R: Plot Empirical Fluctuation Process

plot.efp {strucchange} | R Documentation

## Plot Empirical Fluctuation Process

### Description

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

### Usage

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

Krämer 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., Krämer 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

`efp`, `boundary.efp`, `sctest.efp`

### Examples

    ## 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)

[Package strucchange version 1.5-2 Index]