copMarkovts: maximum likelihood estimation and negative log-likelihood for...

In YafeiXu/CopulaModel: CopulaModel: Dependence Modeling with Copulas

Description

maximum likelihood estimation and negative log-likelihood for copula-based Markov count time series models

Usage

mltscop1(y,x,pcop=pbvncop,start,family="Po",iprint=F,cparlb=0,cparub=30,prlevel=1)
mltscop2(y,x,pcop3=pmxid3ls,pcop2=pmxid2ls,start,family="Po",iprint=F,cparlb=0,cparub=30,prlevel=1)
rmspe.mccop1(param,yy,xdat=0,pcop=pbvncop,family="Po",iprint=F)
rmspe.mccop2(param,yy,xdat=0,pcop3=pmxid3ls,pcop2=pmxid2ls,family="Po",iprint=F)
rmspe.tvn(param,yy,xdat=0,family="Po",iprint=F)
nb1mcnllk(param,yy,xdat=0,pcop=pbvncop,cparlb=0,cparub=30) # NB1, Markov order1
nb2mcnllk(param,yy,xdat=0,pcop=pbvncop,cparlb=0,cparub=30) # NB2, Markov order1
gp1mcnllk(param,yy,xdat=0,pcop=pbvncop,cparlb=0,cparub=30) # GP1, Markov order1
gp2mcnllk(param,yy,xdat=0,pcop=pbvncop,cparlb=0,cparub=30) # GP2, Markov order1
pomcnllk(param,yy,xdat=0,pcop=pbvncop,cparlb=0,cparub=30) # Poisson, Markov order1
# Markov order 2 count time series below
nb1mc2nllk(param,yy,xdat=0,pcop3=pmxid3ls,pcop2=pmxid2ls,cparlb=0,cparub=30)
nb2mc2nllk(param,yy,xdat=0,pcop3=pmxid3ls,pcop2=pmxid2ls,cparlb=0,cparub=30)
gp1mc2nllk(param,yy,xdat=0,pcop3=pmxid3ls,pcop2=pmxid2ls,cparlb=0,cparub=30)
gp2mc2nllk(param,yy,xdat=0,pcop3=pmxid3ls,pcop2=pmxid2ls,cparlb=0,cparub=30)
pomc2nllk(param,yy,xdat=0,pcop3=pmxid3ls,pcop2=pmxid2ls,cparlb=0,cparub=30)
# Markov order 2 count time series based on trivariate Gaussian below
nb1ar2nllk(param,yy,xdat)
nb2ar2nllk(param,yy,xdat)
gp1ar2nllk(param,yy,xdat)
gp2ar2nllk(param,yy,xdat)
poar2nllk(param,yy,xdat)

Arguments

y	count times series vector (nx1)
x	matrix of covariates (n x ncovar), where ncovar is number of covariates/predictors
yy	count times series vector
xdat	matrix of covariates, 0 by default for no covariates
param	parameter vector (includes univariate and dependence parameters)
start	starting point of param for nlm optimization
pcop	function for bivariate copula cdf for Markov order 1 models
pcop3	function for trivariate copula cdf for Markov order 2 models
pcop2	function for bivariate marginal copula cdf for Markov order 2 models
family	univariate count regression model: one of "Po", "NB1", "NB2", "GP1", "GP2"
cparlb	lower bound for copula parameters
cparub	upper bound for copula parameters
iprint	print flag for of intermediate results
prlevel	print.level for nlm()

Details

mltscop1 is a front end to rmspe.mccop1 and one of nb1mcnllk, nb1mcnllk, gp1mcnllk, gp2mcnllk, pomcnllk for maximum likelihood of copula-based Markov order 1 count time series model.

mltscop2 is a front end to rmspe.mccop2 and one of nb1mc2nllk, nb1mc2nllk, gp1mc2nllk, gp2mc2nllk, pomcnllk for maximum likelihood of copula-based Markov order 2 count time series model.

Value

negative log-likelihood for any of the nllk functions,

$rmse and $pred (root mean square prediction error and 1-step predictions for any of the rmspe functions,

$nllk, $mle (maximum likelihood estimate), $acov (asymptotic covariance matrix, $rmpse for the mltscop1, mltscop2 functions

Examples

data(wcb8594)
y=wcb8594$nclaims
cat("Frank NB2, 2 covariates\n")
ucpar2=c(1.7,-.2,-.2,.4,1.5)
frknb2=mltscop1(y,wcb8594[,2:3],pfrk,start=ucpar2,fam="NB2",iprint=TRUE)
cat("pos stable LT + Frank in trivariate mixture of max-id\n")
par1=c(1.7,-.2,-.2,.4,1.5,1.1)
lsfrknb1=mltscop2(y,wcb8594[,2:3],pcop3=pmxid3ls,pcop2=pmxid2ls,start=par1,
  family="NB1", iprint=TRUE,cparlb=c(0,0),cparub=30)
cat("AR(2) Gaussian/ NB1\n")
nb1param=c(1.7,-.2,-.2,.4,.5,.3)
out=nlm(nb1ar2nllk,p=nb1param,hessian=TRUE,steptol=1.e-4,yy=y,xdat=wcb8594[,2:3],
  print.level=1)
acov=solve(out$hess)
SE=sqrt(diag(acov)) 
cat("SEs=",SE,"\n")
outpred=rmspe.tvn(out$estimate,y,wcb8594[,2:3],family="NB1",iprint=TRUE)
cat("RMSPE=",outpred$rmse,"\n")

YafeiXu/CopulaModel documentation built on May 9, 2019, 11:07 p.m.