R: ARMA(p,q) Correlation Structure

corARMA {nlme} | R Documentation

## ARMA(p,q) Correlation Structure

### Description

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.

### 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.

### Author(s)

Jose Pinheiro Jose.Pinheiro@pharma.novartis.com and Douglas Bates bates@stat.wisc.edu

### 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

`corAR1`, `corClasses` `Initialize.corStruct`, `summary.corStruct`

### Examples

    ## 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) )

[Package nlme version 3.1-86 Index]