Question

# A. Use the three- and seven-term moving averages to generate one-step ahead forecasts for 1981 to...

A. Use the three- and seven-term moving averages to generate one-step ahead forecasts for 1981 to the end of the series. Graph the results, and comment on the difference between the two moving averages.

B. Compare the performance of the two procedures by calculating the RMSE and MAE. Why is Mape inappropriate in this case?

Please show to do this in excel, I am having a difficult time understanding how this is done.

 Year GDP Growth 1963 4.4 1964 5.8 1965 6.4 1966 6.5 1967 2.5 1968 4.8 1969 3.1 1970 0.2 1971 3.4 1972 5.3 1973 5.8 1974 -0.5 1975 -0.2 1976 5.3 1977 4.6 1978 5.6 1979 3.2 1980 -0.2 1981 2.5 1982 -1.9 1983 4.5 1984 7.2 1985 4.5 1986 3.5 1987 3.4 1988 4.1 1989 3.5 1990 1.9 1991 -0.2 1992 3.3 1993 2.7 1994 4 1995 2.5 1996 3.7 1997 4.5 1998 4.2 1999 4.5 2000 3.8 2001 0.8 2002 1.9 2003 3 2004 4.4 2005 2.9 2006 2.8 2007 2

1) 3 term moving average is calculated as

For example forecast for 1981 is calculated as

7 term moving average is calculated as

For example forecast for 1981 is calculated as

the following excel shows the calculations, starting from the year 1981

Get the following

Graph the results

select the data and use insert-->scatter-->lines as shown below

get the following

format as needed

We can see that the original GDP Growth series widely fluctuates. Some of these variations could be due to the irregular component of the time series. The purpose of the moving average forecasting is to smooth out the random fluctuations due to the irregular component. In this regard, we can see that 7 term moving average does a better job that 3 term moving average. 7 term moving average does not react as much as the 3 term moving average and it has smoothened out the fluctuations in the original GDP series.

b)

RMSE (Root means squared Error) is calculated as

where Actual(t) is the actual value of GDP Growth in period t and Forecast(t) is the forecasted value in period t. n=27 is the number of periods (from 1981 to 2007) for which the error is calculated.

Mean Absolute Error (MAE) is calculated as

where |value| is the absolute of "value"

The following excel shows the 2 calculations

The values are

7 term moving average has a lower RMSE as well as MAE. Hence 7 term moving average is a better forecasting method.

MAPE is calculated as

The Actual value in the denominator is the GDP growth. If the GDP growth is zero (which it can be), then this devision becomes not calculable. Hence MAPE meaure might not be appropriate for GDP growth as GDP growth can be 0.

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