returns a (ps+1)*ns x n matrix. The ith

column contains a one in row j if st = j, contains a

one in row ns+j if st-1 = j, and so on @

local i1,ix,iq,na;

na = n/ns;

ix = eye(ns).*.ones(1,na);

i1 = 1;

do until i1 > ps;

na = na/ns;

iq = ones(1,ns^i1).*.(eye(ns).*.ones(1,na));

ix = iq|ix;

i1 = i1+1;

endo;

retp(ix);

endp;

hp = pattern1;

#include procs;

/* ================================================================= */

/* ======================================================================= */

proc matpm(xth); @This proc defines the user's conventions for reading

elements of Markov transition probabilities from

parameter vector @

local pm,ixth;

ixth = rows(xth);

pm = zeros(ns,ns);

if ipm == 1; @ for ns =2 this option has parameters as p11 and p22 @

if izz == 1;

pm[1,1] = xth[1,1]^2/(1 +xth[1,1]^2);

pm[2,2] = xth[2,1]^2/(1 + xth[2,1]^2);

else;

pm[1,1] = xth[1,1];

pm[2,2] = xth[2,1];

endif;

pm[2,1] = 1 - pm[1,1];

pm[1,2] = 1 - pm[2,2];

elseif ipm == 2; @ general case has parameters pij for i = 1,...,n and

j = 1,...,n-1 @

pm[1:ns-1,.] = reshape(xth[1:ixth,1],ns-1,ns);

if izz == 1;

pm[ns,.] = ones(1,ns);

pm = pm^2;

pm = pm./(sumc(pm)');

else;

pm[ns,.] = (1 - sumc(pm))';

endif;

elseif ipm == 3; @ This section can be rewritten by user to impose zeros

and ones where desired @

if izz == 1;

pm[1,1] = xth[1,1]^2/(1 + xth[1,1]^2);

pm[1,2] = xth[2,1]^2/(1 + xth[2,1]^2);

pm[2,3] = xth[3,1]^2/(1 + xth[3,1]^2);

elseif izz == 2;

pm[1,1] = xth[1,1];

pm[1,2] = xth[2,1];

pm[2,3] = xth[3,1];

endif;

pm[3,1] = 1 - pm[1,1];

pm[2,2] = 1 - pm[1,2];

pm[3,3] = 1 - pm[2,3];

endif;

retp(pm);

endp;

/* ======================================================================= */

/* ==================================================================== */

@ Set parameters to use Gauss numerical optimizer @

library optmum;

#include optmum.ext;

__btol = 1.e-06; @ This controls convergence criterion for coefficients@

__gtol = 1.e-06; @ This controls convergence criterion for gradient @

__algr = 1; @ This chooses BFGS optimization @

_opalgr = 2; @ This chooses BFGS optimization for newer versions of

GAUSS @

__miter = 150; @ This controls the maximum number of iterations @

__output = 1; @ This causes extra output to be displayed @

__covp = 0; @ This speeds up return from OPTMUM; note that the

program makes a reparameterization to calculate

std. errors @

@ Next call the GAUSS numerical optimizer @

output off;

{x,f,g,h} =optmum(&ofn,startval);

output file=junk on;

"";"";"MLE as parameterized for numerical optimization ";

"Coefficients:";x';

"";"Value of log likelihood:";;-f;

"";"Gradient vector:";g';

/* ======================================================================= */

/*======================================================================== */

@ In general no parts of this section need be changed @

@ Reparameterize for reporting final results @

izz = 2;

"";"Vector is reparameterized to report final results as follows";

"Means for each state:";x[1:ns,1]';

If pphi > 0;

"Autoregressive coefficients:";x[ns+1:ns+pphi,1]';

endif;

ncount = ns + pphi ;

x[ncount+1:ncount+isig,1] = x[ncount+1:ncount+isig,1]^2;

"Variances:";x[ncount+1:ncount+isig,1];

ncount = ncount + isig;

/* ======================================================================= */

/* ======================================================================= */

proc pmth; @ This proc converts the last elements of parameter vector

(which relates to transition probabilities) from the

th[i,j]^2/{sum j th[i,j]^2} form that is used for

numerical estimation into the p[i,j] form that is used

to calculate standard errors @

local pm;

if ipm == 1;

x[ncount+1,1] = x[ncount+1,1]^2/(1 + x[ncount+1,1]^2);

x[ncount+2,1] = x[ncount+2,1]^2/(1 + x[ncount+2,1]^2);

elseif ipm == 2;

pm = zeros(ns,ns);

pm[1:ns-1,.] = reshape(x[ncount+1:nth],ns-1,ns);

pm[ns,.] = ones(1,ns);

pm = pm^2;

pm = pm./(sumc(pm)');

x[ncount+1:nth,1] = reshape(pm[1:ns-1,.],ns*(ns-1),1);

elseif ipm == 3; @ User may want to alter these next lines @

x[ncount+1:nth,1]

= (x[ncount+1:nth,1]^2)./(1 + x[ncount+1:nth,1]^2);

endif;

retp(x);

endp;

/* ======================================================================= */

/* ======================================================================= */

@ In general no changes are necessary from here out @

call pmth;

h = (hessp(&ofn,x));

va = eigrs(h);

kc = 2;

ks = 2;

call ofn(x);

if minc(eigrs(h)) <= 0;

"Negative of Hessian is not positive definite";

"Either you have not found local maximum, or else estimates are up "

"against boundary condition. In latter case, impose the restricted "

"params rather than estimate them to calculate standard errors";

else;

h = invpd(h);

std = diag(h)^.5;

"For vector of coefficients parameterized as follows,";x';

"the standard errors are";std';

endif;

"";"-------------------------------";"";

"Probabilities for primitive states";

"filtered probabilities";format /rd 1,0;

"Obs ";;

t = 0;

do until t > ps;

i = 1;

do until i == ns;

"P(st-";;t;;"=";;i;;") ";;

i = i+1;

endo;

t = t+1;

endo;"";

format /rd 6,4;

skif = (skif*hp')*(eye(ps+1).*.id[.,1:ns-1]);

skif = seqa(nk,1,captst)~skif;skif;

"";"smoothed probabilities";

format /rd 1,0;

"Obs ";;

i = 1;

do until i > ns;

"P(st = ";;i;;") ";;

i = i+1;

endo;

format /rd 6,4;

skis = skis*hp';

skis = seqa(nk,1,captst)~skis[.,1:ns];skis;

/*========================================================================*/

PROCS

@ These GAUSS procedures evaluate Markov transition matrix, evaluate

likelihood function, and evaluate filter and smoothed probababilities @

/* ============================================================== */

proc matf(pm); @This proc returns the (n x n) matrix F of Markov

transition probabilities for state vector @

local iz,iw,ib,na,nb,nc,fz,fm;

@ set initial values for use with iteration @

na = 1;

nb = ns;

nc = ns*ns;

fm = pm;

iz = 1;

do until iz > ps;

fz = fm;

fm = zeros(nc,nc);

iw = 1;

do until iw > ns;

fm[((iw-1)*nb+1):(iw*nb),((iw-1)*na+1):(iw*na)]

= fz[1:nb,((iw-1)*na+1):iw*na];

iw = iw+1;

endo;

ib = 2;

do until ib > ns;

fm[1:nc,((ib-1)*nb+1):ib*nb] = fm[1:nc,1:nb];

ib = ib+1;

endo;

na = na*ns;

nb = nb*ns;

nc = nc*ns;

iz = iz+1;

endo;

retp(fm);

endp;

/* ==================================================================== */

/* ================================================================= */

proc ofn(th); @ this proc evaluates filter probs and likelihood @

local ncount,mu,phi,sig,pm,eta,iz,fm,chsi,it,f,fit,fx,hw,fj,

ij,ap,const,pq,hk,ihk;

@ Convert parameter vector to convenient form @

mu = th[1:ns,1];

ncount = ns + 1; @ ncount is the number of params read @

if pphi == 0;

phi = 1;

else;

phi = 1 | -th[ncount:ncount+pphi-1];

endif;

ncount = ncount + pphi;

if isig == 1;

sig = th[ncount,1]*ones(n,1);

ncount = ncount +1;

elseif isig == ns;

sig = th[ncount:ncount+ns-1,1].*hp[1:ns,.];

sig = sumc(sig);

ncount = ncount + ns;

endif;

if izz == 1;

sig = sig^2;

endif;

pm = matpm(th[ncount:nth,1]);

@ Construct constant term to be subtracted for each observation @

const = phi .*. mu;

const = const'*hp;

@ Convert data to AR resids @

eta = y[nk:capt,1];

iz = 1;

do until iz > pphi;

eta = eta ~y[nk-iz:capt-iz,1];

iz = iz+1;

endo;

eta = ((eta*phi - const)^2)./sig';

@ Adjust data to avoid numeric overflows and underflows

eta = reshape(eta,1,n*(captst));

eta = minc(eta|800*ones(1,n*captst));

eta = reshape(eta',captst,n); @

eta = (1./sqrt(sig')).*exp(-eta/2);

@ Calculate ergodic probabilities @

fm = matf(pm);

ap = (eye(n)-fm)|ones(1,n);

chsi = sumc((invpd(ap'*ap))');

chsi = maxc(chsi'|zeros(1,n)); @ This line eliminates roundoff error @

if kc > 1;

"";"Matrix of Markov transition probabilities:";pm;

"";"Ergodic probs for full state vector:";chsi';

"";"Ergodic probs for primitive states:";

pq = hp*chsi;pq[1:ns,1]';

endif;

@ Filter iteration @

f = 0;

it = 1;

do until it > captst;

fx = chsi .* eta[it,.]';

fit = sumc(fx);

skif[it,.] = fx'/fit;

f = f + ln(fit);

chsi = fm*fx/fit;

it = it+1;

endo;

@ Make Bayesian adjustment to likelihood if desired @

if a > 0;

fj = 0;

ij = 1;

do until ij > ns;

fj = fj + a*ln(sig[ij,1]) + b/sig[ij,1]

+ c*(mu[ij,1]^2/sig[ij,1]);

ij = ij +1;

endo;

f = f - fj/2;

endif;

@ Calculate smoothed probs if desired @

if ks == 2;

skis[captst,.] = skif[captst,.];

it = 1;

do until it == captst;

if minc(skif[captst-it,.]') > 1.e-150;

skis[captst-it,.] = skif[captst-it,.].*

((skis[captst-it+1,.]./(skif[captst-it,.]*fm'))*fm);

else; @ adjust code so as not to divide by zero @

hk = skif[captst-it,.]*fm';

ihk = 1;

do until ihk > n;

if hk[1,ihk] > 1.e-150;

hk[1,ihk] = skis[captst-it+1,ihk]/hk[1,ihk];

else;

hk[1,ihk] = 0;

endif;

ihk = ihk + 1;

endo;

skis[captst-it,.] = skif[captst-it,.].*(hk*fm);

endif;

it = it+1;

endo;

endif;

@ Print out value of log likelihood if desired @

if kc == 2;

"";"Log likelihood:";f;

endif;

retp(-f);

endp;

/*=========================================================================*/

I copied and pasted your code from above into two separate files, `markov_mod.gss` and `procs`. I had to do some find and replace, because the forum website changed some of the quotation marks to two single quotes, subtraction signs to dashes, etc. I also had to close the comment at the very last line of your post. As a note for others, I also did not copy the line that says MAXSEEK or the line that says PROCS into my files. I used those as demarcations between the two files.

After this, I downloaded the `gnp82.dat` dataset from the link that says "Programs for estimation of Markov switching models by numerical optimization" on this page. I placed the `gnp82.dat` file in the same directory as the other two files.

I was then able to run the code successfully with GAUSS version 13.1 on Linux. I have attached a zip file with these contents.

Final note: this code requires the GAUSS Optmum application module.

## Your Answer

## 2 Answers

**MAXSEEK and PROCS codes are given below **

MAXSEEK

@ This GAUSS file reads in data, sets options, and calls numerical

optimization routine for numerical estimation of switching model @

output file=junk reset;

/* ======================================================================= */

@ Replace this first section with a section to read in your data

Example 1 reproduces the GNP results from Hamilton, "A New

Approach to the Economic Analysis of Nonstationary Time Series

and the Business Cycle," Econometrica, March 1989

Example 2 reproduces the interest rate results from Hamilton,

"Rational Expectations Econometric Analysis of Changes in Regime:

An Investigation of the Term Structure of Interest Rates," Journal

of Economic Dynamics and Control, June 1988

Example 3 reproduces the results for the French exchange rate in "Long

Swings in the Exchange Rate: Are They in the Data and Do Markets

Know It?" by Charles Engel and James D. Hamilton (AER, Sept. 1990).

Example 4 fits a three-state model to US real GNP data; estimation

algorithm bogs down due to bumping against corners with nonnegative

definite hessian; Example 5 reestimates with zeros imposed @

/*===============================================

EXAMPLE 1:*/

@ The following lines read in the raw data, and convert to

100 times the first difference of the log @

capt = 135; @ capt is the sample size @

load bbbb[capt+1,1] = C:\gauss10\swarch\gnp82.dat;

bbbb = bbbb[1:capt,1]~bbbb[2:capt+1,1];

y = 100*ln(bbbb[.,2]./bbbb[.,1]);

@ Adjust any of the following to control specification desired @

ns = 2; @ ns is the number of primitive states @

ps = 4; @ ps is the number of lagged states that matter

for y; use ps = 0 if only the current state

matters @

pphi = 4; @ pphi is the number of lags in autoregression

for y; pphi should be greater than or equal

to ps @

isig = 1; @ isig = 1 for constant variances,

isig =ns for changing variances @

ipm = 1; @ ipm specifies way in which transition probs

are parameterized

ipm = 1 implies p11 and p22 estimated

ipm = 2 implies pij for i=1,..,n j=1,..,n-1

ipm = 3 user input code @

a=0;b=0;c=0; @ These parameters control the Bayesian prior

as suggested in Hamilton, "A Quasi-Bayesian

Approach to Estimating Parameters for Mixtures

of Normal Distributions", Journal of Business

and Economic Statistics, January 1991. If

no Bayesian adjustment is desired, set all

parameters to zero @

/* Input initial values for parameters

The order in which variables are represented is as follows

first ns elements: means for states

next pphi elements: autoregressive coefficients

next isig elements: variances for states when izz =1

std. deviations for states when izz =2

next elements: when izz =1 these are the transition probs

when izz =2 these are params v(i,j) such that

p(i,j) = v(i,j)^2 / sum j v(i,j)^2

elements are ordered as p11, p22 when ns =2

ordered as p(1,1),p(2,1),...,p(ns,1),

p(2,1),...,p(ns-1,ns) when ns > 2 */

nth = 9; @ nth is the number of params to be estimated@

mu1 = 1; mu2 = 0; phi1 = .1; phi2 = 0; phi3 = 0; phi4 = 0;

sig = 1; p11 = 1.5; p22 = 1.5;

th = mu1|mu2|phi1|phi2|phi3|phi4|sig|p11|p22;

/* =============================================

EXAMPLE 2:

capt = 103;

load y[capt,1] = rradj.dat;

ns = 2;

ps = 4;

pphi = 4;

isig = 2;

ipm = 1;

a=0;b=0;c=0;

nth = 10;

mu1 = 2; mu2 = 1; phi1 = .9; phi2 = 0.; phi3 = 0.;

phi4 = 0; sig1 = .8; sig2 = .2; p11 = 1; p22 = 1;

th = mu1|mu2|phi1|phi2|phi3|phi4|sig1|sig2|p11|p22; */

/*==============================================

EXAMPLE 3

capt = 58;

load y[capt,3] = exdata.txt; @ this loads exchange rate data

for France, U.K. and Germany @

y = y[.,1]; @ this selects French data @

ns = 2;

ps = 0;

pphi = 0;

isig = 2;

ipm = 1;

a = .2; b = 1.0; c = .1;

nth = 6;

mu1 = 3; mu2 = -3; sig1 = 3; sig2 = 6; p11 = 2; p22 = 2;

th = mu1|mu2|sig1|sig2|p11|p22; */

/* ============================================================

EXAMPLE 4

capt = 135; @ capt is the sample size @

load bbbb[capt+1,1] = gnp82.dat;

bbbb = bbbb[1:capt,1]~bbbb[2:capt+1,1];

y = 100*ln(bbbb[.,2]./bbbb[.,1]);

a=.1;b=.1;c=.1;

ns = 3; ps = 1; pphi = 1; isig = 1; ipm = 2;

nth = 11;

mu1 = -1; mu2 = .2; mu3 = 1.2; phi1 = .1; sig = .8;

p11 = 1.1; p21 = 1.8; p31 = .1; p12 = .15; p22 = 3; p23 = .33;

th = mu1|mu2|mu3|phi1|sig|p11|p21|p31|p12|p22|p23; */

/* ============================================================

EXAMPLE 5

load bbbb[capt+1,1] = gnp82.dat;

bbbb = bbbb[1:capt,1]~bbbb[2:capt+1,1];

y = 100*ln(bbbb[.,2]./bbbb[.,1]);

a=.1;b=.1;c=.1;

ns = 3; ps = 1; pphi = 1; isig = 1; ipm = 3;

nth = 8;

mu1 = -1; mu2 = .2; mu3 = 1.2; phi1 = .1; sig = .8;

p11 = 1; p21 = 1; p23 = 1;

th = mu1|mu2|mu3|phi1|sig|p11|p21|p23; */

/* ======================================================================= */

/* ======================================================================= */

@ In general no parts of this section should be changed @

proc startval; @ This defines starting value for iteration to be th @

retp(th); endp;

nk = pphi+1; @ nk is the first observation for which the

likelihood will be evaluated @

izz = 1; @ izz = 1 when params read in so as to assure inequality

constraints; izz = 2 for final reporting of results @

n = ns^(ps+1); @ n is the dimension of the state vector @

kc = 1; @ kc = 2 to echo parameter values @

ks = 1; @ ks = 2 if smoothed probs are to be calculated @

captst = capt - nk +1; @ captst is the effective sample size @

skif = zeros(captst,n); @ skif is the matrix of filtered probs @

skis = zeros(captst,n); @ skis is the matrix of smoothed probs @

id = eye(ns); @ used in certain calculations below @

"Bayesian prior used";

"a=";;a;;"b=";;b;;"c=";;c;

proc pattern1; @ This proc returns a (ps+1)*ns x n matrix. The ith

column contains a one in row j if st = j, contains a

one in row ns+j if st-1 = j, and so on @

local i1,ix,iq,na;

na = n/ns;

ix = eye(ns).*.ones(1,na);

i1 = 1;

do until i1 > ps;

na = na/ns;

iq = ones(1,ns^i1).*.(eye(ns).*.ones(1,na));

ix = iq|ix;

i1 = i1+1;

endo;

retp(ix);

endp;

hp = pattern1;

#include procs;

/* ================================================================= */

/* ======================================================================= */

proc matpm(xth); @This proc defines the user's conventions for reading

elements of Markov transition probabilities from

parameter vector @

local pm,ixth;

ixth = rows(xth);

pm = zeros(ns,ns);

if ipm == 1; @ for ns =2 this option has parameters as p11 and p22 @

if izz == 1;

pm[1,1] = xth[1,1]^2/(1 +xth[1,1]^2);

pm[2,2] = xth[2,1]^2/(1 + xth[2,1]^2);

else;

pm[1,1] = xth[1,1];

pm[2,2] = xth[2,1];

endif;

pm[2,1] = 1 - pm[1,1];

pm[1,2] = 1 - pm[2,2];

elseif ipm == 2; @ general case has parameters pij for i = 1,...,n and

j = 1,...,n-1 @

pm[1:ns-1,.] = reshape(xth[1:ixth,1],ns-1,ns);

if izz == 1;

pm[ns,.] = ones(1,ns);

pm = pm^2;

pm = pm./(sumc(pm)');

else;

pm[ns,.] = (1 - sumc(pm))';

endif;

elseif ipm == 3; @ This section can be rewritten by user to impose zeros

and ones where desired @

if izz == 1;

pm[1,1] = xth[1,1]^2/(1 + xth[1,1]^2);

pm[1,2] = xth[2,1]^2/(1 + xth[2,1]^2);

pm[2,3] = xth[3,1]^2/(1 + xth[3,1]^2);

elseif izz == 2;

pm[1,1] = xth[1,1];

pm[1,2] = xth[2,1];

pm[2,3] = xth[3,1];

endif;

pm[3,1] = 1 - pm[1,1];

pm[2,2] = 1 - pm[1,2];

pm[3,3] = 1 - pm[2,3];

endif;

retp(pm);

endp;

/* ======================================================================= */

/* ==================================================================== */

@ Set parameters to use Gauss numerical optimizer @

library optmum;

#include optmum.ext;

__btol = 1.e-06; @ This controls convergence criterion for coefficients@

__gtol = 1.e-06; @ This controls convergence criterion for gradient @

__algr = 1; @ This chooses BFGS optimization @

_opalgr = 2; @ This chooses BFGS optimization for newer versions of

GAUSS @

__miter = 150; @ This controls the maximum number of iterations @

__output = 1; @ This causes extra output to be displayed @

__covp = 0; @ This speeds up return from OPTMUM; note that the

program makes a reparameterization to calculate

std. errors @

@ Next call the GAUSS numerical optimizer @

output off;

{x,f,g,h} =optmum(&ofn,startval);

output file=junk on;

"";"";"MLE as parameterized for numerical optimization ";

"Coefficients:";x';

"";"Value of log likelihood:";;-f;

"";"Gradient vector:";g';

/* ======================================================================= */

/*======================================================================== */

@ In general no parts of this section need be changed @

@ Reparameterize for reporting final results @

izz = 2;

"";"Vector is reparameterized to report final results as follows";

"Means for each state:";x[1:ns,1]';

If pphi > 0;

"Autoregressive coefficients:";x[ns+1:ns+pphi,1]';

endif;

ncount = ns + pphi ;

x[ncount+1:ncount+isig,1] = x[ncount+1:ncount+isig,1]^2;

"Variances:";x[ncount+1:ncount+isig,1];

ncount = ncount + isig;

/* ======================================================================= */

/* ======================================================================= */

proc pmth; @ This proc converts the last elements of parameter vector

(which relates to transition probabilities) from the

th[i,j]^2/{sum j th[i,j]^2} form that is used for

numerical estimation into the p[i,j] form that is used

to calculate standard errors @

local pm;

if ipm == 1;

x[ncount+1,1] = x[ncount+1,1]^2/(1 + x[ncount+1,1]^2);

x[ncount+2,1] = x[ncount+2,1]^2/(1 + x[ncount+2,1]^2);

elseif ipm == 2;

pm = zeros(ns,ns);

pm[1:ns-1,.] = reshape(x[ncount+1:nth],ns-1,ns);

pm[ns,.] = ones(1,ns);

pm = pm^2;

pm = pm./(sumc(pm)');

x[ncount+1:nth,1] = reshape(pm[1:ns-1,.],ns*(ns-1),1);

elseif ipm == 3; @ User may want to alter these next lines @

x[ncount+1:nth,1]

= (x[ncount+1:nth,1]^2)./(1 + x[ncount+1:nth,1]^2);

endif;

retp(x);

endp;

/* ======================================================================= */

/* ======================================================================= */

@ In general no changes are necessary from here out @

call pmth;

h = (hessp(&ofn,x));

va = eigrs(h);

kc = 2;

ks = 2;

call ofn(x);

if minc(eigrs(h)) <= 0;

"Negative of Hessian is not positive definite";

"Either you have not found local maximum, or else estimates are up "

"against boundary condition. In latter case, impose the restricted "

"params rather than estimate them to calculate standard errors";

else;

h = invpd(h);

std = diag(h)^.5;

"For vector of coefficients parameterized as follows,";x';

"the standard errors are";std';

endif;

"";"-------------------------------";"";

"Probabilities for primitive states";

"filtered probabilities";format /rd 1,0;

"Obs ";;

t = 0;

do until t > ps;

i = 1;

do until i == ns;

"P(st-";;t;;"=";;i;;") ";;

i = i+1;

endo;

t = t+1;

endo;"";

format /rd 6,4;

skif = (skif*hp')*(eye(ps+1).*.id[.,1:ns-1]);

skif = seqa(nk,1,captst)~skif;skif;

"";"smoothed probabilities";

format /rd 1,0;

"Obs ";;

i = 1;

do until i > ns;

"P(st = ";;i;;") ";;

i = i+1;

endo;

format /rd 6,4;

skis = skis*hp';

skis = seqa(nk,1,captst)~skis[.,1:ns];skis;

/*========================================================================*/

PROCS

@ These GAUSS procedures evaluate Markov transition matrix, evaluate

likelihood function, and evaluate filter and smoothed probababilities @

/* ============================================================== */

proc matf(pm); @This proc returns the (n x n) matrix F of Markov

transition probabilities for state vector @

local iz,iw,ib,na,nb,nc,fz,fm;

@ set initial values for use with iteration @

na = 1;

nb = ns;

nc = ns*ns;

fm = pm;

iz = 1;

do until iz > ps;

fz = fm;

fm = zeros(nc,nc);

iw = 1;

do until iw > ns;

fm[((iw-1)*nb+1):(iw*nb),((iw-1)*na+1):(iw*na)]

= fz[1:nb,((iw-1)*na+1):iw*na];

iw = iw+1;

endo;

ib = 2;

do until ib > ns;

fm[1:nc,((ib-1)*nb+1):ib*nb] = fm[1:nc,1:nb];

ib = ib+1;

endo;

na = na*ns;

nb = nb*ns;

nc = nc*ns;

iz = iz+1;

endo;

retp(fm);

endp;

/* ==================================================================== */

/* ================================================================= */

proc ofn(th); @ this proc evaluates filter probs and likelihood @

local ncount,mu,phi,sig,pm,eta,iz,fm,chsi,it,f,fit,fx,hw,fj,

ij,ap,const,pq,hk,ihk;

@ Convert parameter vector to convenient form @

mu = th[1:ns,1];

ncount = ns + 1; @ ncount is the number of params read @

if pphi == 0;

phi = 1;

else;

phi = 1 | -th[ncount:ncount+pphi-1];

endif;

ncount = ncount + pphi;

if isig == 1;

sig = th[ncount,1]*ones(n,1);

ncount = ncount +1;

elseif isig == ns;

sig = th[ncount:ncount+ns-1,1].*hp[1:ns,.];

sig = sumc(sig);

ncount = ncount + ns;

endif;

if izz == 1;

sig = sig^2;

endif;

pm = matpm(th[ncount:nth,1]);

@ Construct constant term to be subtracted for each observation @

const = phi .*. mu;

const = const'*hp;

@ Convert data to AR resids @

eta = y[nk:capt,1];

iz = 1;

do until iz > pphi;

eta = eta ~y[nk-iz:capt-iz,1];

iz = iz+1;

endo;

eta = ((eta*phi - const)^2)./sig';

@ Adjust data to avoid numeric overflows and underflows

eta = reshape(eta,1,n*(captst));

eta = minc(eta|800*ones(1,n*captst));

eta = reshape(eta',captst,n); @

eta = (1./sqrt(sig')).*exp(-eta/2);

@ Calculate ergodic probabilities @

fm = matf(pm);

ap = (eye(n)-fm)|ones(1,n);

chsi = sumc((invpd(ap'*ap))');

chsi = maxc(chsi'|zeros(1,n)); @ This line eliminates roundoff error @

if kc > 1;

"";"Matrix of Markov transition probabilities:";pm;

"";"Ergodic probs for full state vector:";chsi';

"";"Ergodic probs for primitive states:";

pq = hp*chsi;pq[1:ns,1]';

endif;

@ Filter iteration @

f = 0;

it = 1;

do until it > captst;

fx = chsi .* eta[it,.]';

fit = sumc(fx);

skif[it,.] = fx'/fit;

f = f + ln(fit);

chsi = fm*fx/fit;

it = it+1;

endo;

@ Make Bayesian adjustment to likelihood if desired @

if a > 0;

fj = 0;

ij = 1;

do until ij > ns;

fj = fj + a*ln(sig[ij,1]) + b/sig[ij,1]

+ c*(mu[ij,1]^2/sig[ij,1]);

ij = ij +1;

endo;

f = f - fj/2;

endif;

@ Calculate smoothed probs if desired @

if ks == 2;

skis[captst,.] = skif[captst,.];

it = 1;

do until it == captst;

if minc(skif[captst-it,.]') > 1.e-150;

skis[captst-it,.] = skif[captst-it,.].*

((skis[captst-it+1,.]./(skif[captst-it,.]*fm'))*fm);

else; @ adjust code so as not to divide by zero @

hk = skif[captst-it,.]*fm';

ihk = 1;

do until ihk > n;

if hk[1,ihk] > 1.e-150;

hk[1,ihk] = skis[captst-it+1,ihk]/hk[1,ihk];

else;

hk[1,ihk] = 0;

endif;

ihk = ihk + 1;

endo;

skis[captst-it,.] = skif[captst-it,.].*(hk*fm);

endif;

it = it+1;

endo;

endif;

@ Print out value of log likelihood if desired @

if kc == 2;

"";"Log likelihood:";f;

endif;

retp(-f);

endp;

/*=========================================================================*/

I copied and pasted your code from above into two separate files, `markov_mod.gss` and `procs`. I had to do some find and replace, because the forum website changed some of the quotation marks to two single quotes, subtraction signs to dashes, etc. I also had to close the comment at the very last line of your post. As a note for others, I also did not copy the line that says MAXSEEK or the line that says PROCS into my files. I used those as demarcations between the two files.

After this, I downloaded the `gnp82.dat` dataset from the link that says "Programs for estimation of Markov switching models by numerical optimization" on this page. I placed the `gnp82.dat` file in the same directory as the other two files.

I was then able to run the code successfully with GAUSS version 13.1 on Linux. I have attached a zip file with these contents.

Final note: this code requires the GAUSS Optmum application module.