*! mlcoint--Johansen's maximum likelihood cointegration test *! version 2.0 Ken Heinecke 2/9/93 sts9: STB-21 *! v 2.0.1: corrected to work with more than 9 variables (see CFB below) *! Will probably fail for >=14 variables * C F Baum 0B08 program define mlcoint quietly { version 3.1 local varlist "opt ex" local if "opt" local in "opt" local options "noConstant Lags(int 1) noNormal Regress STANdard Static(str)" parse "`*'" local vars : word count `varlist' /* number of TS vars */ local normal = cond("`normal'"=="",1,0) local standar = cond("`standar'"=="",0,1) local matrix = `normal' | `standar' if ("`regress'" != "") { local regnoi "noi" } capture set matsize 200 /* This can only work in Unix */ local lags = `lags'-1 /* # of lags after differencing */ local dllags "lags(0,`lags')" /* Establish a sample over which the VAR can be run one equation at a time. */ tempvar touse mark `touse' `if' `in' markout `touse' `varlist' _crcnuse `touse' if \$S_2 { di in re "gaps in sample" exit 98 } local infl "in \$S_3/\$S_4" drop `touse' /* save space */ /* Create differences and lags of variables and store separate lists of the names of the differences and lags. */ parse "`varlist'", parse(" ") local j 0 while `j'<`vars' { local j = `j'+1 dif ``j'' _addop ``j'' D local dlist = "`dlist'"+" \$S_1" lag ``j'' _addop ``j'' L local llist = "`llist'"+" \$S_1" } /* Create `vars' different lists of differenced RHS variables to be used in the individual equations of the VAR. */ parse "`dlist'", parse(" ") local j 0 while `j'<`vars' { local j = `j'+1 local m 0 while `m'<`vars' { local m = `m'+1 if (`j'!=`m') { local div`j' = "`div`j''" + " ``m''" } } } /* Create lists of residuals */ local j 0 while `j'<`vars' { local j = `j' +1 local dres = "`dres'" + " d`j'" local lres = "`lres'" + " l`j'" } tempvar `dres' `lres' /* each element will be a tempvar */ /* Create list for labeling final matrices */ local j 0 while `j'<`vars' { local j = `j'+1 local vecl = "`vecl'" + " vec`j'" } /* Estimate first system of regressions and save the residuals as d1, d2, ..., d`vars' */ parse "`dlist'", parse(" ") local i 0 while `i'<`vars' { local i = `i'+1 if (`lags'==0) { `regnoi' tsfit ``i'' `div`i'' `infl', static(`div`i'' `static') nosamp `constan' predict `d`i'', residual } else { if ("`static'" != "") { `regnoi' tsfit ``i'' `div`i'' `infl', static(`static') l(`lags') nosample `constan' } else { `regnoi' tsfit ``i'' `div`i'' `infl', l(`lags') nosample `constan' } predict `d`i'', residual } } /* Estimate second system of regressions and save residuals as l1, l2, ..., l`vars' */ parse "`llist'", parse(" ") local i 0 while `i'<`vars' { local i = `i'+1 if (`lags'==0) { `regnoi' tsfit ``i'' `dlist' `infl', static(`div`i'' `static') nosample `constan' predict `l`i'', residual } else{ if ("`static'" != "") { `regnoi' tsfit ``i'' `dlist' `infl', static(`static') `dllags' nosample `constan' } else { `regnoi' tsfit ``i'' `dlist' `infl', `dllags' nosample `constan' } predict `l`i'', residual } } /* The residuals from the VARs are calculated and stored. Allocate temporary names for the matrix calculations. Global matrices stored by this routine are: S_E_ISDD, S_E_NBET, S_E_SDL, S_E_SLL, S_E_TEVL(TEIGVAL), S_E_TSDL */ tempname A ALPHA CHOLD DIF EIGVALS EVECT EVMAX EVTRACE FINMAT tempname ICHOLD LDIF ONE SALPHA SBETAP SDD SLDIF STALPHA tempname TALPHA TEVECT TICHOLD Z1 Z2 Z3 df idf /* Store degrees of freedom */ scalar `df' = \$S_E_N scalar `idf' = 1/`df' /* set up product moment matrices */ parse "`dres'", parse(" ") local i 0 while `i'<`vars' { local i = `i'+1 * CFB corr local dr = "`dr'" + " ```i'''" local dr "`dr' ```i'''" } parse "`lres'", parse(" ") local i 0 while `i'<`vars' { local i = `i'+1 * CFB corr local lr = "`lr'" + " ```i'''" local lr "`lr' ```i'''" } mat accum `A' = `dr' `lr' `infl', noconstant mat `SDD' = `A'[1..`vars',1..`vars'] local r = `vars'+1 mat S_E_SLL = `A'[`r'...,`r'...] mat S_E_SDL = `A'[1..`vars',`r'...] mat drop `A' /* Scale matrices by degrees of freedom */ mat `SDD' = `idf'*`SDD' mat S_E_SLL = `idf'*S_E_SLL mat S_E_SDL = `idf'*S_E_SDL /* Set up likelihood function matrices */ mat `CHOLD' = cholesky(S_E_SLL) mat `ICHOLD' = inv(`CHOLD') mat S_E_TSDL = S_E_SDL' mat S_E_ISDD = syminv(`SDD') mat `TICHOLD' = `ICHOLD'' mat `Z1' = `ICHOLD'*S_E_TSDL mat `Z2' = `Z1'*S_E_ISDD mat `Z3' = `Z2'*S_E_SDL mat `FINMAT' = `Z3'*`TICHOLD' /* Calculate eigenvalues and eigenvectors */ mat symeigen `EVECT' `EIGVALS' = `FINMAT' mat S_E_TEVL = `EIGVALS'' /* Calculate lambda max stats */ mat `ONE' = J(`vars',1,1) mat `DIF' = `ONE'-S_E_TEVL mat `LDIF' = J(`vars',1,0) local i 0 while `i'<`vars' { local i = `i' + 1 mat `LDIF'[`i',1] = log(`DIF'[`i',1]) } mat `SLDIF' = `df'*`LDIF' mat `EVMAX' = -1*`SLDIF' /* Calculate trace stats */ mat `EVTRACE' = J(`vars',1,0) local sevmax = 0 local n 0 local i 0 while `i'<`vars' { local i = `i'+1 local n = `vars'+1-`i' local sevmax = `sevmax'+`EVMAX'[`n',1] mat `EVTRACE'[`n',1] = `sevmax' } /* Display the eigenvalues, maximal eigenvalue statistics, and the trace statistics. */ noi di in gr _col(16) "Maximal" _new _col(14) "eigenvalue Trace" _new "Eigenvalues statistics statistics" noi di in gr "-----------------------------------" local i 0 while `i'<`vars' { local i = `i' + 1 noi di in ye %10.0g = S_E_TEVL[`i',1] _skip(3) %10.0g = `EVMAX'[`i',1] _skip(3) = `EVTRACE'[`i',1] } /* Calculate normalized and standardized eigenvectors and their corresponding weight matrices, i.e., alpha and beta-prime. First calculate the normalized matrices. */ mat `TEVECT' = `EVECT'' mat S_E_NBET = `TEVECT'*`ICHOLD' mat rownames S_E_NBET = `vecl' mat colnames S_E_NBET = `varlist' /* Remaining matrix calculations are not stored. Calculate only if the `matrix' option is specified. */ if `matrix' { mat `TALPHA' = S_E_NBET*S_E_TSDL mat `ALPHA' = `TALPHA'' mat rownames `ALPHA' = `varlist' mat colnames `ALPHA' = `vecl' if `normal' { noi di _new in gr "Normalized Beta'" noi mat l S_E_NBET, nob noh noi di _new in gr "Normalized Alpha" noi mat l `ALPHA', nob noh } /* end normalized matrices */ /* Now calculate the standardized matrices. */ if `standar' { mat `SBETAP' = J(`vars',`vars',0) local i 0 while `i'<`vars' { local i = `i'+1 local j 1 while `j'<=`vars' { mat `SBETAP'[`i',`j']=S_E_NBET[`i',`j']/S_E_NBET[`i',`i'] local j = `j'+1 } } mat rownames `SBETAP' = `vecl' mat colnames `SBETAP' = `varlist' noi di _new in gr "Standardized Beta'" noi mat l `SBETAP', nob noh mat `STALPHA' = J(`vars',`vars',0) local i 0 while `i'<`vars' { local i = `i'+1 local j 0 while `j'<`vars' { local j = `j'+1 mat `STALPHA'[`i',`j']=`TALPHA'[`i',`j']*S_E_NBET[`i',`i'] } } mat `SALPHA' = `STALPHA'' mat rownames `SALPHA' = `varlist' mat colnames `SALPHA' = `vecl' noi di _new in gr "Standardized Alpha" noi mat l `SALPHA', nob noh } /* end standardized matrices */ } /* end of unstored matrix results */ /* Store estimation results for later use. */ global S_E_cmd "mlcoint" global S_E_if "`if'" global S_E_in "`in'" global S_E_lags = `lags' + 1 /* lags() on input */ global S_E_nv `vars' /* number of vars in varlist */ global S_E_vl "`varlist'" /* original varlist */ global S_E_MISD "S_E_ISDD" global S_E_MNBE "S_E_NBET" global S_E_MSDL "S_E_SDL" global S_E_MSLL "S_E_SLL" global S_E_MTEV "S_E_TEVL" global S_E_MTSD "S_E_TSDL" } /* end quietly */ end