Dow Jones Industrial Average
Weekly closing values of the Dow Jones Industrial Average.
data("DJIA")A weekly univariate time series of class "zoo"
from 1971-07-01 to 1974-08-02.
Appendix A in Hsu (1979).
Hsu D. A. (1979), Detecting Shifts of Parameter in Gamma Sequences with Applications to Stock Price and Air Traffic Flow Analysis, Journal of the American Statistical Association, 74, 31–40.
data("DJIA")
## look at log-difference returns
djia <- diff(log(DJIA))
plot(djia)
## convenience functions
## set up a normal regression model which
## explicitely also models the variance
normlm <- function(formula, data = list()) {
rval <- lm(formula, data = data)
class(rval) <- c("normlm", "lm")
return(rval)
}
estfun.normlm <- function(obj) {
res <- residuals(obj)
ef <- NextMethod(obj)
sigma2 <- mean(res^2)
rval <- cbind(ef, res^2 - sigma2)
colnames(rval) <- c(colnames(ef), "(Variance)")
return(rval)
}
## normal model (with constant mean and variance) for log returns
m1 <- gefp(djia ~ 1, fit = normlm, vcov = meatHAC, sandwich = FALSE)
plot(m1, aggregate = FALSE)
## suggests a clear break in the variance (but not the mean)
## dating
bp <- breakpoints(I(djia^2) ~ 1)
plot(bp)
## -> clearly one break
bp
time(djia)[bp$breakpoints]
## visualization
plot(djia)
abline(v = time(djia)[bp$breakpoints], lty = 2)
lines(time(djia)[confint(bp)$confint[c(1,3)]], rep(min(djia), 2), col = 2, type = "b", pch = 3)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.