strucchange (version 0.9-3)

efp: Empirical Fluctuation Process

Description

Computes an empirical fluctuation process according to a specified method from the generalized fluctuation test framework

Usage

efp(formula, data, type = <>, h = 0.15, dynamic = FALSE,
  rescale = TRUE, tol = 1e-7)

Arguments

formula

a symbolic describtion for the model to be tested.

data

an optional data frame containing the variables in the model. By default the variables are taken from the environment which efp is called from.

type

specifies which type of fluctuation process will be computed. For details see below.

h

a numeric from interval (0,1) sepcifying the bandwidth. determins the size of the data window relative to sample size (for MOSUM and ME processes only).

dynamic

logical. If TRUE the lagged observations are included as a regressor.

rescale

logical. If 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

tol

tolerance when solve is used

Value

• efp 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.

Details

If 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.

References

Brown R.L., Durbin J., Evans J.M. (1975), Techniques for testing constancy of regression relationships over time, Journal of the Royal Statistal 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.

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.

See Also

plot.efp, print.efp, sctest.efp, boundary.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 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)