# plot.efp

##### Plot Empirical Fluctuation Process

Plot and lines method for objects of class `"efp"`

- Keywords
- hplot

##### Usage

```
# S3 method for efp
plot(x, alpha = 0.05, alt.boundary = FALSE, boundary = TRUE,
functional = "max", main = NULL, ylim = NULL,
ylab = "Empirical fluctuation process", ...)
# S3 method for efp
lines(x, functional = "max", ...)
```

##### Arguments

- x
an object of class

`"efp"`

.- alpha
numeric from interval (0,1) indicating the confidence level for which the boundary of the corresponding test will be computed.

- alt.boundary
logical. If set to

`TRUE`

alternative boundaries (instead of the standard linear boundaries) will be plotted (for CUSUM processes only).- boundary
logical. If set to

`FALSE`

the boundary will be computed but not plotted.- functional
indicates which functional should be applied to the process before plotting and which boundaries should be used. If set to

`NULL`

a multiple process with boundaries for the`"max"`

functional is plotted. For more details see below.- main, ylim, ylab, ...
high-level

`plot`

function parameters.

##### Details

Plots are available for the `"max"`

functional for all process types.
For Brownian bridge type processes the maximum or mean squared Euclidean norm
(`"maxL2"`

and `"meanL2"`

) can be used for aggregating before plotting.
No plots are available for the `"range"`

functional.

Alternative boundaries that are proportional to the standard deviation of the corresponding limiting process are available for processes with Brownian motion or Brownian bridge limiting processes.

##### Value

`efp`

returns an object of class `"efp"`

which inherits
from the class `"ts"`

or `"mts"`

respectively. The function
`plot`

has a method to plot the
empirical fluctuation process; with `sctest`

the corresponding test for
structural change can be performed.

##### References

Brown R.L., Durbin J., Evans J.M. (1975), Techniques for
testing constancy of regression relationships over time, *Journal of the
Royal Statistical Society*, B, **37**, 149-163.

Chu C.-S., Hornik K., Kuan C.-M. (1995), MOSUM tests for parameter
constancy, *Biometrika*, **82**, 603-617.

Chu C.-S., Hornik K., Kuan C.-M. (1995), The moving-estimates test for
parameter stability, *Econometric Theory*, **11**, 669-720.

Kr<e4>mer W., Ploberger W., Alt R. (1988), Testing for structural change in
dynamic models, *Econometrica*, **56**, 1355-1369.

Kuan C.-M., Hornik K. (1995), The generalized fluctuation test: A
unifying view, *Econometric Reviews*, **14**, 135 - 161.

Kuan C.-M., Chen (1994), Implementing the fluctuation and moving estimates
tests in dynamic econometric models, *Economics Letters*, **44**,
235-239.

Ploberger W., Kr<e4>mer W. (1992), The CUSUM test with OLS residuals,
*Econometrica*, **60**, 271-285.

Zeileis A., Leisch F., Hornik K., Kleiber C. (2002), `strucchange`

:
An R Package for Testing for Structural Change in Linear Regression Models,
*Journal of Statistical Software*, **7**(2), 1-38.
URL http://www.jstatsoft.org/v07/i02/.

Zeileis A. (2004), Alternative Boundaries for CUSUM Tests,
*Statistical Papers*, **45**, 123--131.

##### See Also

##### Examples

```
# NOT RUN {
## Load dataset "nhtemp" with average yearly temperatures in New Haven
data("nhtemp")
## plot the data
plot(nhtemp)
## test the model null hypothesis that the average temperature remains
## constant over the years
## compute Rec-CUSUM fluctuation process
temp.cus <- efp(nhtemp ~ 1)
## plot the process
plot(temp.cus, alpha = 0.01)
## and calculate the test statistic
sctest(temp.cus)
## compute (recursive estimates) fluctuation process
## with an additional linear trend regressor
lin.trend <- 1:60
temp.me <- efp(nhtemp ~ lin.trend, type = "fluctuation")
## plot the bivariate process
plot(temp.me, functional = NULL)
## and perform the corresponding test
sctest(temp.me)
# }
```

*Documentation reproduced from package strucchange, version 1.5-2, License: GPL-2 | GPL-3*