Plot Empirical Fluctuation Process

Plot and lines method for objects of class "efp"

# 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", ...)

an object of class "efp".


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


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


logical. If set to FALSE the boundary will be computed but not plotted.


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.


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.


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.


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

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

See Also

efp, boundary.efp, sctest.efp

  • plot.efp
  • lines.efp
## Load dataset "nhtemp" with average yearly temperatures in New Haven
## plot the data

## 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

## compute (recursive estimates) fluctuation process
## with an additional linear trend regressor
lin.trend <- 1:60 <- efp(nhtemp ~ lin.trend, type = "fluctuation")
## plot the bivariate process
plot(, functional = NULL)
## and perform the corresponding test
# }
Documentation reproduced from package strucchange, version 1.5-2, License: GPL-2 | GPL-3

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