? ret = garchm(r, 1, 2, l1, 1, 0, 0, 0, 0.7, 1, 1, null, null)
================================================================
GJR-GARCH-in-Mean fucntion for gretl by Yi-Nung Yang
Chung Yuan Christian University, Taiwan
http://yaya.it.cycu.edu.tw/gretl
================================================================
The coefficient of GJR Term is gamma_i
Presample variance: backcast (parameter = 0.7)
Initial Values:
b1=-0.131806, omega=1.126780, alpha1=0.120000, alpha2=0.040000, gamma1=0.040000, beta1=0.600000,
------- mean eq & variance eq in this GARCH model --------
e= y -b1*X1
h = omega +alpha1*(e(-1))^2+alpha2*(e(-2))^2+gamma1*(e(-1))^2*(e(-1)<0)+beta1*h(-1)
================================================================
Using numerical derivatives
Tolerance = 1.81899e-012
Function evaluations: 166
Evaluations of gradient: 39
Model 8: 最大概似法 (ML), using observations 3-1361 (T = 1359)
ll = -0.5*(log(2*pi)+log(h) + (e^2)/h)
Standard errors based on Outer Products matrix
estimate std. error t-ratio p-value
--------------------------------------------------------
b1 -0.0670351 0.0246001 -2.725 0.0064 ***
omega 0.0101593 0.00146715 6.924 4.38e-012 ***
alpha1 -0.0870361 0.0151949 -5.728 1.02e-08 ***
alpha2 0.0597284 0.0162602 3.673 0.0002 ***
gamma1 0.146400 0.0172923 8.466 2.53e-017 ***
beta1 0.940360 0.00960635 97.89 0.0000 ***
Log-likelihood -1772.480 Akaike criterion 3556.959
Schwarz criterion 3588.246 Hannan-Quinn 3568.673
Replaced list ret
Evniews 估計結果
Dependent Variable: R
Method: ML - ARCH (Marquardt) - Normal distribution
Date: 01/22/10 Time: 01:34
Sample (adjusted): 1/06/2004 5/29/2009
Included observations: 1359 after adjustments
Estimation settings: tol= 0.00010, derivs=accurate numeric (linear)
Initial Values: C(1)=-0.13181, C(2)=1.19673, C(3)=0.13333, C(4)=0.04444,
C(5)=0.04444, C(6)=0.53333
Convergence achieved after 22 iterations
Presample variance: backcast (parameter = 0.7)
GARCH = C(2) + C(3)*RESID(-1)^2 + C(4)*RESID(-1)^2*(RESID(-1)<0) +
C(5)*RESID(-2)^2 + C(6)*GARCH(-1)
Coefficient Std. Error z-Statistic Prob.
R(-1) -0.068286 0.024528 -2.784002 0.0054
Variance Equation
C 0.010315 0.001488 6.934109 0.0000
RESID(-1)^2 -0.086935 0.015597 -5.573912 0.0000
RESID(-1)^2*(RESID(-1)<0) 0.146578 0.017262 8.491349 0.0000
RESID(-2)^2 0.059067 0.016569 3.564933 0.0004
GARCH(-1) 0.940811 0.009581 98.19407 0.0000
R-squared 0.013200 Mean dependent var -0.015854
Adjusted R-squared 0.009553 S.D. dependent var 1.330019
S.E. of regression 1.323651 Akaike info criterion 2.617407
Sum squared resid 2370.525 Schwarz criterion 2.640429
Log likelihood -1772.528 Hannan-Quinn criter. 2.626026
Durbin-Watson stat 2.145564
function list garchm (series depvar "Dep. var (應變數)", int GARCH[0:9:1] "GARCH p", int ARCH[1:9:1] "ARCH q", list indepvar[null] "Indpe var (自變數) list", int gjr_order[0:9:0] "GJR order (階次)", int option[0:3:0] "GRACH-in-Mean (選項 0:none; 1:stdev; 2:h; 3:lnh)", int LB_Q[0:200:0] "Ljung-Box Q (殘差 Q 檢定階次)", int LB_Q2[0:200:0] "Ljung-Box Q2 (殘差 Q2 檢定階次)", scalar backcast[0:1:0.7] "backcasting (參數)", bool ShowInit[0] "Show Init. (顯示起始值)?", bool save_resid[0] "Save standardized residual and h (儲存殘差和 h)?", string res_name[null] "User-defined residual (自訂殘差名稱)", string ht_name[null] "User-defined h (自訂 h 名稱)")
#================================================================
# GJR-GARCH-in-Mean fucntion for gretl by Yi-Nung Yang
# Chung Yuan Christian University, Taiwan
# http://yaya.it.cycu.edu.tw/gretl
#================================================================
set echo off
set messages off
# -------- variance equation -----------
# series h = omega + alpha*(e(-1))^2 + beta*h(-1)
if ARCH=0
funcerr "ARCH q 必須大於 0"
else
string v_eq = "h = omega "
string arch_param = "omega "
loop j=1..ARCH --quiet
sprintf arch_term "+alpha%d*(e(-%d))^2",j,j
sprintf v_param "alpha%d ",j
scalar @v_param = 0.04
string v_eq = v_eq ~ arch_term
string arch_param = arch_param ~ v_param
endloop
if gjr_order>0
loop j=1..gjr_order --quiet
sprintf arch_term "+gamma%d*(e(-%d))^2*(e(-%d)<0)",j,j,j
sprintf v_param "gamma%d ",j
scalar @v_param = 0.05
string v_eq = v_eq ~ arch_term
string arch_param = arch_param ~ v_param
endloop
endif
if GARCH>0
loop j=1..GARCH --quiet
sprintf arch_term "+beta%d*h(-%d)",j,j
sprintf v_param "beta%d ",j
scalar @v_param = 0.04
string v_eq = v_eq ~ arch_term
string arch_param = arch_param ~ v_param
endloop
endif
endif
# printf "%s\n", v_eq
# printf "%s\n", arch_param
tL2 = indepvar
tL3 = indepvar || const
genr is_const = (tL2 = tL3)
if is_const = 1
tL2 -= const
endif
i=1
loop foreach j tL2 --quiet
string temp="x"
sprintf temp "X%d",i
#producing tmp%d independent variables
genr @temp = tL2.$j
i=i+1
endloop
scalar n_x = i-1
scalar j=1
# define ----------> mean eq.
if is_const = 1
string m_eq = "e = y - b0 "
string tParam = "b0 "
else
string m_eq = "e= y "
string tParam = " "
endif
if n_x >=1
loop j=1..n_x --quiet
sprintf tx "-b%d*X%d", j,j
sprintf tparameter "b%d ", j
scalar @tparameter = 0.0001
string m_eq = m_eq ~ tx
string tParam = tParam ~ tparameter
endloop
endif
if option>0
if option=1
string m_eq = m_eq ~ "-theta*h^0.5"
string tPremium="SQRT(h)"
endif
if option=2
string m_eq = m_eq ~ "-theta*h"
string tPremium="h"
endif
if option=3
string m_eq = m_eq ~ "-theta*log(h)"
string tPremium="ln(h)"
endif
if option>3
funcerr "The GARCH-in-mean options are 1, 2, 3."
endif
string tParam = "theta " ~ tParam
else
string tPremium="None"
endif
# printf "%s\n", m_eq
#scalar backcast=0.7
series y=depvar
scalar mu = -0.037
scalar alpha1 = 0.15 - 0.03*(ARCH>1)
scalar beta1 = 0.6 - 0.12*(GARCH>1)
scalar gamma1=0.05 - 0.01*(ARCH>1)
#### scalar theta =0.01879
scalar b0=-0.00377
scalar b1=0.5
scalar b2=0.4
#scalar omega = 1.149
#scalar omega =var(y)*(1-alpha1-beta1)
scalar omega =var(y)*backcast*0.91
printf "\n\n\n\n"
printf "================================================================\n"
printf " GJR-GARCH-in-Mean fucntion for gretl by Yi-Nung Yang\n"
printf " Chung Yuan Christian University, Taiwan\n"
printf " http://yaya.it.cycu.edu.tw/gretl\n"
printf "================================================================\n"
if gjr_order>0
printf "The coefficient of GJR Term is gamma_i\n"
endif
if option>0
printf "GARCH in mean Term is %s\n",tPremium
printf "The coefficient of GARCH in mean Term is theta\n"
printf "----------------------------------------------------------------\n"
endif
printf "Presample variance: backcast (parameter = %.1f)\n",backcast
# obtaining intiatial values from OLS and printing intial values
# -----------ols ty const
# -----------printf "islist()=%d, nelem()=%d ===>\n",islist(indepvar) ,nelem(indepvar)
if nelem(indepvar) > 0
ols y indepvar --quiet
# to keep the sample in use
genr dum_original = $sample
/*
garch GARCH ARCH ; y indepvar
if option=1
series tInMean=$h^0.5
elif option=2
series tInMean=$h
elif option=3
series tInMean=log($h)
endif
*/
# ----- obtaining initial value for theta (nelem>0)
if option > 0
#garch GARCH ARCH ; y indepvar
ols y indepvar --quiet
if option=1
series tInMean=($uhat^2)^0.5
elif option=2
series tInMean=($uhat^2)
elif option=3
series tInMean=log(($uhat^2))
endif
ols y indepvar --quiet
#series tInMean=($uhat^2)^0.5
ols y indepvar tInMean --quiet
#ols y tInMean --quiet
scalar theta= $coeff(tInMean)
endif
if ShowInit = 1 ### --- printing intial values
printf "Initial Values:\n"
if option >0
printf "theta=%.6f, ",theta
endif
endif
ols y indepvar --quiet
if is_const = 1
scalar b0=$coeff(const)
if ShowInit = 1 ### --- printing intial values
printf "b0=%.6f, ",b0
endif
matrix B=$coeff
k=$ncoeff-1
loop j=1..k --quiet
scalar b$j = B[j+1]
if ShowInit = 1 ### --- printing intial values
printf "b%d=%.6f, ",j,b$j
endif
endloop
else
matrix B=$coeff
k=$ncoeff
loop j=1..k --quiet
scalar b$j = B[j]
if ShowInit = 1 ### --- printing intial values
printf "b%d=%.6f, ",j,b$j
endif
endloop
endif
else # ======================--------if nelem = 0
ols y const --quiet
# to keep the sample in use
genr dum_original = $sample
# ----- obtaining initial value for theta (nelem=0)
if option > 0
#garch GARCH ARCH ; y indepvar
if option=1
series tInMean=($uhat^2)^0.5
elif option=2
series tInMean=($uhat^2)
elif option=3
series tInMean=log(($uhat^2))
endif
ols y tInMean --quiet
scalar theta= $coeff(tInMean)
endif
if ShowInit = 1 ### --- printing intial values
printf "Initial Values:\n"
if option >0
printf "theta=%.6f, ",theta
endif
endif
endif
if ShowInit = 1 ### --- printing intial values
printf "omega=%.6f, ",omega
loop j=1..ARCH --quiet
printf "alpha%d=%.6f, ",j, alpha$j
endloop
if gjr_order>0
loop j=1..gjr_order --quiet
printf "gamma%d=%.6f, ",j, gamma$j
endloop
endif
if GARCH>0
loop j=1..GARCH --quiet
printf "beta%d=%.6f, ",j, beta$j
endloop
endif
endif
string tAllParams = tParam ~ " " ~ arch_param
# --- delete ---> printf "%s\n", tParam
printf "\n------- mean eq & variance eq in this GARCH model --------\n"
printf " %s\n",m_eq
printf " %s\n",v_eq
printf "================================================================\n"
scalar presample=0 ####y[1]/backcast #see Eviews 6 Users guide, p.320 for algorithm
loop j=2..100 --quiet
presample = presample + backcast^(j-2)*y[j]^2
endloop
mle ll = -0.5*(log(2*pi)+log(h) + (e^2)/h)
series h = backcast^($nobs)*var(y) + (1-backcast)*presample
#####series h = backcast^($nobs)*var(y) + (1-backcast)*(y[2]^2+backcast*y[3]^2+backcast^2*y[4]^2+backcast^3*y[5]^2+backcast^4*y[6]^2+backcast^5*y[7]^2)
#------------------------series e = y - theta*h^0.5
series @m_eq
#------------------------series e= y - b0 -b1*X1-b2*X2
# ---> to be deleted -----> series h = omega + alpha*(e(-1))^2 + beta*h(-1)
series @v_eq
params @tAllParams
end mle
genr dum_in_mle = $sample
##### printf ">>>>>>>>>>>>>>>>>>sample size in MLE, nobs=%d, T=%d\n",$nobs, $T
# 定義計算 estimated residuals 要取幾個落後期
scalar start = $nobs-$T+1
# --- to be deleted ---> printf "NOBS=%d T=%d\n",$nobs,$T
# ---- generating standardized residual and ht
# ---- diagnosis of standardized residuals
/*
if LB_Q>0 && LB_Q2>0
smpl full
series h = backcast^($nobs)*var(y) + (1-backcast)*presample
series e=0
if option>0
End=$T-1
loop for j=1..End
smpl j j
genr @m_eq
smpl +1 +1
genr @v_eq
endloop
genr @m_eq
smpl full
else
series @m_eq
series @v_eq
endif
series stz_u=e/h^0.5
series stz_u2 = stz_u^2
corrgm stz_u LB_Q --quiet
corrgm stz_u2 LB_Q2 --quiet
endif
*/
# ---- generating standardized residual (=e/h^0.5) and ht (=h)
series h = backcast^($nobs)*var(y) + (1-backcast)*presample
#series e=0
if option>0
End=$T-1
loop for j=start..End --quiet
smpl j j
genr @m_eq
smpl +1 +1
genr @v_eq
endloop
genr @m_eq
# 回復為原來的樣本
smpl dum_original --dummy --replace
else
series @m_eq
series @v_eq
endif
if isstring(res_name) =0
sprintf res_name "stz_u" # default name for e(t)
endif
if isstring(ht_name) =0
sprintf ht_name "h" # default name for h(t)
endif
# 回復為原來的樣本
smpl dum_original --dummy --replace
series @res_name =e/h^0.5
series @ht_name=h
if LB_Q >0
corrgm @res_name LB_Q --quiet
endif
if LB_Q2>0
series stz_u2=@res_name^2
corrgm stz_u2 LB_Q2 --quiet
endif
if save_resid=1
list retlist= @res_name @ht_name
return retlist
else
list retlist = const
return retlist
endif
end function
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