Question

FOR1. Open file Nuclear Power. Select data for Canada. Address the following questions.

a. Provide a plot of the data over time in the space below. (2 pts)

[plot here]

b. Choose an appropriate forecasting model and forecast for the next 3 periods (provide forecast in the table below). Explain model selection approach. (8 pts)

Period	Forecast
2007
2008
2009

c. Using the same data, forecast the next 3 periods in the time series using the 5-period moving average and indicate the values below. (3 pts)

Period	Forecast
2007
2008
2009

d. Using the same data, forecast for the next 3 periods in the time series using the single exponential smoothing technique with a smoothing constant of 0.3 and indicate the values below. (3 pts)

Period	Forecast
2007
2008
2009

e. Compare results from models b, c and d. Which forecast model do you recommend to use for the next 3 periods? Justify your recommendation (6 pts)

DATA:

Nuclear Electric Power Production (Billion KWH)
Year	US	Canada	France
1980	251.12	35.88	63.42
1981	272.67	37.8	99.24
1982	282.77	36.17	102.63
1983	293.68	46.22	135.99
1984	327.63	49.26	180.47
1985	383.69	57.1	211.19
1986	414.04	67.23	239.56
1987	455.27	72.89	249.27
1988	526.97	78.18	260.29
1989	529.35	75.35	288.72
1990	576.86	69.24	298.38
1991	612.57	80.68	314.77
1992	618.78	76.55	321.52
1993	610.29	90.08	349.78
1994	640.44	102.44	341.98
1995	673.4	92.95	358.37
1996	674.73	88.13	377.47
1997	628.64	77.86	375.71
1998	673.7	67.74	368.59
1999	728.25	69.82	374.53
2000	753.89	69.16	394.4
2001	768.83	72.86	400.02
2002	780.06	71.75	414.92
2003	763.73	71.15	419.02
2004	788.53	85.87	425.83
2005	781.99	87.44	428.95
2006	787.22	93.07	427.68

Answer 1

We shall be doing this for only Canada as provided in the question. The work will be done on excel. The images are provided after the explanation.

a) Please see the plot below for the data on Canada against years in the screenshot

b) We can see that there is an overall general upward trend. Hence we can use a linear regression model for forecasting. In order to do this, we need to determine the slope and the intercept of the equation

Y = a + bX, where b is slope and a is intercept. Y is the value and X is the year.

On excel we can use the “slope” and “intercept” formula. However you could also use the formula below. The slope is 1.54 and the intercept is -2999 hence the equation becomes

Y = 1.54X – 2999.38

So we have

Y₂₀₀₇ = 1.54*2007 – 2999.38 = 92.78

Y₂₀₀₈ = 1.54*2008 – 2999.38 = 94.32

Y₂₀₀₉ = 1.54*2009 – 2999.38 = 95.86

Using this the forecasted values are 92.78, 94.32 and 95.86 for 2007, 2008, and 2009 respectively.

c) Moving average method take the previous periods average and places it for the current period. For the 5 period moving average

MA₂₀₀₇ = (A₂₀₀₆ + A₂₀₀₅ + A₂₀₀₄ + A₂₀₀₃ + A₂₀₀₂)

Here A_t is the actual value for period t.

This way we get (use similar method for the next two years as well)

MA₂₀₀₇ = 81.56

MA₂₀₀₈ = 84.38

MA₂₀₀₉ = 88.79

d) Exponential smoothing forecast is given by

F_t+1 = aD_t + (1-a)F_t

Here F_t+1 is the forecast for the period, D_t is the actual demand for previous period, F_t is the forecast for previous period and a is the smoothing factor.

This process needs to be calculated from 1980. For the first value (forecasted value of 1980, use the same value as the actual demand). The data is shown on the excel sheet.

The values are 83.83, 58.68, and 41.08

e) For the next three period I recommend using the exponential smoothing method. The Mean Square Error if Exponential smoothing with a factor of 0.3 is the lowest among all other methods.