strucchange (version 0.9-4)

Fstats: F Statistics

Description

Computes a series of F statistics for a specified data window.

Usage

Fstats(formula, from = 0.15, to = NULL, data,
       cov.type = c("const", "HC", "HC1"), tol=1e-7)

Arguments

formula

a symbolic description for the model to be tested

from, to

numeric. If from is smaller than 1 they are interpreted as percentages of data and by default to is taken to be 1 - from. F statistics will be calculated for the observations (n*from):(n*to)

data

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

cov.type

a string indicating which type of covariance matrix estimator should be used. Constant homoskedastic variances are assumed if set to "const" and White's heteroskedasticity consistent estimator is used if set to "HC"

tol

tolerance when solve is used.

Value

• Fstats returns an object of class "Fstats", which contains mainly a time series of F statistics. The function plot has a method to plot the F statistics or the corresponding p values; with sctest a supF-, aveF- or expF-test on structural change can be performed.

Details

For every potential change point in from:to a F statistic (Chow test statistic) is computed. For this an OLS model is fitted for the observations before and after the potential change point, i.e. 2k parameters have to be estimated, and the error sum of squares is computed (ESS). Another OLS model for all obervations with a restricted sum of squares (RSS) is computed, hence k parameters have to be estimated here. If n is the number of observations and k the number of regressors in the model, the formula is:

$$F = \frac{(RSS - ESS)}{ESS/(n - 2 k)}$$

References

Andrews D.W.K. (1993), Tests for parameter instability and structural change with unknown change point, Econometrica, 61, 821-856.

Hansen B. (1992), Tests for parameter instability in regressions with I(1) processes, Journal of Business & Economic Statistics, 10, 321-335.

Hansen B. (1997), Approximate asymptotic p values for structural-change tests, Journal of Business & Economic Statistics, 15, 60-67.

See Also

plot.Fstats, sctest.Fstats, boundary.Fstats

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 for potential break points between 1941 (corresponds to from =
## 0.5) and 1962 (corresponds to to = 0.85)
## compute F statistics
fs <- Fstats(nhtemp ~ 1, from = 0.5, to = 0.85)
## this gives the same result
fs <- Fstats(nhtemp ~ 1, from = c(1941,1), to = c(1962,1))
## plot the F statistics
plot(fs, alpha = 0.01)
## and the corresponding p values
plot(fs, pval = TRUE, alpha = 0.01)
## perform the aveF test
sctest(fs, type = "aveF")