For the data of given Exercise, fit an exponentially smoothed curve with smoothing constant α = 0.4; with smoothing constant α = 0.7. Which constant provides more "smoothing" and why? Which curve is quicker to "catch up" whenever the original series changes direction and why?
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.