'Generalized Autoregressive Score (GAS) approach to univariate GARCH Models

'Open the workfile
wfopen ".\usdtry.wf1"

'Convert log returns to approximate percentages
returns = 100*returns

'Generate series for squared returns
series returnsq = returns^2

'Visually compare the size of shocks
freeze(mode=overwrite,figure1) returnsq.line
figure1.axis dual
figure1.setupdate(a)

'Estimate GARCH(1,1) model with normally distributed innovations
equation eq_garch_normal.arch(backcast=1) returns c 
eq_garch_normal.makegarch garchvar_n 'save conditional variance series
freeze(mode=overwrite,table1a) eq_garch_normal.results

'Estimate GAS(1,1) model with normally distributed innovations
eq_garch_normal.gasmodelu(results,makescores)
rename outtab table1b

'Compare conditional variance estimates for normal distribution
rename score condvar_n
graph figure3.line garchvar_n condvar_n
figure3.setupdate(a)
figure3.axis dual
figure3.legend columns(2)
figure3.setelem(1) legend(GARCH-normal)
figure3.setelem(2) legend(GAS-normal)

'Estimate GARCH(1,1) model with Student's-t distributed innovations
equation eq_garch_student.arch(tdist,backcast=1) returns c
eq_garch_student.makegarch garchvar_t 'save conditional variance series
freeze(mode=overwrite,table2a) eq_garch_student.results

'Estimate GAS(1,1) model with Student's-t distributed innovations
eq_garch_student.gasmodelu(results,makescores)
rename outtab table2b

'Compare conditional variance estimates for Student's-t distribution
rename score condvar_t
graph figure4.line garchvar_t condvar_t
figure4.setupdate(a)
figure4.axis dual
figure4.legend columns(2)
figure4.setelem(1) legend(GARCH-Student)
figure4.setelem(2) legend(GAS-Student)

'Estimate GARCH(1,1) model with assuming skewed Student's-t innovations
eq_garch_student.skewedugarch(results,makegarch)
rename outtab table3a

'Estimate GAS(1,1) model with skewed Student's-t distributed innovations
eq_garch_student.gasmodelu(skewt,logasy,results,makescores)
rename outtab table3b

'Compare conditional variance estimates for Skewed Student's-t distribution
rename garchskew garchvar_s
rename score condvar_s
graph figure5.line garchvar_s condvar_s
figure5.setupdate(a)
figure5.axis dual
figure5.legend columns(2)
figure5.setelem(1) legend(GARCH-Skewed Student)
figure5.setelem(2) legend(GAS-Skewed Student)