Dow Jones Industrial Average

Description

Weekly closing values of the Dow Jones Industrial Average.

Usage

data("DJIA")

Format

A weekly univariate time series of class “zoo” from 1971-07-01 to 1974-08-02.

Source

Appendix A in Hsu (1979).

References

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.

Examples

library("strucchange")

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

     Optimal 2-segment partition: 

Call:
breakpoints.formula(formula = I(djia^2) ~ 1)

Breakpoints at observation number:
89 

Corresponding to breakdates:
0.552795 

time(djia)[bp$breakpoints]

[1] "1973-03-16"

## 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)