How to use optim.jl to estimate ARMA(p,q) MLE? - julia

Question

I'm trying to estimate ARMA(p,q) models with julia. I have a problem with the optimization of the log-likelihood function.
I have a function named "SsfLogLikConc" that estimates my concentrated log-likelihood and i would like to see it as function of vP, that is the value of my parameters phi and theta, and then optimize this function starting from the value vP0=zeros(cp+cq,1)where cp and cp represent the p and q orders of my ARMA(p,q) model. I tried to do it in this way:
vP0=zeros(cp+cq,1)
function f(vP)
SsfLogLikConc(vP, vy, cp, cq)
end
using Optim
res=optimize(f, vP0, BFGS())
But i keep getting errors from the optimize function even if change the method. Here is the full code:
function FisherInvTransform(Vp)
vt = (exp(2*vP)-1) ./ (exp(2*vP)+1)
end
function ReparAR(vr)
cp = length(vr)
vphi = zeros(cp,1);
vphi[1] = vr[1]
for k=2:cp
vphi[1:k-1] = vphi[1:k-1] - vr[k] * vphi[k-1:-1:1]
vphi[k] = vr[k]
end
end
function ReparMA(vr)
cq = length(vr)
vtheta = zeros(cq,1)
vtheta[1] = vr[1]
for k = 2:cq
vtheta[1:k-1] = vtheta[1:k-1] + vr[k] * vtheta[k-1:-1:1]
vtheta[k] = vr[k]
end
end
function SetStateSpaceModel(vP, cp, cq)
cm = max(cp,cq)
vphi = zeros(cm, 1)
vtheta = zeros(cm, 1)
if (cp > 0)
vphi[1:cp] = ReparAR(FisherInvTransform(vP[1:cp]))
end
if (cq > 0)
vtheta[1:cq] = ReparMA(FisherInvTransform(vP[cp+1:cp+cq]));
end
#Measurement equation: % y_{t} = Z_t \alpha_{t} + G_t \epsilon_t
mZ = [1, zeros(1, cm-1)]
mGG = 1 #G_t * G_t'
#Transition equation: % \alpha_{t+1} = T_t \alpha_{t} + H_t \epsilon_t
mT = [vphi, [eye(cm-1); zeros(1, cm-1)] ]
disp(mT)
disp( vphi)
mH = vtheta+vphi
mHH = mH*mH' #H_t * H_t'
mHG = mH
#initial conditions
va = zeros(cm,1)
mP = reshape(inv(eye(cm^2)-kron(mT,mT)) * reshape(mHH, cm^2,1) , cm, cm)
end
function KalmanFilter(vy, mZ, mGG, mT, mHH, mHG, va, mP)
cm = length(va) #n. of state elements and of diffuse elements
ck = 1
cn = length(vy)
#Initialisation of matrices and scalars
dLogf = 0
dSumSquares = 0
vInnovations = NaN(1, cn) #stores the KF innovations
vVarInnovations = NaN(1, cn)
mStatePred = NaN(cm, cn) #stores the states predictions
mCovStatePred = NaN(cm, cn)
for i = 1:cn
dv = vy[i] - mZ * va; dF = mZ * mP * mZ' + mGG;
vK = (mT * mP * mZ' + mHG) / dF;
va = mT * va + vK * dv; mP = mT * mP * mT' + mHH - vK * vK' * dF ;
if (i > ck)
vInnovations[i] = dv; vVarInnovations[i] = dF;
dLogf = dLogf + log(dF); dSumSquares = dSumSquares + dv^2 /dF;
end
mStatePred[:,i] = va; mCovStatePred[:,i] = diag(mP);
end
dSigma = dSumSquares/(cn-ck);
dLogLik = -0.5 * ((cn - ck) * log(2 * pi) + dLogf + dSumSquares );
dLogLikConc = -0.5*((cn - ck)* (log(2 * pi * dSigma)+1) + dLogf );
dPev = dSigma * dF ; # Final prediction error variance
end
function SsfLogLikConc(vP, vy, cp, cq)
SetStateSpaceModel(vP, cp, cq)
dLogF = 0; dSumSquares = 0;
cn = length(vy)
for i = 1:cn
dv = vy[i] - mZ * va; dF = mZ * mP * mZ' + mGG;
vK = (mT * mP * mZ' + mHG) / dF;
va = mT * va + vK * dv; mP = mT * mP * mT' + mHH - vK * dF * vK' ;
dLogF = dLogF + log(dF);
dSumSquares = dSumSquares + dv^2 /dF;
end
dSigma2 = dSumSquares/cn;
dLogLikConc = 0.5*( cn * (log(dSigma2)+1) + dLogF ); # concentrated LF (change of sign)
end
#Pkg.add("DataFrames")
using DataFrames;
cd("$(homedir())/Desktop")
pwd()
df=readtable("df.csv")
df
o=df[2]
mean(o)
vy=zeros(1000)
for i=1:length(o)
vy[i]=o[i]-mean(o)
end
cp = 1; cq =1;
vP0 = zeros(cp+cq,1)
function f(vP)
SsfLogLikConc(vP, vy, cp, cq)
end
#Pkg.add("Optim")
using Optim
res=optimize(f, vP0, BFGS())
Thank you for reading, I hope that someone will help me!