ECON 6313-001
Fall semester, 2012
Class Forecasting Assignment
October 10, 2012
Objective: Perform the best possible forecast of farm machinery sales in the U.S. for the 1st six
months of 2013.
The Data: You will need to download an Excel file to complete this exercise. Browse to
wmyweb.astate.edu/6313.html and obtain the file ECON6313FMSf11.xlsx. You will find 200
monthly observations (January 1996 to August 2012) for the following variables:
t: Time period—Jan 1996 = 1 and August 2012 = 200.
FMS: Farm machinery sales, seasonally unadjusted, in millions of dollars.
FPI: Index of prices of farms products.
FCPI: Index of prices of farm chemicals.
PR: Prime rate—rate of interest paid on bank loans by prime corporate borrowers.
SDU: Seasonal dummy variable. Equal to 1 for February, March, April, and May; 0 otherwise.
Descriptive Statistics: Might as well familiarize ourselves with some Excel features while we are
at it. Go to the Data menu and select the data analysis option.1 For input range activate cells D1
to F201 (Be sure to check the labels in the first row box). Check summary statistics and click OK.
Model 1: Estimate the following model specification using Excel’s regression tool.
FMSt  0  1FPIt   2 FPCIt  3 PRt
Take the following steps to perform the regression:
1. From the Data menu select the data analysis option and then regression.
2. The Input Y Range should contain D1 to D201. The Input X Range should contain E1 to
G201. Be sure that you have checked the labels box.
3. Click OK
Questions about the Model 1 estimates:
1. Is your estimate of β1 statistically significant at the .05 level?
2. Can you give an interpretation of your estimate of β3?
3. Would you say this equation gives a good fit based on R2 or the standard error of the
regression?
1
If you fail to find a data analysis option on your Data menu, then select add-ins and check the Analysis
Toolpak option and click OK.
2
Model 2: The fit of the equation estimated above leaves a lot to be desired. It is likely that
seasonal factors are important in explaining month-to-month variations in farm equipment
sales. But model 1 failed to take these into account.
Estimate the following model specification using Excel’s regression tool:
FMSt  0  1FPIt   2 FPCIt  3 PRt   4 SDU t
Take the following steps to perform the regression:
1. From the Data menu select the data analysis option and then regression.
2. The Input Y Range should contain D1 to D201. The Input X Range should contain E1 to
H201. Be sure that you have checked the labels box.
3. Click OK
4. Record on paper your estimates of the coefficients (don’t forget the intercept or
“constant”).
5. Now click on the sheet 1 tab at the bottom of the spreadsheet.
Questions about Model 2?
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

Is there improvement from model 1 based on the goodness of fit statistics?
Can you give an interpretation of the estimates of the β3 and β4? Is the estimate of β4
statistically significant at the .05 level?
Can you give an interpretation of the standard error of the regression?
Model 3: The Multiplicative Time Series Model. The model is written as:
FMSt  Tt  St  Ct  I t
Where Tt is the trend component is time period t; St is the seasonal component; Ct is the cyclical
component, and; It is the irregular component. Assume that Ct = 1 and of course the irregular
component is unknowable for forecasting purposes. To find the trend component, take the
following steps:
1. From the Data menu select the data analysis option and then regression.
2. The Input Y Range should contain D1 to D201. The Input X Range should contain A1 to
A201. Be sure that you have checked the labels box.
3. Click OK
4. Record on a paper your estimates of the intercept and slope coefficients.
5. Now click on the sheet 1 tab at the bottom of the spreadsheet.
A centered 12-month moving average of FMS should be free of seasonality since it contains one
observation from each month of the year. We can produce a seasonal index (SI) for the FMS
series by dividing the original series through by the centered moving average of FMS (or
CMAFMS). That is:
SI 
FMSt
CMAFMSt
3
Take the following steps to compute CMAFMS:
1. Activate cell I7 and type the following in the formula bar:
= (d2+d3+d4+d5+d6+d7+d8+d9+d10+d11+d12+d13)/12 and click on the green check
mark.
2. Move your cursor to the southeast corner of I7 until you see the little + and then hold
down right on your mouse and scroll down column j to the last value, which should
appear in I195.
The moving average you have arrayed in column I is not centered. Take the following steps to
compute CMAFMS:
1. Activate cell J8. In the formula bar type: = (i7+i8)/2 and hit enter (or click on the green
checkmark).
2. Move your cursor to the southeast corner of J8 until you see the little + and then hold
down right on your mouse and scroll down column j to the last value, which should
appear in J195.
Take the following steps to calculate SI.
1. Activate K8. In the formula bar type: = d8/j8 and hit enter (or click on the green
checkmark).
2. Move your cursor to the southeast corner of K8 until you see the little + and then hold
down right on your mouse and scroll down column K to the last value, which should
appear in K195.
In-Sample Forecasting: We will perform in-sample forecasts using models 2 and 3. Take the
following steps:
1. Activate cell L2 and in the formula bar type:





  0  1* e2   2 * f2   3 * g2   4 * h2 and hit enter (or click on the green
2.
3.
4.
5.
6.
checkmark).
Move your cursor to the southeast corner of L2 until you see the little + and then hold
down right on your mouse and scroll down column L to the last value, which should
appear in L201.
Activate cell M2 and in the formula bar type: =(d2-L2)^2 and click on the green check
mark (or hit enter).
Move your cursor to the southeast corner of M2 until you see the little + and then hold
down right on your mouse and scroll down column M to the last value, which should
appear in M201.
Activate cell N8 and in the formula bar type:
=(intercept + slope *a8)*k8 *1 and hit enter (or click on the green checkmark).
Move your cursor to the southeast corner of N8 until you see the little + and then hold
down right on your mouse and scroll down column N to the last value, which should
appear in N195.
4
7. Activate cell O8 and in the formula bar type: =(d8-n8)^2 and click on the green check
mark (or hit enter).
8. Move your cursor to the southeast corner of O8 until you see the little + and then hold
down right on your mouse and scroll down column o to the last value, which should
appear in O195.
Question: You have what is needed to compute MSE for models 2 and 3 in columns M
and O. Which model performs better for the in-sample forecast based on this statistic? To
compute
MSE take the following steps:
1. Sum the figures in columns M and O respectively.
2. To obtain MSE, divide your column M total by n = 200. Divide your column O total by
n = 188.
Now find the square roots.
3.
Preparing a Forecast for January–June 2013: We will use the equation obtained from the
model 2 regression as well as the multiplicative time series model to forecast farm machinery
sales for the first 6 months of 2013. Take the following steps:
1. You should use the equation you obtained for the model 2 regression written on a piece
of paper.
2. Click on “sheet 2” at the bottom of your Excel window. Here you will find predicted
values for the independent variables (FPI, FCPI, SI, and PR) as well as SDU and t. Notice
also that you have predicted values for the cyclical index in column H2
3. Activate cell J2. In the formula bar type:





  0  1* d 2   2 * e2   3 * f2   4 * g2 and hit enter (or click on the green
checkmark).
4. Move your cursor to the southeast corner of J2 until you see the little + and then hold
down right on your mouse and scroll down column J to the last value, which should
appear in J7.There is your forecast using model 2.
5. Activate cell K2. in the formula bar type:
=(intercept + slope *a2)*h2 *i2 and hit enter (or click on the green checkmark).
6. Move your cursor to the southeast corner of K2 until you see the little + and then hold
down right on your mouse and scroll down column K to the last value, which should
appear in K7.There is your forecast using model 3.