sandbox/Shubhankit/sandbox/Week6-7/Code/Tests/Time Series Data.R

In braverock/PerformanceAnalytics: Econometric Tools for Performance and Risk Analysis

## Willam H. Greene, Econometric Analysis, 2nd Ed.
## Chapter 15
## load data set, p. 411, Table 15.1
data(Investment)

## fit linear model, p. 412, Table 15.2
fm <- lm(RealInv ~ RealGNP + RealInt, data = Investment)
summary(fm)

## visualize residuals, p. 412, Figure 15.1
plot(ts(residuals(fm), start = 1964),
     type = "b", pch = 19, ylim = c(-35, 35), ylab = "Residuals")
sigma <- sqrt(sum(residuals(fm)^2)/fm$df.residual) ## maybe used df = 26 instead of 16 ??
abline(h = c(-2, 0, 2) * sigma, lty = 2)

if(require(lmtest)) {
  ## Newey-West covariances, Example 15.3
  coeftest(fm, vcov = NeweyWest(fm, lag = 4))
  ## Note, that the following is equivalent:
  coeftest(fm, vcov = kernHAC(fm, kernel = "Bartlett", bw = 5, prewhite = FALSE, adjust = FALSE))
  
  ## Durbin-Watson test, p. 424, Example 15.4
  dwtest(fm)
  
  ## Breusch-Godfrey test, p. 427, Example 15.6
  bgtest(fm, order = 4)
}

## visualize fitted series
plot(Investment[, "RealInv"], type = "b", pch = 19, ylab = "Real investment")
lines(ts(fitted(fm), start = 1964), col = 4)

## 3-d visualization of fitted model
if(require(scatterplot3d)) {
  s3d <- scatterplot3d(Investment[,c(5,7,6)],
                       type = "b", angle = 65, scale.y = 1, pch = 16)
  s3d$plane3d(fm, lty.box = "solid", col = 4)
}
## fit investment equation
data(Investment)
fm <- lm(RealInv ~ RealGNP + RealInt, data = Investment)

## Newey & West (1994) compute this type of estimator
NeweyWest(fm)

## The Newey & West (1987) estimator requires specification
## of the lag and suppression of prewhitening
NeweyWest(fm, lag = 4, prewhite = FALSE)

## bwNeweyWest() can also be passed to kernHAC(), e.g.
## for the quadratic spectral kernel
kernHAC(fm, bw = bwNeweyWest)

curve(kweights(x, kernel = "Quadratic", normalize = TRUE),
      from = 0, to = 3.2, xlab = "x", ylab = "k(x)")
curve(kweights(x, kernel = "Bartlett", normalize = TRUE),
      from = 0, to = 3.2, col = 2, add = TRUE)
curve(kweights(x, kernel = "Parzen", normalize = TRUE),
      from = 0, to = 3.2, col = 3, add = TRUE)
curve(kweights(x, kernel = "Tukey", normalize = TRUE),
      from = 0, to = 3.2, col = 4, add = TRUE)
curve(kweights(x, kernel = "Truncated", normalize = TRUE),
      from = 0, to = 3.2, col = 5, add = TRUE)

## fit investment equation
data(Investment)
fm <- lm(RealInv ~ RealGNP + RealInt, data = Investment)

## compute quadratic spectral kernel HAC estimator
kernHAC(fm)
kernHAC(fm, verbose = TRUE)

## use Parzen kernel instead, VAR(2) prewhitening, no finite sample
## adjustment and Newey & West (1994) bandwidth selection
kernHAC(fm, kernel = "Parzen", prewhite = 2, adjust = FALSE,
        bw = bwNeweyWest, verbose = TRUE)
## compare with estimate under assumption of spheric errors
vcov(fm)