|Data Scientist|Business Analyst|Business Intelligence Specialist|Senior Project Management Officer|Senior Project Planning|
|EASA Part M CAMO 145 Technical Service Engineer|Aircraft Asset Management Specialist|
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)
lines(c(0, 0.5), c(1, 1), col = 6)
lines(c(0.5, 0.5), c(1, 0), lty = 3, col = 6)
lines(c(0.5, 3.2), c(0, 0), col = 6)
curve(kweights(x, kernel = "Quadratic", normalize = TRUE),
from = 0, to = 3.2, col = 1, add = TRUE)
text(0.5, 0.98, "Truncated", pos = 4)
text(0.8, kweights(0.8, "Bartlett", normalize = TRUE), "Bartlett", pos = 4)
text(1.35, kweights(1.4, "Quadratic", normalize = TRUE), "Quadratic Spectral", pos = 2)
text(1.15, 0.29, "Parzen", pos = 4)
arrows(1.17, 0.29, 1, kweights(1, "Parzen", normalize = TRUE), length = 0.1)
text(1.3, 0.2, "Tukey-Hanning", pos = 4)
arrows(1.32, 0.2, 1.1, kweights(1.1, "Tukey", normalize = TRUE), length = 0.1)
coeftest(fm.ps, df = Inf, vcov = vcovHC(fm.ps, type = "HC0"))
##
## z test of coefficients:
##
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 832.91 460.89 1.8072 0.07073 .
## Income -1834.20 1243.04 -1.4756 0.14006
## I(Income^2) 1587.04 829.99 1.9121 0.05586 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
coeftest(fm.ps, df = Inf, vcov = vcovHC(fm.ps, type = "HC4"))
##
## z test of coefficients:
##
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 832.91 3008.01 0.2769 0.7819
## Income -1834.20 8183.19 -0.2241 0.8226
## I(Income^2) 1587.04 5488.93 0.2891 0.7725
plot(Expenditure ~ Income, data = ps,
xlab = "per capita income",
ylab = "per capita spending on public schools")
inc <- seq(0.5, 1.2, by = 0.001)
lines(inc, predict(fm.ps, data.frame(Income = inc)), col = 4, lty = 2)
fm.ps2 <- lm(Expenditure ~ Income, data = ps)
abline(fm.ps2, col = 4)
text(ps[2,2], ps[2,1], rownames(ps)[2], pos = 2)
##
## z test of coefficients:
##
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -12.533601 18.958298 -0.6611 0.5085
## RealGNP 0.169136 0.016751 10.0972 <2e-16 ***
## RealInt -1.001438 3.342375 -0.2996 0.7645
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
coeftest(fm.inv, df = Inf, vcov = NeweyWest)
##
## z test of coefficients:
##
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -12.533601 24.374177 -0.5142 0.6071
## RealGNP 0.169136 0.023586 7.1709 7.449e-13 ***
## RealInt -1.001438 3.639935 -0.2751 0.7832
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
parzenHAC <- function(x, ...) kernHAC(x, kernel = "Parzen", prewhite = 2,
adjust = FALSE, bw = bwNeweyWest, ...)
coeftest(fm.inv, df = Inf, vcov = parzenHAC)
##
## z test of coefficients:
##
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -12.533601 24.663944 -0.5082 0.6113
## RealGNP 0.169136 0.020835 8.1181 4.737e-16 ***
## RealInt -1.001438 3.947469 -0.2537 0.7997
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
library("scatterplot3d")
s3d <- scatterplot3d(Investment[,c(5,7,6)],
type = "b", angle = 65, scale.y = 1, pch = 16)
s3d$plane3d(fm.inv, lty.box = "solid", col = 4)
library("strucchange")
data("RealInt")
ocus <- gefp(RealInt ~ 1, fit = lm, vcov = kernHAC)
bp <- breakpoints(RealInt ~ 1)
confint(bp, vcov = kernHAC)
##
## Confidence intervals for breakpoints
## of optimal 3-segment partition:
##
## Call:
## confint.breakpointsfull(object = bp, vcov. = kernHAC)
##
## Breakpoints at observation number:
## 2.5 % breakpoints 97.5 %
## 1 37 47 48
## 2 77 79 81
##
## Corresponding to breakdates:
## 2.5 % breakpoints 97.5 %
## 1 1970(1) 1972(3) 1972(4)
## 2 1980(1) 1980(3) 1981(1)
par(mfrow = c(1, 2))
plot(ocus, aggregate = FALSE, main = "")
plot(RealInt, ylab = "Real interest rate")
lines(ts(fitted(bp), start = start(RealInt), freq = 4), col = 4)
lines(confint(bp, vcov = kernHAC))
library("sandwich")
library("lmtest")
library("strucchange")
data("PublicSchools")
ps <- na.omit(PublicSchools)
ps$Income <- ps$Income * 0.0001
fm.ps <- lm(Expenditure ~ Income + I(Income^2), data = ps)
## (Intercept) Income I(Income^2)
## 327.2925 828.9855 519.0768
sqrt(diag(vcovHC(fm.ps, type = "const")))
## (Intercept) Income I(Income^2)
## 327.2925 828.9855 519.0768
sqrt(diag(vcovHC(fm.ps, type = "HC0")))
## (Intercept) Income I(Income^2)
## 460.8917 1243.0430 829.9927
sqrt(diag(vcovHC(fm.ps, type = "HC3")))
## (Intercept) Income I(Income^2)
## 1095.001 2975.411 1995.242
sqrt(diag(vcovHC(fm.ps, type = "HC4")))
## (Intercept) Income I(Income^2)
## 3008.010 8183.191 5488.929
coeftest(fm.ps, df = Inf, vcov = vcovHC(fm.ps, type = "HC0"))
##
## z test of coefficients:
##
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 832.91 460.89 1.8072 0.07073 .
## Income -1834.20 1243.04 -1.4756 0.14006
## I(Income^2) 1587.04 829.99 1.9121 0.05586 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
coeftest(fm.ps, df = Inf, vcov = vcovHC(fm.ps, type = "HC4"))
##
## z test of coefficients:
##
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 832.91 3008.01 0.2769 0.7819
## Income -1834.20 8183.19 -0.2241 0.8226
## I(Income^2) 1587.04 5488.93 0.2891 0.7725
fm.inv <- lm(RealInv ~ RealGNP + RealInt, data = Investment)
plot(Investment[, "RealInv"], type = "b", pch = 19, ylab = "Real investment")
lines(ts(fitted(fm.inv), start = 1964), col = 4)
ocus <- gefp(RealInt ~ 1, fit = lm, vcov = kernHAC)
plot(ocus, aggregate = FALSE)
##
## M-fluctuation test
##
## data: ocus
## f(efp) = 1.6586, p-value = 0.008159
fs <- Fstats(RealInt ~ 1, vcov = kernHAC)
plot(fs)
##
## supF test
##
## data: fs
## sup.F = 78.198, p-value < 2.2e-16
bp <- breakpoints(RealInt ~ 1)
confint(bp, vcov = kernHAC)
##
## Confidence intervals for breakpoints
## of optimal 3-segment partition:
##
## Call:
## confint.breakpointsfull(object = bp, vcov. = kernHAC)
##
## Breakpoints at observation number:
## 2.5 % breakpoints 97.5 %
## 1 37 47 48
## 2 77 79 81
##
## Corresponding to breakdates:
## 2.5 % breakpoints 97.5 %
## 1 1970(1) 1972(3) 1972(4)
## 2 1980(1) 1980(3) 1981(1)
plot(RealInt, ylab = "Real interest rate")
lines(ts(fitted(bp), start = start(RealInt), freq = 4), col = 4)
lines(confint(bp, vcov = kernHAC))
