DATA624 HW2

usnetelec

Description: Annual US net electricity generation (billion kwh) for 1949-2003

usnetelec <- expsmooth::usnetelec
# before BoxCox
autoplot(usnetelec)

frequency(usnetelec)

## [1] 1

# ggseasonplot(usnetelec)
# ggseasonplot(usnetelec, polar = TRUE)
# ggsubseriesplot(usnetelec)
ggAcf(usnetelec)

lambda <- BoxCox.lambda(usnetelec)
lambda

## [1] 0.5167714

# after BoxCox
autoplot(BoxCox(usnetelec,lambda))

The usnetelec series does not show any seasonality in the time, or ACF plots, so there is no increase in seasonal variation that corresponds with the increase in the level of the series. Therefore, a Box-Cox transformation does not make sense in this case. This can be seen in the before and after Box-Cox plots as well which show almost no change in the variation after the transformation.

usgdp

Description: Quarterly US GDP. 1947:1 - 2006.1.

usgdp <- expsmooth::usgdp
# before BoxCox
autoplot(usgdp)

frequency(usgdp)

## [1] 4

ggseasonplot(usgdp)

ggseasonplot(usgdp, polar = TRUE)

ggsubseriesplot(usgdp)

ggAcf(usgdp)

lambda <- BoxCox.lambda(usgdp)
lambda

## [1] 0.366352

# after BoxCox
autoplot(BoxCox(usgdp,lambda))

The usgdp series does not show any seasonality in the time, season, subseries or ACF plots, so there is no increase in seasonal variation (or seasonal variation at all for that matter) to correspond with the increase in the level of the series. Therefore, a Box-Cox transformation does not make sense in this case. This can be seen in the before and after Box-Cox plots as well which show almost no change in the variation after the transformation.

mcopper

Description: Monthly copper prices. Copper, grade A, electrolytic wire bars/cathodes,LME,cash (pounds/ton)

Source: UNCTAD http://stats.unctad.org/Handbook.

mcopper <- expsmooth::mcopper
# before BoxCox
autoplot(mcopper)

frequency(mcopper)

## [1] 12

ggseasonplot(mcopper)

ggseasonplot(mcopper, polar = TRUE)

ggsubseriesplot(mcopper)

ggAcf(mcopper)

lambda <- BoxCox.lambda(mcopper)
lambda

## [1] 0.1919047

# after BoxCox
autoplot(BoxCox(mcopper,lambda))

Once again, the mcopper series does not show any seasonality in the time, season, subseries or ACF plots, so there is no increase in seasonal variation (or seasonal variation at all) to correspond with the increase in the level of the series. Therefore, a Box-Cox transformation does not make sense in this case. This can be seen in the before and after Box-Cox plots as well which show almost no change in the variation after the transformation.

enplanements

Description: "Domestic Revenue Enplanements (millions): 1996-2000.

Source: Department of Transportation, Bureau of Transportation Statistics, Air Carrier Traffic Statistic Monthly.

enplanements <- expsmooth::enplanements
# before BoxCox
autoplot(enplanements)

frequency(enplanements)

## [1] 12

ggseasonplot(enplanements)

ggseasonplot(enplanements, polar = TRUE)

ggsubseriesplot(enplanements)

ggAcf(enplanements)

lambda <- BoxCox.lambda(enplanements)
lambda

## [1] -0.2269461

# after BoxCox
autoplot(BoxCox(enplanements,lambda))

The enplanements series is the only one of the four that shows a clear seasonality that increases with the increase in the level of the series, so it is the only one of the four series for which a Box-Cox transformation is warranted and useful. You can see this in the before and after Box-Cox plots as well which show a evening out of the seasonal variation so that it becomes relatively consistent throughout the series.

a. Split the data into two parts using

myts.train <- window(myts, end=c(2010,12))
myts.test <- window(myts, start=2011)

b. Check that your data have been split appropriately by producing the following plot.

autoplot(myts) +
  autolayer(myts.train, series="Training") +
  autolayer(myts.test, series="Test")

c. Calculate forecasts using snaive applied to myts.train.

fc <- snaive(myts.train)

d. Compare the accuracy of your forecasts against the actual values stored in myts.test.

data.frame(accuracy(fc,myts.test))

e. Check the residuals.

checkresiduals(fc)

## 
##  Ljung-Box test
## 
## data:  Residuals from Seasonal naive method
## Q* = 812.76, df = 24, p-value < 2.2e-16
## 
## Model df: 0.   Total lags used: 24

Do the residuals appear to be uncorrelated and normally distributed?

The residuals do not appear to be uncorrelated or normally distributed. The p-value is extremely low and in the ACF plot above you can see that most of the lags extend far beyond the significance range (between the blue lines). Lags beyond this range are significantly different from zero. The histogram shows a clear right skew.

f. How sensitive are the accuracy measures to the training/test split?

train2 <- window(myts, end = c(2008, 12))
test.BIG <- window(myts, start = 2009)

train3 <- window(myts, end = c(2012, 12))
test.small <- window(myts, start = 2013)
fc.BIG <- snaive(train2)
fc.small <- snaive(train3)

autoplot(myts) +
  autolayer(fc, series = "Orig Split", PI = FALSE) +
  autolayer(fc.BIG, series = "Large Test Group", PI = FALSE) +
  autolayer(fc.small, series = "Small Test Group", PI = FALSE) +
  ggtitle("Split Comparison") + 
  guides(colour = guide_legend(title = "Forecasts"))

data.frame(accuracy(fc, myts.test))

data.frame(accuracy(fc.BIG, test.BIG))

data.frame(accuracy(fc.small, test.small))

The accuracy measures are very sensitive to the training/test split. There is a big difference in the measures depending on how small or large we make the split.