GARCHUVMAX.RPF

GARCHUVMAX.RPF provides examples of estimates of less-standard univariate GARCH models using MAXIMIZE. For standard models, see GARCHUV.RPF.

The list of models is from Cappiello, Engle & Sheppard(2006).

Full Program

open data garch.asc
data(format=free,org=columns) 1 1867 bp cd dm jy sf
*
set dlogdm = 100*log(dm/dm{1})
*
* Estimate a GARCH(1,1) with an AR(1) mean model
*
garch(p=1,q=1,reg) / dlogdm
# constant dlogdm{1}
*
* Same model estimated using MAXIMIZE
*
linreg dlogdm
# constant dlogdm{1}
frml(lastreg,vector=beta) meanf
nonlin(parmset=meanparms) beta
*
set uu = %seesq
set h = %seesq
set u = 0.0
*
nonlin(parmset=garchparms) c a b
compute a=.05,b=.75,c=%seesq*(1-a-b)
frml varf = c+a*uu{1}+b*h{1}
*
* This computes the variance first, since the mean formula *can* depend upon
* current H (in an "M" model), while the variance has to be computed from lagged
* information.
*
frml logl = (h(t)=varf(t)),(u=dlogdm-meanf),$
(uu(t)=u^2),%logdensity(h,u)
maximize(parmset=meanparms+garchparms) logl 3 *
*
* Parameter sets used in some of the models
*
nonlin(parmset=powerparms) lambda
nonlin(parmset=asymmparms) d
****************************************************************************
*
* AVGARCH (absolute value)
*
frml varf = (c+a*sqrt(uu{1})+b*sqrt(h{1}))^2
compute c=sqrt(%seesq)
maximize(parmset=meanparms+garchparms,title="Absolute Value GARCH") logl 3 *
****************************************************************************
*
* NGARCH (non-linear (power) GARCH)
*
compute lambda=2.0
frml varf = (c+a*uu{1}^(.5*lambda)+b*h{1}^(.5*lambda))^(2.0/lambda)
compute c=%seesq
maximize(parmset=meanparms+garchparms+powerparms,title="Non-linear GARCH") logl 3 *
****************************************************************************
*
* APARCH (asymmetric power GARCH)
*
compute lambda=2.0
frml varf = uupower=uu{1}^(.5*lambda),$
(c+a*uupower+d*%if(u{1}<0,uupower,0.0)+b*h{1}^(.5*lambda))^(2.0/lambda)
compute c=%seesq,d=0.0
maximize(parmset=meanparms+garchparms+asymmparms+powerparms,title="Asymmetric power GARCH") logl 3 *
****************************************************************************
*
* ZARCH (threshold). This could be done as APARCH with lambda pegged to 1.0
*
frml varf = uupower=sqrt(uu{1}),(c+a*uupower+d*%if(u{1}<0,uupower,0.0)+b*sqrt(h{1}))^2.0
compute c=%seesq
maximize(parmset=meanparms+garchparms+asymmparms,title="ZARCH") logl 3 *
*****************************************************************************
*****************************************************************************
*
* Models with an recentering of the news impact curve can't use the
* lagged u^2 terms.
*
* AGARCH (asymmetric with recentering)
*
frml varf = (c+a*(u{1}+d)^2+b*h{1})
compute d=0.0
compute c=%seesq
maximize(parmset=meanparms+garchparms+asymmparms,title="AGARCH") logl 3 *
*****************************************************************************
*
* NAGARCH (non-linear asymmetric)
*
frml varf = (c+a*(u{1}+d*sqrt(h{1}))^2+b*h{1})
compute d=0.0
compute c=%seesq
maximize(parmset=meanparms+garchparms+asymmparms,title="NAGARCH") logl 3 *

Output

GARCH Model - Estimation by BFGS

Convergence in 28 Iterations. Final criterion was 0.0000093 <= 0.0000100

Dependent Variable DLOGDM

Usable Observations 1865

Log Likelihood -2063.0356

Variable Coeff Std Error T-Stat Signif

************************************************************************************

1. Constant -0.022621703 0.015610504 -1.44913 0.14730032

2. DLOGDM{1} -0.075889879 0.023563027 -3.22072 0.00127870

3. C 0.015799598 0.004710060 3.35444 0.00079527

4. A 0.110535373 0.015870409 6.96487 0.00000000

5. B 0.868634155 0.017976476 48.32060 0.00000000

Linear Regression - Estimation by Least Squares

Dependent Variable DLOGDM

Usable Observations 1865

Degrees of Freedom 1863

Centered R^2 0.0035975

R-Bar^2 0.0030627

Uncentered R^2 0.0036039

Mean of Dependent Variable -0.001964639

Std Error of Dependent Variable 0.777020180

Standard Error of Estimate 0.775829392

Sum of Squared Residuals 1121.3606491

Regression F(1,1863) 6.7263

Significance Level of F 0.0095743

Log Likelihood -2171.9406

Durbin-Watson Statistic 1.9961

Variable Coeff Std Error T-Stat Signif

************************************************************************************

1. Constant -0.002092808 0.017965051 -0.11649 0.90727417

2. DLOGDM{1} -0.059974943 0.023124922 -2.59352 0.00957431

MAXIMIZE - Estimation by BFGS

Convergence in 20 Iterations. Final criterion was 0.0000022 <= 0.0000100

Usable Observations 1865

Function Value -2063.0240

Variable Coeff Std Error T-Stat Signif

************************************************************************************

1. BETA(1) -0.022623391 0.016203039 -1.39624 0.16264112

2. BETA(2) -0.075892034 0.026794253 -2.83240 0.00462001

3. C 0.015794165 0.004747697 3.32670 0.00087881

4. A 0.110520531 0.015950955 6.92877 0.00000000

5. B 0.868657113 0.018042122 48.14606 0.00000000

Absolute Value GARCH - Estimation by BFGS

Convergence in 47 Iterations. Final criterion was 0.0000084 <= 0.0000100

Usable Observations 1865

Function Value -2061.5041

Variable Coeff Std Error T-Stat Signif

************************************************************************************

1. BETA(1) -0.026919813 0.012790471 -2.10468 0.03531942

2. BETA(2) -0.079408104 0.011105814 -7.15014 0.00000000

3. C 0.023015729 0.005601336 4.10897 0.00003974

4. A 0.110630929 0.012570237 8.80102 0.00000000

5. B 0.885150425 0.013634391 64.92042 0.00000000

Non-linear GARCH - Estimation by BFGS

Convergence in 36 Iterations. Final criterion was 0.0000004 <= 0.0000100

Usable Observations 1865

Function Value -2060.8529

Variable Coeff Std Error T-Stat Signif

************************************************************************************

1. BETA(1) -0.024384271 0.016403460 -1.48653 0.13713841

2. BETA(2) -0.078483020 0.023028808 -3.40804 0.00065432

3. C 0.020323544 0.006069570 3.34843 0.00081270

4. A 0.115017348 0.014152503 8.12700 0.00000000

5. B 0.880155595 0.016038306 54.87834 0.00000000

6. LAMBDA 1.309962163 0.291926099 4.48731 0.00000721

## NL6. NONLIN Parameter D Has Not Been Initialized. Trying 0

Asymmetric power GARCH - Estimation by BFGS

Convergence in 42 Iterations. Final criterion was 0.0000006 <= 0.0000100

Usable Observations 1865

Function Value -2059.5575

Variable Coeff Std Error T-Stat Signif

************************************************************************************

1. BETA(1) -0.030208846 0.016457843 -1.83553 0.06642736

2. BETA(2) -0.079082987 0.024333247 -3.25000 0.00115406

3. C 0.017355530 0.005905951 2.93865 0.00329644

4. A 0.099436867 0.016570877 6.00070 0.00000000

5. B 0.886523720 0.016247909 54.56233 0.00000000

6. D 0.025615715 0.016750165 1.52928 0.12619471

7. LAMBDA 1.341885661 0.298443347 4.49628 0.00000692

ZARCH - Estimation by BFGS

Convergence in 31 Iterations. Final criterion was 0.0000004 <= 0.0000100

Usable Observations 1865

Function Value -2060.3065

Variable Coeff Std Error T-Stat Signif

************************************************************************************

1. BETA(1) -0.032112685 0.015428720 -2.08136 0.03740118

2. BETA(2) -0.080649265 0.023493793 -3.43279 0.00059740

3. C 0.020206127 0.006055521 3.33681 0.00084746

4. A 0.098293164 0.015300427 6.42421 0.00000000

5. B 0.891043847 0.015459736 57.63642 0.00000000

6. D 0.019852281 0.012532918 1.58401 0.11319121

AGARCH - Estimation by BFGS

Convergence in 28 Iterations. Final criterion was 0.0000065 <= 0.0000100

Usable Observations 1865

Function Value -2062.1389

Variable Coeff Std Error T-Stat Signif

************************************************************************************

1. BETA(1) -0.026033888 0.015509378 -1.67859 0.09323196

2. BETA(2) -0.076276400 0.023559595 -3.23759 0.00120542

3. C 0.014603149 0.005032134 2.90198 0.00370813

4. A 0.108802103 0.015793791 6.88892 0.00000000

5. B 0.872234990 0.018760091 46.49418 0.00000000

6. D -0.036439841 0.046844054 -0.77790 0.43662984

NAGARCH - Estimation by BFGS

Convergence in 58 Iterations. Final criterion was 0.0000009 <= 0.0000100

Usable Observations 1865

Function Value -2061.8880

Variable Coeff Std Error T-Stat Signif

************************************************************************************

1. BETA(1) -0.027072535 0.015942802 -1.69810 0.08948815

2. BETA(2) -0.076891600 0.024073901 -3.19398 0.00140325

3. C 0.014337891 0.004348731 3.29703 0.00097713

4. A 0.108715550 0.014836108 7.32777 0.00000000

5. B 0.872723345 0.017346038 50.31255 0.00000000

6. D -0.078073853 0.075084625 -1.03981 0.29842750