Natural gas is a major Canadian export and hence a major source of foreign exchange. The data file contains monthly Canadian exports of natural gas from April 2006 to March 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 April 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 March 2008 and for March 2009? What forecast does this model give for April 2009?

c) Perform exponential smoothing on these data using a smoothing parameter of α = 0.2. Use the initial condition that the smoothed value for April 2006 is the same as the data value for April 2006. What is the smoothed value for May 2006 and for March 2009? What forecast does this model give for April 2009?