NGSSEML (version 1.0)

ngssm.mle: Maximum likelihood estimation of the non-Gaussian state space models with exact marginal likelihood

Description

The function performs the marginal likelihood estimation for the static parameters of the model.

Usage

ngssm.mle(formula, data,na.action="na.omit",pz=NULL,
nBreaks=NULL,model="Poisson",StaPar=NULL,amp=FALSE,
a0=0.01,b0=0.01,ci=0.95,LabelParTheta=NULL,verbose=TRUE)

Arguments

formula

an object of class "formula" (or one that can be coerced to that class): a symbolic description of the model to be fitted.

data

a data frame containing the variables in the model. The variables are: - the time series of interest Yt (first column of the data frame). the explanatory time series to be inserted in the model. - Xt must be always specified as a matrix of order n by p (after Yt). - the explanatory time series to be inserted in the mean of volatility model. Zt must be always specified as a matrix of order n by p (after Xt). - a censoring indicator of the event (a vector), only for the PEM. If the model is the PEM, put the variable Event in the secon column of tha data frame after Yt, and he explanatory time series after the variable Event. The value 1 indicates failure.

na.action

a function which indicates what should happen when the data contain NAs. The default is set by the na.action setting of options, and is na.fail if that is unset. Optional argument.

pz

the number of the explanatory time series to be inserted in the mean of volatility model. Default: NULL. Optional argument.

nBreaks

the number of breaks used to build a vector with the interval limits, only for the PEM. Optional argument.

model

the chosen model for the observations. The options are: Poisson, Normal, Gamma, Weibull, Generalized Gamma, Laplace, GED and PEM models.

StaPar

a numeric vector of initial values for the static parameters. Optional argument.

amp

the interval width is taken in account in the estimation of parameter w which controls the loss of information over time, only for the PEM. For more details see Santos et al. (2017). Default: FALSE. Optional argument.

a0

the shape parameter of the initial Gamma distribution. Optional argument. Default: a0=0.01.

b0

the scale parameter of the initial Gamma distribution. Optional argument. Default: b0=0.01.

ci

the nominal level of confidence interval for the parameters. Default: ci=0.95. Optional argument.

LabelParTheta

If not NULL, the static parameters are called by the specified label. Optional argument.

verbose

A logical variable that gives the user the output of the model fit in the console. Default: TRUE. Optional argument.

Value

[[1]]

the output of the model fit, presenting the maximum likelihood estimators, standard errors, Z statistics, and asymptotic confidence intervals of the model parameters.

Details

Typical usages are

fit=ngssm.mle(Ytm~Trend+CosAnnual+SinAnnual+CosSemiAnnual+SinSemiAnnual,
data=data1,model="Poisson",StaPar=c(0.8,-0.8,0.01,0.01,0.01,0.01),
a0=0.01,b0=0.01,ci=0.95)

References

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.

Santos T. R., Gamerman, D., Franco, G. C. (2017). Reliability Analysis via Non-Gaussian State-Space Models. IEEE Transactions on Reliability, 66, 309-318.

See Also

FilteringF SmoothingF ngssm.bayes

Examples

# NOT RUN {
##########################################################
#
## PEM Example: the GTE data
##
##########################################################
# MLE estimation:
library(NGSSEML)
data(gte_data)
Ytm=gte_data$V1
Xtm=NULL
Ztm=NULL
model="PEM"
amp=FALSE
Eventm=gte_data$V2        # Event: failure, 1.
Break=GridP(Ytm, Eventm, nT = NULL)
#LabelParTheta=c("w")
StaPar=c(0.73)
a0=0.01
b0=0.01
ci=0.95
fit=ngssm.mle(Ytm~1,data=data.frame(Ytm,Eventm),model=model,nBreaks=NULL,
amp=amp,a0=a0,b0=b0,ci=ci)

##########################################################
##
##  SR GAMMA MODEL: the SYS1 data
##
##########################################################
# MLE estimation:
#library(NGSSEML)
data(sys1_data)
Ytm=sys1_data[,1]+0.00001
Xtm=sys1_data[,2]   # Xt as matrix always!
Zt=NULL
model="SRWeibull"
#LabelParTheta=c("w","alpha","Beta1")
StaPar=c(0.9,0.7,0.01)
fit=ngssm.mle(Ytm~Xtm,data=data.frame(Ytm,Xtm),
model=model,pz=NULL,StaPar=StaPar,a0=0.01,b0=0.01,ci=0.95)

# }