Description Usage Arguments Details Value References See Also Examples

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

1 |

`formula` |
a symbolic description for the model to be tested |

`from, to` |
numeric. If |

`data` |
an optional data frame containing the variables in the model. By
default the variables are taken from the environment which |

`vcov.` |
a function to extract the covariance matrix
for the coefficients of a fitted model of class |

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 observations 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 = (RSS-ESS)/ESS * (n-2*k)*

Note that this statistic has an asymptotic chi-squared distribution with k degrees of freedom and (under the assumption of normality) F/k has an exact F distribution with k and n - 2k degrees of freedom.

`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.

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.

`plot.Fstats`

, `sctest.Fstats`

,
`boundary.Fstats`

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 | ```
## Nile data with one breakpoint: the annual flows drop in 1898
## because the first Ashwan dam was built
data("Nile")
plot(Nile)
## test the null hypothesis that the annual flow remains constant
## over the years
fs.nile <- Fstats(Nile ~ 1)
plot(fs.nile)
sctest(fs.nile)
## visualize the breakpoint implied by the argmax of the F statistics
plot(Nile)
lines(breakpoints(fs.nile))
## UK Seatbelt data: a SARIMA(1,0,0)(1,0,0)_12 model
## (fitted by OLS) is used and reveals (at least) two
## breakpoints - one in 1973 associated with the oil crisis and
## one in 1983 due to the introduction of compulsory
## wearing of seatbelts in the UK.
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))
plot(seatbelt[,"y"], ylab = expression(log[10](casualties)))
## compute F statistics for potential breakpoints between
## 1971(6) (corresponds to from = 0.1) and 1983(6) (corresponds to
## to = 0.9 = 1 - from, the default)
## compute F statistics
fs <- Fstats(y ~ ylag1 + ylag12, data = seatbelt, from = 0.1)
## this gives the same result
fs <- Fstats(y ~ ylag1 + ylag12, data = seatbelt, from = c(1971, 6),
to = c(1983, 6))
## plot the F statistics
plot(fs, alpha = 0.01)
## plot F statistics with aveF boundary
plot(fs, aveF = TRUE)
## perform the expF test
sctest(fs, type = "expF")
``` |

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