BoxCox.Arima: Box-Cox Analysis for "Arima" Objects

In FitAR: Subset AR Model Fitting

Description

Implements Box-Cox analysis for "Arima" class objects, the output from arima, a R built-in function. Variance change in time series is an important topic. In some cases using a Box-Cox transformation will provide a much simpler analysis than the much more complex ARMA-GARCH approach. See US Tobacco series example given below for an example.

Usage

## S3 method for class 'Arima'
BoxCox(object, interval = c(-1, 1), type = "BoxCox", InitLambda = "none", ...)

Arguments

object	output from arima, a R built-in function
interval	interval to be searched for the optimal transformation
type	ignored unless, InitLambda!="none". Type of transformation, default is "BoxCox". Otherwise a simple power transformation.
InitLambda	default "none". Otherwise a numerical value giving the transformation parameter.
...	optional arguments passed to optimize

Details

If no transformation is used on the data, then the original data is used. But if a transformation has already been used, we need to inverse transform the data to recover the untransformed data.

For lambda!=0, the Box-Cox transformation is of x is (x^lambda-1)/lambda. If the minimum data value is <= 0, a small positive constant, equal to the negative of the minimum plus 0.25, is added to all the data values.

The log of the Jacobian is (lambda-1)*sum(log(z[(D+1):n]), where lambda is the transformation, n=length(z), z is the vector of data and D = d + ds*s, where d is the degree of regular differencing, ds is the degree of seasonal differencing and s is the seasonal period. The correct expression for the loglikelihood function was first given in Hipel and McLeod (1977, eqn. 10). Using the wrong expression for the Jacobian has a disasterous effect in many situations. For example with the international airline passenger time series, the MLE for lambda would be about 1.958 instead of close to zero.

If the minimum data value is <= 0, a small positive constant, equal to the negative of the minimum plus 0.25, is added to all the data values.

Value

No value returned. Graphical output is produced as side-effect. The plot shows relative likelihood function as well as the MLE and a confidence interval.

Note

The MASS package has a similar function boxcox but this is implemented only for regression and analysis of variance.

Author(s)

A.I. McLeod and Y. Zhang

References

Hipel, K.W. and McLeod, A.I. (1977). Advances in Box-Jenkins Modelling. Part 1, Model Construction. Water Resources Research 13, 567-575.

See Also

arima, BoxCox, BoxCox.FitAR

Examples

## Not run:  #not run to save time!
#Tobacco Production
 plot(USTobacco)
 USTobacco.arima<-arima(USTobacco,order=c(0,1,1))
 BoxCox(USTobacco.arima)
#
 air.arima<-arima(AirPassengers, c(0,1,1), seasonal=list(order=c(0,1,1), period=12))
 BoxCox(air.arima)
#
#In this example, we fit a model to the square-root of the sunspots and
#back transform in BoxCox.
sqrtsun.arima<-arima(sqrt(sunspot.year),c(2,0,0))
BoxCox(sqrtsun.arima, InitLambda=0.5, type="power")
#
#Back transform with AirPassengers
Garima<-arima(log(AirPassengers), c(0,1,1), seasonal=list(order=c(0,1,1),period=12))
BoxCox(Garima, InitLambda=0)

## End(Not run)

Example output

Loading required package: lattice
Loading required package: leaps
Loading required package: ltsa
Loading required package: bestglm
Warning: modified inverse Box-Cox transformation used
 minimum data value <= 0 so -min+0.25 added to all values

FitAR documentation built on May 2, 2019, 3:22 a.m.