# corARMA

##### ARMA(p,q) Correlation Structure

This function is a constructor for the `corARMA`

class,
representing an autocorrelation-moving average correlation structure
of order (p, q). Objects created using this constructor must later
be initialized using the appropriate `Initialize`

method.

- Keywords
- models

##### Usage

`corARMA(value, form, p, q, fixed)`

##### Arguments

- value
a vector with the values of the autoregressive and moving average parameters, which must have length

`p + q`

and all elements between -1 and 1. Defaults to a vector of zeros, corresponding to uncorrelated observations.- form
a one sided formula of the form

`~ t`

, or`~ t | g`

, specifying a time covariate`t`

and, optionally, a grouping factor`g`

. A covariate for this correlation structure must be integer valued. When a grouping factor is present in`form`

, the correlation structure is assumed to apply only to observations within the same grouping level; observations with different grouping levels are assumed to be uncorrelated. Defaults to`~ 1`

, which corresponds to using the order of the observations in the data as a covariate, and no groups.- p, q
non-negative integers specifying respectively the autoregressive order and the moving average order of the

`ARMA`

structure. Both default to 0.- fixed
an optional logical value indicating whether the coefficients should be allowed to vary in the optimization, or kept fixed at their initial value. Defaults to

`FALSE`

, in which case the coefficients are allowed to vary.

##### Value

an object of class `corARMA`

, representing an
autocorrelation-moving average correlation structure.

##### References

Box, G.E.P., Jenkins, G.M., and Reinsel G.C. (1994) "Time Series Analysis: Forecasting and Control", 3rd Edition, Holden-Day.

Pinheiro, J.C., and Bates, D.M. (2000) "Mixed-Effects Models in S and S-PLUS", Springer, esp. pp. 236, 397.

##### See Also

##### Examples

```
# NOT RUN {
## ARMA(1,2) structure, with observation order as a covariate and
## Mare as grouping factor
cs1 <- corARMA(c(0.2, 0.3, -0.1), form = ~ 1 | Mare, p = 1, q = 2)
# Pinheiro and Bates, p. 237
cs1ARMA <- corARMA(0.4, form = ~ 1 | Subject, q = 1)
cs1ARMA <- Initialize(cs1ARMA, data = Orthodont)
corMatrix(cs1ARMA)
cs2ARMA <- corARMA(c(0.8, 0.4), form = ~ 1 | Subject, p=1, q=1)
cs2ARMA <- Initialize(cs2ARMA, data = Orthodont)
corMatrix(cs2ARMA)
# Pinheiro and Bates use in nlme:
# from p. 240 needed on p. 396
fm1Ovar.lme <- lme(follicles ~ sin(2*pi*Time) + cos(2*pi*Time),
data = Ovary, random = pdDiag(~sin(2*pi*Time)))
fm5Ovar.lme <- update(fm1Ovar.lme,
corr = corARMA(p = 1, q = 1))
# p. 396
fm1Ovar.nlme <- nlme(follicles~
A+B*sin(2*pi*w*Time)+C*cos(2*pi*w*Time),
data=Ovary, fixed=A+B+C+w~1,
random=pdDiag(A+B+w~1),
start=c(fixef(fm5Ovar.lme), 1) )
# p. 397
fm3Ovar.nlme <- update(fm1Ovar.nlme,
corr=corARMA(p=0, q=2) )
# }
```

*Documentation reproduced from package nlme, version 3.1-145, License: GPL (>= 2) | file LICENCE*