fit actual vs fitted first difference of the dependent variable *!
resid residuals over time with +/- 2 sigma bands *!
hist residual histogram with a fitted normal density *!
qq normal quantile-quantile plot of the residuals *!
ac residual autocorrelation function *!
pac residual partial autocorrelation function *!
ect the error-correction term over time *!
bounds the three bounds statistics against their critical values *!
bootFov bootstrap null distribution of F_overall *!
boottDV bootstrap null distribution of t_DV *!
bootFind bootstrap null distribution of F_ind *!
dash a combined dashboard of the six residual panels capture program drop _aardl_graphs program define _aardl_graphs version 17 syntax , RESid(varname) FItted(varname) DY(varname) ESample(varname) /// TIMevar(varname) [ ECT(varname) GRAPHPrefix(string) /// BOUNDSmat(string) BOOTmat(string) BOOTStats(string) /// DEPvar(string) NODASHboard ] local p "`graphprefix'" // ---- 1. actual vs fitted -------------------------------------------- capture noisily { twoway (line `dy' `timevar' if `esample', lcolor("31 119 180") lwidth(medium)) /// (line `fitted' `timevar' if `esample', lcolor("214 39 40") /// lpattern(shortdash) lwidth(medium)), /// title("Actual vs fitted", size(medium)) /// subtitle("First difference of `depvar'", size(small)) /// ytitle("D.`depvar'", size(small)) xtitle("`timevar'", size(small)) /// legend(order(1 "Actual" 2 "Fitted") size(small) rows(1)) /// scheme(s2color) name(`p'fit, replace) nodraw } // ---- 2. residuals with +/- 2 sigma ---------------------------------- qui summarize `resid' if `esample' local sd = r(sd) capture noisily { twoway (line `resid' `timevar' if `esample', lcolor("31 119 180") lwidth(medium)), /// yline(0, lcolor(gs10)) /// yline(`=2*`sd'', lcolor("214 39 40") lpattern(dash)) /// yline(`=-2*`sd'', lcolor("214 39 40") lpattern(dash)) /// title("Residuals", size(medium)) /// subtitle("with +/- 2 standard-deviation bands", size(small)) /// ytitle("Residual", size(small)) xtitle("`timevar'", size(small)) /// legend(off) scheme(s2color) name(`p'resid, replace) nodraw } // ---- 3. histogram + normal ------------------------------------------ capture noisily { histogram `resid' if `esample', normal fcolor("31 119 180*.55") /// lcolor("31 119 180") normopts(lcolor("214 39 40") lwidth(medthick)) /// title("Residual distribution", size(medium)) /// subtitle("with fitted normal density", size(small)) /// xtitle("Residual", size(small)) /// scheme(s2color) name(`p'hist, replace) nodraw } // ---- 4. normal Q-Q ---------------------------------------------------- capture noisily { qnorm `resid' if `esample', /// mcolor("31 119 180") msize(small) /// rlopts(lcolor("214 39 40") lpattern(dash)) /// title("Normal Q-Q plot of residuals", size(medium)) /// scheme(s2color) name(`p'qq, replace) nodraw } // ---- 5-6. residual ACF and PACF -------------------------------------- capture noisily { ac `resid' if `esample', lags(16) /// title("Residual autocorrelation", size(medium)) /// scheme(s2color) name(`p'ac, replace) nodraw } capture noisily { pac `resid' if `esample', lags(16) /// title("Residual partial autocorrelation", size(medium)) /// scheme(s2color) name(`p'pac, replace) nodraw } // ---- 7. error-correction term ---------------------------------------- if "`ect'" != "" { capture noisily { twoway (line `ect' `timevar' if `esample', lcolor("44 160 44") /// lwidth(medthick)), /// yline(0, lcolor("214 39 40") lpattern(dash)) /// title("Error-correction term", size(medium)) /// subtitle("Deviation from the long-run relationship", size(small)) /// ytitle("ECT", size(small)) xtitle("`timevar'", size(small)) /// legend(off) scheme(s2color) name(`p'ect, replace) nodraw } } // ---- 8. bounds-test summary ------------------------------------------ // boundsmat rows: F_overall, t_DV, F_ind ; cols: statistic, lower, upper if "`boundsmat'" != "" { capture noisily { mat _aardl_bnd = `boundsmat' preserve qui clear qui set obs 3 qui gen byte id = _n qui gen double st = . qui gen double lb = . qui gen double ub = . forvalues i = 1/3 { qui replace st = el(_aardl_bnd,`i',1) in `i' qui replace lb = el(_aardl_bnd,`i',2) in `i' qui replace ub = el(_aardl_bnd,`i',3) in `i' } label define _aardlb 1 "F_overall" 2 "t_DV" 3 "F_ind", replace label values id _aardlb twoway (rbar lb ub id, barwidth(.45) color("128 128 128*.35")) /// (scatter st id, mcolor("214 39 40") msymbol(diamond) /// msize(large)), /// xlabel(1 2 3, valuelabel) xscale(range(0.5 3.5)) /// title("Bounds tests vs critical values", size(medium)) /// subtitle("Bar = I(0)-I(1) band or bootstrap 5% level", size(small)) /// ytitle("Statistic", size(small)) xtitle("") /// legend(order(2 "Test statistic" 1 "Critical band") size(small) rows(1)) /// scheme(s2color) name(`p'bounds, replace) nodraw restore capture mat drop _aardl_bnd } } // ---- 9. bootstrap null distributions --------------------------------- if "`bootmat'" != "" { capture confirm matrix `bootmat' if _rc == 0 { local nms "Fov tDV Find" local ttl1 "F_overall" local ttl2 "t_DV" local ttl3 "F_ind" forvalues j = 1/3 { local nm : word `j' of `nms' local ob : word `j' of `bootstats' capture noisily { mat _aardl_bd = `bootmat' preserve qui clear qui svmat double _aardl_bd, names(bs) qui keep if bs`j' < . qui count if r(N) > 10 { local ttl "`ttl`j''" twoway (histogram bs`j', fcolor("31 119 180*.45") /// lcolor("31 119 180") bin(40)), /// xline(`ob', lcolor("214 39 40") lwidth(medthick)) /// title("Bootstrap null distribution: `ttl'", size(medium)) /// subtitle("Red line = observed statistic", size(small)) /// xtitle("`ttl' under H0", size(small)) /// legend(off) scheme(s2color) /// name(`p'boot`nm', replace) nodraw } restore capture mat drop _aardl_bd } } } } // ---- 10. dashboard ---------------------------------------------------- if "`nodashboard'" == "" { capture noisily { graph combine `p'fit `p'resid `p'hist `p'qq `p'ac `p'pac, /// cols(2) iscale(.55) imargin(small) /// title("aardl residual diagnostics", size(medsmall)) /// scheme(s2color) name(`p'dash, replace) nodraw } } // draw everything that was built foreach g in fit resid hist qq ac pac ect bounds bootFov boottDV bootFind dash { capture graph display `p'`g' } end