The annual bituminous coal production in the United States from 1920 to 1968 is in data set bicoal .
a. Produce a time plot of the data.
b. You decide to t the following model to the series:
Where yt
is the coal production in year t and εt
is a white noise series. What sort of ARIMA model is this (i.e., what are p, d, and q)?
c. Explain why this model was chosen using the ACF and PACF.
d. The last five values of the series are given below.
The estimated parameters are c = 162.00,
1
= 0.83,
2
= −0.34,
3
= 0.55 and
4
= −0.38. Without using the forecast function, calculate forecasts for the next three years (1969–1971).
e. Now t the model in R and obtain the forecasts from the same model. How are they dierent from yours? Why?