gamlss.util (version 4.3-4)

garmaFit: A function to fit a GARMA model

Description

This function is for fitting a GARMA model, see Benjamin et al. (2003).

Usage

garmaFit(formula = formula(data), order = c(0, 0),  weights = NULL, data = sys.parent(),  family = NO(), alpha = 0.1,  phi.start = NULL, theta.start = NULL,  tail = max(order), control = list())

Arguments

formula

A formula for linear terms i.e. like in lm()

order

order specify the order of the generalised arm model

weights

prior weighs, they are working like in gamlss

data

the relevant data.frame

family

A gamlss.family distribution

alpha

This parameter is used in the definition of the link function of the response variable i.e. $\log(y^*)$ will be $y^*=max(y, \alpha)$

phi.start

starting values for the AR parameters

theta.start

starting values for the MA part

tail

how many observation from the tall of the response variable should be suppressed

control

control for optim() or nlminb() function use for optimisation.

Value

It returns a fitted garma model.

Details

The model is described in Benjamin et al. (2003). The implementation here is more general that it allows all the gamlss.family distributions to be fitted rather than only for the exponential family which was described in the original paper. Note that in this formulation only the mu can be modelled as ARMA.

References

Benjamin M. A., Rigby R. A. and Stasinopoulos D.M. (2003) Generalised Autoregressive Moving Average Models. J. Am. Statist. Ass., 98, 214-223.

Rigby, R. A. and Stasinopoulos D. M. (2005). Generalized additive models for location, scale and shape,(with discussion), Appl. Statist., 54, part 3, pp 507-554.

Stasinopoulos D. M., Rigby R.A. and Akantziliotou C. (2006) Instructions on how to use the GAMLSS package in R. Accompanying documentation in the current GAMLSS help files, (see also http://www.gamlss.org/).

Stasinopoulos D. M. Rigby R.A. (2007) Generalized additive models for location scale and shape (GAMLSS) in R. Journal of Statistical Software, Vol. 23, Issue 7, Dec 2007, http://www.jstatsoft.org/v23/i07.

See Also

gamlss.family, gamlss

Examples

data(polio)
ti <- as.numeric(time(polio))
mo <- as.factor(cycle(polio))
x1 <- 0:167    #Index used in Tutz p197
x2 <- cos(2*pi*x1/12)
x3 <- sin(2*pi*x1/12)
x4 <- cos(2*pi*x1/6)
x5 <- sin(2*pi*x1/6)
# all the data here 
da <-data.frame(polio,x1,x2,x3,x4,x5, ti, mo)
rm(ti,mo,x1,x2,x3,x4,x5)

#-------------------------------------------------------------------
# with linear trend 
m00 <- garmaFit(polio~x1+x2+x3+x4+x5, data=da, order=c(0,0), family=NBI, tail=3) # 
m10 <- garmaFit(polio~x1+x2+x3+x4+x5, data=da, order=c(1,0), family=NBI, tail=3) # 

## Not run: 
# m01 <- garmaFit(polio~x1+x2+x3+x4+x5, order=c(0,1), data=da, family=NBI, tail=3)
# m20 <- garmaFit(polio~x1+x2+x3+x4+x5, order=c(2,0), data=da, family=NBI, tail=3)
# m11 <- garmaFit(polio~x1+x2+x3+x4+x5, order=c(1,1), data=da, family=NBI, tail=3)
# m02 <- garmaFit(polio~x1+x2+x3+x4+x5, order=c(0,2), data=da, family=NBI, tail=3)
# m30 <- garmaFit(polio~x1+x2+x3+x4+x5, order=c(3,0), data=da, family=NBI, tail=3)
# m21 <- garmaFit(polio~x1+x2+x3+x4+x5, order=c(2,1), data=da, family=NBI, tail=3)
# m12 <- garmaFit(polio~x1+x2+x3+x4+x5, order=c(1,2), data=da, family=NBI, tail=3)
# m03 <- garmaFit(polio~x1+x2+x3+x4+x5, order=c(0,3), data=da, family=NBI, tail=3)
# AIC(m00,m10,m01,m20,m11,m02,m30,m21,m12,m03 , k=0)
# AIC(m00,m10,m01,m20,m11,m02,m30,m21,m12,m03 , k=log(168))
# # without linear trend 
# n00 <- garmaFit(polio~x2+x3+x4+x5, data=da, order=c(0,0), family=NBI, tail=3) # 
# n10 <- garmaFit(polio~x2+x3+x4+x5, data=da, order=c(1,0), family=NBI, tail=3) # OK
# n01 <- garmaFit(polio~x2+x3+x4+x5, order=c(0,1), data=da, family=NBI, tail=3)
# n20 <- garmaFit(polio~x2+x3+x4+x5, order=c(2,0), data=da, family=NBI, tail=3)
# n11 <- garmaFit(polio~x2+x3+x4+x5, order=c(1,1), data=da, family=NBI, tail=3)
# n02 <- garmaFit(polio~x2+x3+x4+x5, order=c(0,2), data=da, family=NBI, tail=3)
# n30 <- garmaFit(polio~x2+x3+x4+x5, order=c(3,0), data=da, family=NBI, tail=3)
# n21 <- garmaFit(polio~x2+x3+x4+x5, order=c(2,1), data=da, family=NBI, tail=3)
# n12 <- garmaFit(polio~x2+x3+x4+x5, order=c(1,2), data=da, family=NBI, tail=3)
# n03 <- garmaFit(polio~x2+x3+x4+x5, order=c(0,3), data=da, family=NBI, tail=3)
# 
# AIC(m00,n10,n01,n20,n11,n02,n30,n21,n12,  k=0)
# AIC(m00,n10,n01,n20,n11,n02,n30,n21,n12, k=log(168))
# ## End(Not run)