I have seen the discussion in the following link for programming Multivariate GARCH-mean model.
http://forums.eviews.com/viewtopic.php?f=4&t=273#p971
However, the discussion is about bi/trivariate GARCH. In these cases, we could spread out the var-covariance matrix to compute the matrix determinant easily. When the variables are going to be large, saying 7 variables in my cases, I think it's better to use matrix operation to @det(X) for determinants and others like a matrix multiplying a group.
Thus, I have modified the TV_GARCH example. But the results I got are not correct as following. Also, I have my code below. appreciate anyone help.
- error infor
- Capture.JPG (137.44 KiB) Viewed 5293 times
Here is my code. I suspect whether the matrix operation is incorrect. I appreciate anyone's help.
' TV_GARCH.PRG (10/10/2000)
' example program for EViews LogL object
' revised for version 5.0 (11/19/2009)
'
' restricted version of
' tri-variate BEKK of Engle and Kroner (1995):
'
' y = mu + res
' res ~ N(0,H)
'
' H = omega*omega' + beta H(-1) beta' + alpha res(-1) res(-1)' alpha'
'
' where,
' y = 3 x 1
' mu = 3 x 1
' H = 3 x 3 (symmetric)
' H(1,1) = variance of y1 (saved as var_y1)
' H(1,2) = cov of y1 and y2 (saved as cov_y1y2)
' H(1,3) = cov of y1 and y2 (saved as cov_y1y3)
' H(2,2) = variance of y2 (saved as var_y2)
' H(2,3) = cov of y1 and y3 (saved as cov_y2y3)
' H(3,3) = variance of y3 (saved as var_y3)
' omega = 3 x 3 low triangular
' beta = 3 x 3 diagonal
' alpha = 3 x 3 diagonal
'
'change path to program path
wfopen "G:\Liu Xiaochun\Research\2010 papers\Pre topics for papers\International Finance\Expenditure switching effect estimatin paper\Expenditure switching paper writing\ESE eviews code\ese eviews data.wf1"
delete s0
delete s1
delete deth
delete var
delete cov
' dependent variables of all series must be continues
series y1 = logusuk
series y2 = log(us_exppr)
series y3 =log(us_imppr)
series y4 =log(us_ppi)
series y5 =log(us_cpi)
series y6=log(us_mpuk)
series y7 = log(us_hcuk)
' set sample
' first observation of s1 need to be one or two periods after
' the first observation of s0
sample s0 1980M02 2010M04
sample s1 1980M04 2010M04
' initialization of parameters and starting values
' change below only to change the specification of model
smpl s0
'get starting values from univariate GARCH
equation eq1.arch(m=100,c=1e-5) y1 c
equation eq2.arch(m=100,c=1e-5) y2 c
equation eq3.arch(m=100,c=1e-5) y3 c
equation eq4.arch(m=100,c=1e-5) y4 c
equation eq5.arch(m=100,c=1e-5) y5 c
equation eq6.arch(m=100,c=1e-5) y6 c
equation eq7.arch(m=100,c=1e-5) y7 c
' declare coef vectors to use in GARCH model
coef(8) mu
mu(1) = eq1.c(1)
mu(2) = eq2.c(1)
mu(3) = eq3.c(1)
mu(4) = eq4.c(1)
mu(5) =eq5.c(1)
mu(6) =eq6.c(1)
mu(7) =eq7.c(1)
mu(8)=0.01
coef(14) omega
omega(1) = (eq1.c(2))^.5
omega(2) = 0
omega(3) = 0
omega(4) = eq2.c(2)^.5
omega(5) = 0
omega(6) = eq3.c(3)^.5
omega(7) =0
omega(8) =eq4.c(3)^.5
omega(9)=0
omega(10)=eq5.c(3)^.5
omega(11)=0
omega(12)=eq6.c(3)^.5
omega(13)=0
omega(14)=eq7.c(3)^.5
coef(7) alpha
alpha(1) = (eq1.c(3))^.5
alpha(2) = (eq2.c(3))^.5
alpha(3) = (eq3.c(3))^.5
alpha(4) = (eq4.c(3))^.5
alpha(5) = (eq5.c(3))^.5
alpha(6) = (eq6.c(3))^.5
alpha(7) = (eq7.c(3))^.5
coef(7) beta
beta(1) = (@abs(eq1.c(4)))^.5
beta(2) = (@abs(eq2.c(4)))^.5
beta(3) = (@abs(eq3.c(4)))^.5
beta(4) = (@abs(eq4.c(4)))^.5
beta(5) = (@abs(eq5.c(4)))^.5
beta(6) = (@abs(eq6.c(4)))^.5
beta(7) = (@abs(eq7.c(4)))^.5
' use sample var-cov as starting value of variance-covariance matrix
series res1 = y1-mu(1)+mu(8)*var_y1
series res2 = y2-mu(2)
series res3 = y3-mu(3)
series res4 = y4-mu(4)
series res5 = y5-mu(5)
series res6 = y6-mu(6)
series res7 = y7-mu(7)
series cov_y1y2 = @cov(res1, res2)
series cov_y1y3 = @cov(y1-mu(1), y3-mu(3))
series cov_y1y4 = @cov(y1-mu(1), y4-mu(4))
series cov_y1y5 = @cov(y1-mu(1), y5-mu(5))
series cov_y1y6 = @cov(y1-mu(1), y6-mu(6))
series cov_y1y7 = @cov(y1-mu(1), y7-mu(7))
series cov_y2y3 = @cov(y2-mu(2), y3-mu(3))
series cov_y2y4 = @cov(y2-mu(2), y4-mu(4))
series cov_y2y5 = @cov(y2-mu(2), y5-mu(5))
series cov_y2y6 = @cov(y2-mu(2), y6-mu(6))
series cov_y2y7 = @cov(y2-mu(2), y7-mu(7))
series cov_y3y4 = @cov(y3-mu(3), y4-mu(4))
series cov_y3y5 = @cov(y3-mu(3), y5-mu(5))
series cov_y3y6 = @cov(y3-mu(3), y6-mu(6))
series cov_y3y7 = @cov(y3-mu(3), y7-mu(7))
series cov_y4y5 = @cov(y4-mu(4), y5-mu(5))
series cov_y4y6 = @cov(y4-mu(4), y6-mu(6))
series cov_y4y7 = @cov(y4-mu(4), y7-mu(7))
series cov_y5y6 = @cov(y5-mu(5), y6-mu(6))
series cov_y5y7 = @cov(y5-mu(5), y7-mu(7))
series cov_y6y7 = @cov(y6-mu(6), y7-mu(7))
series var_y1 = @var(y1)
series var_y2 = @var(y2)
series var_y3 = @var(y3)
series var_y4 = @var(y4)
series var_y5 = @var(y5)
series var_y6 = @var(y6)
series var_y7 = @var(y7)
series sqres1 = res1^2
series sqres2 = res2^2
series sqres3 = res3^2
series sqres4 = res4^2
series sqres5 = res5^2
series sqres6 = res6^2
series sqres7 = res7^2
series res1res2 = res1*res2
series res1res3 = res1*res3
series res1res4 = res1*res4
series res1res5 = res1*res5
series res1res6 = res1*res6
series res1res7 = res1*res7
series res2res3 = res2*res3
series res2res4 = res2*res4
series res2res5 = res2*res5
series res2res6 = res2*res6
series res2res7 = res2*res7
series res3res4 = res3*res4
series res3res5 = res3*res5
series res3res6 = res3*res6
series res3res7 = res3*res7
series res4res5 = res4*res5
series res4res6 = res4*res6
series res4res7 = res4*res7
series res5res6 = res5*res6
series res5res7 = res5*res7
series res6res7 = res6*res7
' constant adjustment for log likelihood
!mlog2pi = 7*log(2*@acos(-1))
' ...........................................................
' LOG LIKELIHOOD
' set up the likelihood
' 1) open a new blank likelihood object name tvgarch
' 2) specify the log likelihood model by append
' ...........................................................
logl tvgarch
' squared errors and cross errors
tvgarch.append @logl logl
tvgarch.append res1 = y1-mu(1)+mu(8)*var_y1
tvgarch.append res2 = y2-mu(2)
tvgarch.append res3 = y3-mu(3)
tvgarch.append res4 = y4-mu(4)
tvgarch.append res5 = y5-mu(5)
tvgarch.append res6 = y6-mu(6)
tvgarch.append res7 = y7-mu(7)
tvgarch.append sqres1 = res1^2
tvgarch.append sqres2 = res2^2
tvgarch.append sqres3 = res3^2
tvgarch.append sqres4 = res4^2
tvgarch.append sqres5 = res5^2
tvgarch.append sqres6 = res6^2
tvgarch.append sqres7 = res7^2
tvgarch.append res1res2 = res1*res2
tvgarch.append res1res3 = res1*res3
tvgarch.append res1res4 = res1*res4
tvgarch.append res1res5 = res1*res5
tvgarch.append res1res6 = res1*res6
tvgarch.append res1res7 = res1*res7
tvgarch.append res2res3 = res2*res3
tvgarch.append res2res4 = res2*res4
tvgarch.append res2res5 = res2*res5
tvgarch.append res2res6 = res2*res6
tvgarch.append res2res7 = res2*res7
tvgarch.append res3res4 = res3*res4
tvgarch.append res3res5 = res3*res5
tvgarch.append res3res6 = res3*res6
tvgarch.append res3res7 = res3*res7
tvgarch.append res4res5 = res4*res5
tvgarch.append res4res6 = res4*res6
tvgarch.append res4res7 = res4*res7
tvgarch.append res5res6 = res5*res6
tvgarch.append res5res7 = res5*res7
tvgarch.append res6res7 = res6*res7
' variance and covariance series
tvgarch.append var_y1 = omega(1)^2 + beta(1)^2*var_y1(-1) + alpha(1)^2*sqres1(-1)
tvgarch.append var_y2 = omega(2)^2 +omega(4)^2 + beta(2)^2*var_y2(-1) + alpha(2)^2*sqres2(-1)
tvgarch.append var_y3 = omega(3)^2 +omega(5)^2 +omega(6)^2 + beta(3)^2*var_y3(-1) + alpha(3)^2*sqres3(-1)
tvgarch.append var_y4 = omega(5)^2 +omega(7)^2 +omega(8)^2 +beta(4)^2*var_y4(-1) + alpha(4)^2*sqres4(-1)
tvgarch.append var_y5 = omega(7)^2 +omega(9)^2 +omega(10)^2 +beta(5)^2*var_y5(-1) + alpha(5)^2*sqres5(-1)
tvgarch.append var_y6 = omega(9)^2 +omega(11)^2 +omega(12)^2 +beta(6)^2*var_y6(-1) + alpha(6)^2*sqres6(-1)
tvgarch.append var_y7 = omega(11)^2+omega(13)^2 +omega(14)^2 +beta(7)^2*var_y7(-1) + alpha(7)^2*sqres7(-1)
tvgarch.append cov_y1y2 = omega(1)*omega(2) +beta(1)* beta(2)*cov_y1y2(-1) + alpha(1)*alpha(2)*res1res2(-1)
tvgarch.append cov_y1y3 = omega(1)*omega(3) + beta(1)*beta(3)*cov_y1y3(-1) + alpha(1)*alpha(3)*res1res3(-1)
tvgarch.append cov_y1y4 = omega(1)*omega(5) + beta(1)*beta(4)*cov_y1y4(-1) + alpha(1)*alpha(4)*res1res4(-1)
tvgarch.append cov_y1y5 = omega(1)*omega(7) + beta(1)*beta(5)*cov_y1y5(-1) + alpha(1)*alpha(5)*res1res5(-1)
tvgarch.append cov_y1y6 = omega(1)*omega(9) + beta(1)*beta(6)*cov_y1y6(-1) + alpha(1)*alpha(6)*res1res6(-1)
tvgarch.append cov_y1y7 = omega(1)*omega(11) + beta(1)*beta(7)*cov_y1y7(-1) + alpha(1)*alpha(7)*res1res7(-1)
tvgarch.append cov_y2y3 = omega(2)*omega(3) + omega(4)*omega(5) +beta(2)* beta(3)*cov_y2y3(-1) + alpha(2)*alpha(3)*res2res3(-1)
tvgarch.append cov_y2y4 = omega(2)*omega(5) + omega(6)*omega(7) +beta(2)* beta(4)*cov_y2y4(-1) + alpha(2)*alpha(4)*res2res4(-1)
tvgarch.append cov_y2y5 = omega(2)*omega(7) + omega(8)*omega(9) +beta(2)* beta(5)*cov_y2y5(-1) + alpha(2)*alpha(5)*res2res5(-1)
tvgarch.append cov_y2y6 = omega(2)*omega(9) + omega(10)*omega(11) +beta(2)* beta(6)*cov_y2y6(-1) + alpha(2)*alpha(6)*res2res6(-1)
tvgarch.append cov_y2y7 = omega(2)*omega(11) + omega(12)*omega(13) +beta(2)* beta(7)*cov_y2y7(-1) + alpha(2)*alpha(7)*res2res7(-1)
tvgarch.append cov_y3y4 = omega(3)*omega(5) + omega(6)*omega(7) +beta(3)* beta(4)*cov_y3y4(-1) + alpha(3)*alpha(4)*res3res4(-1)
tvgarch.append cov_y3y5 = omega(3)*omega(7) + omega(8)*omega(9) +beta(3)* beta(5)*cov_y3y5(-1) + alpha(3)*alpha(5)*res3res5(-1)
tvgarch.append cov_y3y6 = omega(3)*omega(9) + omega(10)*omega(11) +beta(3)* beta(6)*cov_y3y6(-1) + alpha(3)*alpha(6)*res3res6(-1)
tvgarch.append cov_y3y7 = omega(3)*omega(11) + omega(12)*omega(13) +beta(3)* beta(7)*cov_y3y7(-1) + alpha(3)*alpha(7)*res3res7(-1)
tvgarch.append cov_y4y5 = omega(4)*omega(7) + omega(8)*omega(9) +beta(4)* beta(5)*cov_y4y5(-1) + alpha(4)*alpha(5)*res4res5(-1)
tvgarch.append cov_y4y6 = omega(4)*omega(9) + omega(10)*omega(11) +beta(4)* beta(6)*cov_y4y6(-1) + alpha(4)*alpha(6)*res4res6(-1)
tvgarch.append cov_y4y7 = omega(4)*omega(11) + omega(12)*omega(13) +beta(4)* beta(7)*cov_y4y7(-1) + alpha(4)*alpha(7)*res4res7(-1)
tvgarch.append cov_y5y6 = omega(5)*omega(9) + omega(10)*omega(11) +beta(5)* beta(6)*cov_y5y6(-1) + alpha(5)*alpha(6)*res5res6(-1)
tvgarch.append cov_y5y7 = omega(5)*omega(11) + omega(12)*omega(13) +beta(5)* beta(7)*cov_y5y7(-1) + alpha(5)*alpha(7)*res5res7(-1)
tvgarch.append cov_y6y7 = omega(6)*omega(11) + omega(12)*omega(13) +beta(6)* beta(7)*cov_y6y7(-1) + alpha(6)*alpha(7)*res6res7(-1)
' determinant of the variance-covariance matrix
group group_var1 var_y1 cov_y1y2 cov_y1y3 cov_y1y4 cov_y1y5 cov_y1y6 cov_y1y7
group group_var2 cov_y1y2 var_y2 cov_y2y3 cov_y2y4 cov_y2y5 cov_y2y6 cov_y2y7
group group_var3 cov_y1y3 cov_y2y3 var_y3 cov_y3y4 cov_y3y5 cov_y3y6 cov_y3y7
group group_var4 cov_y1y4 cov_y2y4 cov_y3y4 var_y4 cov_y4y5 cov_y4y6 cov_y4y7
group group_var5 cov_y1y5 cov_y2y5 cov_y3y5 cov_y4y5 var_y5 cov_y5y6 cov_y5y7
group group_var6 cov_y1y6 cov_y2y6 cov_y3y6 cov_y4y6 cov_y5y6 var_y6 cov_y6y7
group group_var7 cov_y1y7 cov_y2y7 cov_y3y7 cov_y4y7 cov_y5y7 cov_y6y7 var_y7
group group_res res1 res2 res3 res4 res5 res6 res7
matrix mat_var1=group_var1
matrix mat_var2=group_var2
matrix mat_var3=group_var3
matrix mat_var4=group_var4
matrix mat_var5=group_var5
matrix mat_var6=group_var6
matrix mat_var7=group_var7
matrix mat_res=group_res
!m1=@rows(mat_var1)
!m2=@columns(mat_var1)
matrix(!m2,!m2) mat_var
rowvector(!m2) vect_var1
rowvector(!m2) vect_var2
rowvector(!m2) vect_var3
rowvector(!m2) vect_var4
rowvector(!m2) vect_var5
rowvector(!m2) vect_var6
rowvector(!m2) vect_var7
rowvector(!m2) vect_res
vector(!m1) vect_h
vector(!m1) deth
for !i=1 to !m1
matrix mat_varr=mat_var
vect_var1=@rowextract(mat_var1,!i)
vect_var2=@rowextract(mat_var2,!i)
vect_var3=@rowextract(mat_var3,!i)
vect_var4=@rowextract(mat_var4,!i)
vect_var5=@rowextract(mat_var5,!i)
vect_var6=@rowextract(mat_var6,!i)
vect_var7=@rowextract(mat_var7,!i)
vect_res =@rowextract(mat_res,!i)
rowplace(mat_var,vect_var1,1)
rowplace(mat_var,vect_var2,2)
rowplace(mat_var,vect_var3,3)
rowplace(mat_var,vect_var4,4)
rowplace(mat_var,vect_var5,5)
rowplace(mat_var,vect_var6,6)
rowplace(mat_var,vect_var7,7)
vector(1) my=vect_res*@inverse(mat_var)*@transpose(vect_res)
vect_h(!i)=my(1)
deth(!i)=@det(mat_var)
next
mtos(vect_h, s_h)
mtos(deth, s_deth)
' log-likelihood series
'tvgarch.append logl = -0.5*(!mlog2pi + s_h+ log(mu(8)) )
tvgarch.append logl = log(@dnorm(@sqrt(s_h)))-log(@abs(s_deth))/2
' remove some of the intermediary series
'tvgarch.append @temp invh1 invh2 invh3 invh4 invh5 invh6 sqres1 sqres2 sqres3 res1res2 res1res3 res2res3 deth
' estimate the model
smpl s1
tvgarch.ml(showopts, m=500, c=1e-5)
' change below to display different output
show tvgarch.output
graph var.line var_y1 var_y2 var_y3 var_y4 var_y5 var_y6 var_y7
graph cov.line cov_y1y2 cov_y1y3 cov_y1y4 cov_y1y5 cov_y1y6 cov_y1y7 cov_y2y3 cov_y2y4 cov_y2y5 cov_y2y6 cov_y2y7 cov_y3y4 cov_y3y5 cov_y3y6 cov_y3y7 cov_y4y5 cov_y4y6 cov_y4y7 cov_y5y6 cov_y5y7 cov_y6y7
show var
show cov