Trends in exports of industrial machinery are extremely important to Canada because of overseas competition from countries with lower wage rates. The data file contains monthly Canadian exports of industrial machinery from June 2006 to May 2009 in millions of dollars.

a) Fit an AR(2) model to the data. Which range of months do you use to fit the model? Give the regression output plus the equation for the model. What forecast does this model give for June 2009?

b) Calculate a fourth-order moving average, MA-4, of the data. Which is the first month for which the MA-4 can be calculated? What is the value of the MA-4 for May 2008 and for May 2009? What forecast does this model give for June 2009?

c) Perform exponential smoothing on these data using a smoothing parameter of α = 0.3. Use the initial condition that the smoothed value for June 2006 is the same as the data value for June 2006. What is the smoothed value for July 2006 and for May 2009? What forecast does this model give for June 2009?