Description
In this lab you will apply the Box–Jenkins forecasting method using a case study. The “lake
levels” data is a built–in dataset in R. It measures the annual level of Lake Huron from 1875
to 1972, in feet.
The data in data(LakeHuron) are already in time series format. Using the
window command or otherwise, first subset the Lake Huron data into two separate datasets:
LakeHuron.train, which should contain the first 93 lake levels, and LakeHuron.test containing
the last 5 lake levels. We will use LakeHuron.train to “train” a model and forecast the next
three points based on the fitted model.
1. The data may show a slightly decreasing trend. Ignore this possible decreasing trend in
what follows. Plot the LakeHuron.train data, its acf and pacf. Determine an appropriate
ARMA model and explain your choice.
2. Fit the model you chose above using the function arima(). Write down the fitted model.
3. Examine appropriate diagnostics for your fitted model. Specifically, first plot the acf of the
residuals to see if there are significant autocorrelations after lag 0. Then, use tsdiag()
to observe the standardized residuals and the p-values of the Ljung-Box version for the
portmanteau test. Report what you observe and then comment on the fit.
4. Use the predict command in R to forecast the Lake Huron level for the next three years,
i.e., 1968, 1969, and 1970. Provide 95% prediction intervals for each forecast.
5. Compare the forecast with the true values (in LakeHuron.test). Comment on what you
find.