efp(formula, data, type = <>, h = 0.15, dynamic = FALSE,
rescale = TRUE, tol = 1e-7) efp is
called from.TRUE the lagged observations are included as
a regressor.TRUE the estimates will be standardized by
the regressor matrix of the corresponding subsample according to Kuan & Chen
(1994); if FALSE the whole regressor matrix will be used.
(only if type solve is usedefp returns an object of class "efp" which inherits
from the class "ts" or "mts" respectively, to which a string
with the type of the process, the number of regressors (nreg),
the bandwidth (h) and the function call {call) are added as
attributes. The function plot has a method to plot the empirical
fluctuation process; with sctest the corresponding test on structural
change can be performed.}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.
Kraemer 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., Kraemer W. (1992), The CUSUM test with OLS residuals, Econometrica, 60, 271-285.
[object Object]
plot.efp, print.efp,
sctest.efp, boundary.efp
## test the model null hypothesis that the average temperature remains constant ## over the years ## compute OLS-CUSUM fluctuation process temp.cus <- efp(nhtemp ~ 1, type = "OLS-CUSUM") ## plot the process with alternative boundaries plot(temp.cus, alpha = 0.01, alt.boundary = TRUE) ## and calculate the test statistic sctest(temp.cus)
## Load dataset "USIncExp" with income and expenditure in the US ## and choose a suitable subset data(USIncExp) USIncExp2 <- window(USIncExp, start=c(1970,1), end=c(1989,12))
## test the null hypothesis that the way the income is spent in expenditure
## does not change over time
## compute moving estimates fluctuation process
me <- efp(expenditure~income, type="ME", data=USIncExp2, h=0.2)
## plot the two dimensional fluctuation process with boundaries
plot(me, functional=NULL)
## and perform the corresponding test
sctest(me)
type is one of "Rec-CUSUM", "OLS-CUSUM",
"Rec-MOSUM" or "OLS-MOSUM" the function efp will return a
one-dimensional empiricial process of sums of residuals. Either it will be based
on recursive residuals or on OLS residuals and the process will contain
CUmulative SUMs or MOving SUMs of residuals in a certain data window.
For the MOSUM and ME processes all estimations are done for the
observations in a moving data window, whose size is determined by h and
which is shifted over the whole sample.If there is a single structural change point $t^*$, the standard CUSUM path starts to depart from its mean 0 at $t^*$. The OLS-based CUSUM path will have its peak around $t^*$. The MOSUM path should have a strong change at $t^*$.
If type is either "fluctuation" or "ME" a
k-dimensional process will be returned, if k is the number of
regressors in the model, as it is based on recursive OLS estimates of the
regression coefficients or moving OLS estimates respectively.
Both paths should have a peak around $t^*$ if there is a single structural shift.