*! xtpanelgarch_pretest 1.0.0 06nov2026 *! Pre-estimation identification strategy for panel GARCH *! Cermeno & Grier (2001, sec. 5; 2006, sec. 10.3) *! Author: Dr Merwan Roudane (merwanroudane920@gmail.com) *! https://github.com/merwanroudane * * Step -> source map * [1] individual effects in the mean: LSDV + HAC Wald, chi2(N-1) CG(2001) 5.1, CG(2006) 10.3.1 * [2] PACF of squared residuals + Engle LM-ARCH(j) CG(2001) 5.2, Table 1; Engle (1982) * [3] individual effects in the variance: AR regression of u^2 with and * without unit intercepts (F, chi2) + LR groupwise heteroskedasticity CG(2001) 5.2; CG(2006) 10.3.2 * [4] cross-sectional correlation: LR diagonal-Sigma test, Breusch-Pagan * LM, Pesaran CD CG(2006) 10.3.2 / 10.4.1 * [5] AR regression of residual cross products + pair-specific effects CG(2006) 10.3.2 program define xtpanelgarch_pretest, rclass version 14.0 syntax varlist(ts min=1) [if] [in] , [ HACLags(integer -1) Lags(integer 10) /// ARFE(integer 1) CPLags(integer 1) SIGlevel(real 0.05) noXS ] qui xtset local ivar "`r(panelvar)'" local tvar "`r(timevar)'" if "`ivar'" == "" | "`tvar'" == "" { di as err "data must be {bf:xtset} with a panel and a time variable" exit 459 } local tdelta = r(tdelta) marksample touse gettoken yorig xorig : varlist tsrevar `varlist' local tsv "`r(varlist)'" gettoken y xv : tsv _xtpg_balance `touse' `ivar' `tvar' `tdelta' "xtpanelgarch pretest" local N = r(N) local T = r(T) local units "`r(units)'" if `N' < 2 { di as err "pretest needs at least 2 panels" exit 2001 } if `haclags' < 0 local haclags = floor(4 * (`T' / 100)^(2 / 9)) if `lags' >= `T' - 5 local lags = max(1, `T' - 6) tempname h capture _estimates hold `h', restore nullok // [1] individual effects in the mean ---------------------------------- qui newey `y' `xv' i.`ivar' if `touse', lag(`haclags') force qui testparm i.`ivar' local Wmu = r(F) * r(df) local Wdf = r(df) local Wp = chi2tail(`Wdf', `Wmu') local usefe = (`Wp' < `siglevel') tempvar e e2 if `usefe' { qui regress `y' `xv' i.`ivar' if `touse' local rtype "LSDV" } else { qui regress `y' `xv' if `touse' local rtype "OLS" } qui predict double `e' if `touse', residuals qui gen double `e2' = `e' * `e' if `touse' // [2]-[3] squared residuals ------------------------------------------ tempname W E PAC LM FE XS CP CPFE mata: _xtpg_getE("`e2'", "`touse'", `N', "`W'") mata: _xtpg_getE("`e'", "`touse'", `N', "`E'") mata: _xtpg_pre_ar(st_matrix("`W'"), `lags', "`PAC'", "`LM'", "`FE'", `arfe') if "`xs'" == "" { mata: _xtpg_pre_xs(st_matrix("`E'"), `cplags', "`XS'", "`CP'", "`CPFE'") } // ---------------- display -------------------------------------------- di _n as txt "{hline 78}" di as txt "Panel GARCH pre-tests (Cermeño & Grier 2001, 2006)" _col(56) "N = " as res `N' as txt ", T = " as res `T' di as txt "Dependent variable: " as res "`yorig'" as txt " regressors: " as res "`xorig'" di as txt "{hline 78}" di as txt "[1] Individual effects in the mean (LSDV, HAC lag = `haclags')" di as txt " H0: mu_1 = ... = mu_N" _col(44) "Wald chi2(" as res `Wdf' as txt ") = " as res %9.3f `Wmu' _col(68) as txt "p = " as res %6.4f `Wp' di as txt " -> residuals used below: " as res "`rtype'" di as txt "{hline 78}" di as txt "[2] Squared `rtype' residuals: partial autocorrelations and LM-ARCH" di as txt _col(8) "lag" _col(17) "PAC" _col(28) "t-ratio" _col(40) "p (1-sided)" _col(55) "LM-ARCH(j)" _col(70) "p-value" forvalues k = 1/`lags' { local pv = `PAC'[`k', 3] local st "" if `pv' < 0.10 local st "*" if `pv' < 0.05 local st "**" if `pv' < 0.01 local st "***" di as txt _col(6) %4.0f `k' as res _col(12) %9.4f `PAC'[`k', 1] as txt "`st'" _col(26) as res %9.3f `PAC'[`k', 2] _col(40) %9.4f `pv' _col(53) %11.3f `LM'[`k', 1] _col(68) %8.4f `LM'[`k', 3] } local nsig 0 forvalues k = 1/`lags' { if `PAC'[`k', 3] < `siglevel' local nsig = `nsig' + 1 } local sig1 = (`PAC'[1, 3] < `siglevel') di as txt "{hline 78}" di as txt "[3] Individual effects in the variance" di as txt " AR(`arfe') of u^2 with vs without unit intercepts" _col(52) "F(" as res `FE'[1,2] as txt "," as res `FE'[1,3] as txt ") = " as res %8.3f `FE'[1,1] _col(71) as txt " p = " as res %5.3f `FE'[1,4] di as txt _col(52) "chi2(" as res `FE'[1,2] as txt ") = " as res %8.3f `FE'[1,5] _col(71) as txt " p = " as res %5.3f `FE'[1,6] if "`xs'" == "" { di as txt " LR groupwise heteroskedasticity" _col(52) "chi2(" as res `XS'[1,2] as txt ") = " as res %8.3f `XS'[1,1] _col(71) as txt " p = " as res %5.3f `XS'[1,3] di as txt "{hline 78}" di as txt "[4] Cross-sectional correlation of `rtype' residuals" di as txt " LR test, H0: Sigma diagonal" _col(52) "chi2(" as res `XS'[2,2] as txt ") = " as res %8.3f `XS'[2,1] _col(71) as txt " p = " as res %5.3f `XS'[2,3] di as txt " Breusch-Pagan LM" _col(52) "chi2(" as res `XS'[3,2] as txt ") = " as res %8.3f `XS'[3,1] _col(71) as txt " p = " as res %5.3f `XS'[3,3] di as txt " Pesaran CD" _col(52) "N(0,1) = " as res %8.3f `XS'[4,1] _col(71) as txt " p = " as res %5.3f `XS'[4,3] di as txt "{hline 78}" di as txt "[5] Cross products u_it*u_jt: pooled AR(`cplags')" forvalues k = 1/`cplags' { di as txt " lag `k'" _col(20) "coef = " as res %9.4f `CP'[`k',1] as txt " t = " as res %8.3f `CP'[`k',2] as txt " p = " as res %6.4f `CP'[`k',3] } capture confirm matrix `CPFE' if _rc == 0 { di as txt " pair-specific intercepts" _col(52) "F(" as res `CPFE'[1,2] as txt "," as res `CPFE'[1,3] as txt ") = " as res %8.3f `CPFE'[1,1] _col(71) as txt " p = " as res %5.3f `CPFE'[1,4] } } di as txt "{hline 78}" // ---------------- recommendation ------------------------------------- local vfe = (`FE'[1, 4] < `siglevel') if "`xs'" == "" { if `XS'[1, 3] < `siglevel' local vfe 1 } local mdl "A" if `usefe' & !`vfe' local mdl "B" if !`usefe' & `vfe' local mdl "C" if `usefe' & `vfe' local mdl "D" local vspec "arch(1)" if `nsig' > 1 local vspec "arch(1) garch(1)" if `nsig' == 0 local vspec "none detected" local cvspec "none" if "`xs'" == "" { if `XS'[2, 3] < `siglevel' { local cvspec "common" capture confirm matrix `CPFE' if _rc == 0 { if `CPFE'[1, 4] < `siglevel' local cvspec "pair" } } } di as txt "Suggested starting specification (informal, CG 2006 p. 266):" di as txt " model(" as res "`mdl'" as txt ") variance: " as res "`vspec'" as txt " cov(" as res "`cvspec'" as txt ")" di as txt " Significant PACs of u^2 at `=100*`siglevel''%: " as res `nsig' as txt " of `lags'" di as txt " CG (2006) stress that several ML specifications should still be compared (LR tests)." di as txt "{hline 78}" return scalar N = `N' return scalar T = `T' return scalar wald_mu = `Wmu' return scalar wald_mu_df = `Wdf' return scalar wald_mu_p = `Wp' return scalar haclags = `haclags' return scalar F_varfe = `FE'[1, 1] return scalar p_varfe = `FE'[1, 4] return scalar chi2_varfe = `FE'[1, 5] return scalar n_sig_pac = `nsig' if "`xs'" == "" { return scalar lr_grouphet = `XS'[1, 1] return scalar p_grouphet = `XS'[1, 3] return scalar lr_xcorr = `XS'[2, 1] return scalar p_xcorr = `XS'[2, 3] return scalar lm_bp = `XS'[3, 1] return scalar p_bp = `XS'[3, 3] return scalar cd = `XS'[4, 1] return scalar p_cd = `XS'[4, 3] return matrix crossprod_ar = `CP' } return local residuals "`rtype'" return local suggest_model "`mdl'" return local suggest_var "`vspec'" return local suggest_cov "`cvspec'" return matrix pac = `PAC' return matrix lmarch = `LM' end