garmaFit: A function to fit a GARMA model

In mstasinopoulos/GAMLSS-utilities: Generalised Additive Models for Location Scale and Shape Utilities

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, 
         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.

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.

Value

It returns a fitted garma model.

Note

There is no check done whether the fitted model is stationary.

Author(s)

Mikis Stasinopoulos [e-mail], Bob Rigby and Vlasios Voudouris

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)

mstasinopoulos/GAMLSS-utilities documentation built on July 8, 2023, 11:25 p.m.