For the data of given Exercise:
a. Obtain the centered moving average for N = 4; for N = 12.
b. When N 12 months, the centered moving average is relatively smooth compared to when N = 4. Aside from the fact that it includes a greater number of months at a time, is there any other reason why the moving average with N = 12 should be so smooth?
Exercise
According to the U.S. Energy Information Administration, a heating degree-day is a relative measurement of outdoor temperature that indicates how far the average daily temperature is below 65° Fahrenheit. The higher the number of heating degree-days, the greater the national demand for heating energy from sources like natural gas and electricity. The following monthly data show the number of heating degree-days from 1992 through 1995.
a. Construct a graph of the time series. Does the overall trend appear to be upward or downward?
b. Determine the three-month and five-month centered moving average curves and superimpose each on the original time series.