strucchange (version 1.5-4)

efpFunctional: Functionals for Fluctuation Processes

Description

Computes an object for aggregating, plotting and testing empirical fluctuation processes.

Usage

efpFunctional(functional = list(comp = function(x) max(abs(x)), time = max),
  boundary = function(x) rep(1, length(x)),
  computePval = NULL, computeCritval = NULL,
  plotProcess = NULL, lim.process = "Brownian bridge",
  nobs = 10000, nrep = 50000, nproc = 1:20, h = 0.5,
  probs = c(0:84/100, 850:1000/1000))

Value

efpFunctional returns a list of class "efpFunctional" with components including:

plotProcess

a function for plotting empirical fluctuation processes,

computeStatistic

a function for computing a test statistic from an empirical fluctuation process,

computePval

a function for computing the corresponding p value,

computeCritval

a function for computing critical values.

Arguments

functional

either a function for aggregating fluctuation processes or a list with two functions names "comp" and "time".

boundary

a boundary function.

computePval

a function for computing p values. If neither computePval nor computeCritval are specified critical values are simulated with settings as specified below.

computeCritval

a function for computing critical values. If neither computePval nor computeCritval are specified critical values are simulated with settings as specified below.

plotProcess

a function for plotting the empirical process, if set to NULL a suitable function is set up.

lim.process

a string specifying the limiting process.

nobs

integer specifying the number of observations of each Brownian motion simulated.

nrep

integer specifying the number of replications.

nproc

integer specifying for which number of processes Brownian motions should be simulated. If set to NULL only nproc = 1 is used and all other values are derived from a Bonferroni correction.

h

bandwidth parameter for increment processes.

probs

numeric vector specifying for which probabilities critical values should be tabulated.

Details

efpFunctional computes an object of class "efpFunctional" which then knows how to do inference based on empirical fluctuation processes (currently only for gefp objects and not yet for efp objects) and how to visualize the corresponding processes.

efpFunctionals for many frequently used test statistics are provided: maxBB for the double maximum statistic, meanL2BB for the Cramer-von Mises statistic, or rangeBB for the range statistic. Furthermore, supLM generates an object of class "efpFunctional" for a certain trimming parameter, see the examples. More details can be found in Zeileis (2006). Based on Merkle, Fan, and Zeileis (2014), further efpFunctional generators for aggregating along (ordered) categorical variables have been added: catL2BB, ordL2BB, ordwmax.

For setting up an efpFunctional, the functions computeStatistic, computePval, and plotProcess need to be supplied. These should have the following interfaces: computeStatistic should take a single argument which is the process itself, i.e., essentially a n x k matrix where n is the number of observations and k the number of processes (regressors). computePval should take two arguments: a scalar test statistic and the number of processes k. plotProcess should take two arguments: an object of class "gefp" and alpha the level of significance for any boundaries or critical values to be visualized.

References

Merkle E.C., Zeileis A. (2013), Tests of Measurement Invariance without Subgroups: A Generalization of Classical Methods. Psychometrika, 78(1), 59--82. doi:10.1007/S11336-012-9302-4

Merkle E.C., Fan J., Zeileis A. (2014), Testing for Measurement Invariance with Respect to an Ordinal Variable. Psychometrika, 79(4), 569--584. doi:10.1007/S11336-013-9376-7.

Zeileis A. (2005), A Unified Approach to Structural Change Tests Based on ML Scores, F Statistics, and OLS Residuals. Econometric Reviews, 24, 445--466. doi:10.1080/07474930500406053.

Zeileis A. (2006), Implementing a Class of Structural Change Tests: An Econometric Computing Approach. Computational Statistics & Data Analysis, 50, 2987--3008. doi:10.1016/j.csda.2005.07.001.

Zeileis A., Hornik K. (2007), Generalized M-Fluctuation Tests for Parameter Instability, Statistica Neerlandica, 61, 488--508. doi:10.1111/j.1467-9574.2007.00371.x.

See Also

gefp, supLM, catL2BB, sctest.default

Examples

data("BostonHomicide")
gcus <- gefp(homicides ~ 1, family = poisson, vcov = kernHAC,
  data = BostonHomicide)
plot(gcus, functional = meanL2BB)	 
gcus
sctest(gcus, functional = meanL2BB)

y <- rnorm(1000)
x1 <- runif(1000)
x2 <- runif(1000)

## supWald statistic computed by Fstats()
fs <- Fstats(y ~ x1 + x2, from = 0.1)
plot(fs)
sctest(fs)

## compare with supLM statistic
scus <- gefp(y ~ x1 + x2, fit = lm)
plot(scus, functional = supLM(0.1))
sctest(scus, functional = supLM(0.1))

## seatbelt data
data("UKDriverDeaths")
seatbelt <- log10(UKDriverDeaths)
seatbelt <- cbind(seatbelt, lag(seatbelt, k = -1), lag(seatbelt, k = -12))
colnames(seatbelt) <- c("y", "ylag1", "ylag12")
seatbelt <- window(seatbelt, start = c(1970, 1), end = c(1984,12))

scus.seat <- gefp(y ~ ylag1 + ylag12, data = seatbelt)

## double maximum test
plot(scus.seat)
## range test
plot(scus.seat, functional = rangeBB)
## Cramer-von Mises statistic (Nyblom-Hansen test)
plot(scus.seat, functional = meanL2BB)
## supLM test
plot(scus.seat, functional = supLM(0.1))