| LikeF {NGSSMEL} | R Documentation |
This function computes the marginal maximum likelihood function of the static parameters of the model.
LikeF(StaPar,Yt,Xt=NULL,model="Poisson",a0=0.01,b0=0.01)
StaPar |
is the static parameter vector |
Yt |
is the time series of interest |
Xt |
are the explanatory time series to be inserted in the model |
model |
is the chosen model for the observations |
a0 |
is the shape parameter of the initial Gamma distribution |
b0 |
is the scale parameter of the initial Gamma distribution |
llik |
This function returns of the value of the marginal likelihood function in the logarithmic scale. |
Thiago Rezende dos Santos
Gamerman, D., Santos, T. R., and Franco, G. C. (2013). A Non-Gaussian Family of State-Space Models with Exact Marginal Likelihood. Journal of Time Series Analysis, 34(6), 625-645.
Harvey, A. C., and Fernandes, C. (1989). Time series models for count or qualitative observations. Journal of Business and Economic Statistics, 7(4), 407-417.
##########################################################
##
## Poisson Example with Covariate Cosine
##
##########################################################
data(Ytm)
Yt=Ytm[,1]
Ytm[,2]
Xt=as.matrix(Ytm[,2])
StaPar=c(0.88,0.90)
LikeF(StaPar,Yt,Xt=Xt,model="Poisson",a0=0.01,b0=0.01)
resultsopt=optim(StaPar, hessian=TRUE,LikeF,lower=c(0.0001,-1000),upper=c(0.9999,1000),
,method="L-BFGS-B",Yt=Yt,Xt=Xt,model="Poisson",
control = list(maxit = 30000, temp = 2000, trace = TRUE,REPORT = 500))
estopt=resultsopt$par
estopt
Hessianmatrixopt=-resultsopt$hessian
Hessianmatrixopt
MIFopt=-solve(Hessianmatrixopt)
MIFopt
linfwopt=estopt[1]-1.96*sqrt(MIFopt[1,1])
linfwopt
lsupwopt=estopt[1]+1.96*sqrt(MIFopt[1,1])
lsupwopt
linfbetaopt=estopt[2]-1.96*sqrt(MIFopt[2,2])
linfbetaopt
lsupbetaopt=estopt[2]+1.96*sqrt(MIFopt[2,2])
lsupbetaopt
# -1*log-lik:
resultsopt$value
# log-lik:
-resultsopt$value
set.seed(1000)
MeanSmooth=SmoothingF(estopt,Yt=Yt,Xt=Xt,model="Poisson",
a0=0.01,b0=0.01,samples=500,alpha=0.05)
#MeanSmooth
filpar=ForecastingF(estopt,Yt=Yt,Xt=Xt,model="Poisson",
a0=0.01,b0=0.01)
n1=length(Yt)
ytm=matrix(0,n1,5)
ytm[,1]=Yt
ytm[,2]=MeanSmooth$Mean
ytm[,3]=filpar[1,]/ filpar[2,]
ytm[,4]=MeanSmooth$Perc1
ytm[,5]=MeanSmooth$Perc2
ts.plot(ytm,xlab="t",ylab="Y_t",lty=c(1,2,3,2,2),
col=c("black","blue","red","blue","blue"))
legend("topright", c("Time Series","Smoothed Mean",
"Prediction", "Smoothed Lower 95 CI",
"Smoothed Upper 95 CI"),lty=c(1,2,3,2,2),
col=c("black","blue","red","blue","blue"),
cex=0.68, bty="n", pt.cex = 1)
##########################################################
##
## Example PETR3
##
##########################################################
data(Rt)
StStaPar=c(0.9818846,1.2367185)
Yt=Rt
resultsopt=optim(StStaPar, hessian=TRUE,LikeF,
lower=c(0.0001,0.0001),upper=c(0.9999,1000),
,method="L-BFGS-B",Yt,Xt=NULL,a0=0.01,b0=0.01,
model="GED",control = list(maxit = 30000, temp = 2000,
trace = TRUE,REPORT = 500))
estopt=resultsopt$par # Point Estimates:
estopt
Hessianmatrixopt=-resultsopt$hessian #Hessian Matrix
Hessianmatrixopt
MIFopt=-solve(Hessianmatrixopt) #MIF
MIFopt
linfwopt=estopt[1]-1.96*sqrt(MIFopt[1,1]) # CI Asymptotic for w:
linfwopt
lsupwopt=estopt[1]+1.96*sqrt(MIFopt[1,1])
lsupwopt
linfropt=estopt[2]-1.96*sqrt(MIFopt[2,2]) # CI Asymptotic for r:
linfropt
lsupropt=estopt[2]+1.96*sqrt(MIFopt[2,2])
lsupropt
# -1*log-lik:
resultsopt$value
# log-lik:
-resultsopt$value
#Smoothing:
set.seed(1000)
MeanSmooth=SmoothingF(estopt,Yt=Yt,Xt=NULL,model="GED",
a0=0.01,b0=0.01,samples=500,alpha=0.05)
#MeanSmooth
filpar=ForecastingF(estopt,Yt=Yt,Xt=NULL,model="GED",
a0=0.01,b0=0.01)
n1=length(Yt)
ytm=matrix(0,n1,5)
ytm[,1]=(Yt^2)
ytm[,2]=(MeanSmooth$Mean^(-1/estopt[2]))
ytm[,3]=((filpar[1,]/ filpar[2,])^(-1/estopt[2]))
ytm[,4]=(MeanSmooth$Perc1^(-1/estopt[2]))
ytm[,5]=(MeanSmooth$Perc2^(-1/estopt[2]))
ts.plot(ytm,xlab="t",ylab="Y_t",lty=c(1,2,3,2,2),
col=c("black","blue","red","blue","blue"))
legend("topleft", c("Square of Returns",
"Smoothed estimate of the square root of the stochastic volatility",
"Prediction one-step-ahead of the square root of the stochastic volatility",
"Smoothed Lower 95 percent CI", "Smoothed Upper 95 percent CI"),lty=c(1,2,3,2,2),
col=c("black","blue","red","blue","blue"), cex=0.68, bty="n", pt.cex = 1)