chapter 13 forecasting
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Chapter 13Forecasting
MGS3100Julie Liggett De Jong
It is difficult toforecast,especially in
regards to thefuture.
It isn’t difficultto forecast,just to forecastcorrectly.
Numbers, iftorturedenough, willconfess tojust aboutanything.
Economic Forecasts Influence:
Government policies & businessdecisions
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Insurance companies’ investmentdecisions in mortgages and bonds
Service industries’ forecasts ofdemand as input for revenuemanagement
FEATURES
• Regression
• Solver
• Sorting
FUNCTIONS
• SUMPRODUCT( )
• SUMXMY2( )
• YEAR( )
• MONTH( )• RIGHT( )
Excel Features & Functions
Quantitative vs Qualitative
Forecasting Models
Quantitative Forecasting Models Expressed in mathematical notation
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Based on an amazing quantity of data
1. Causal (Curve Fitting)a. Linear
b. Quadratic
2. Moving Averages (Naive)a. Simple n-Period Moving Averageb. Weighted n-Period Moving Average
3. Exponential Smoothinga. Basic modelb. Holt’s Model (exponential smoothing with trend)
4. Seasonality
Quantitative Forecasting Models
Important Variables
Average value of dependent variable (Y bar)Y
Predicted or forecasted dependent variable(Y hat)Y
True value of dependent variableY
Independent variable(s)X
Causal vs Time Series Models
Causal Forecasting Models Requirements
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Independent and dependentvariables must share a relationship
We must know the values of theindependent variables when wemake the forecast
Curve FittingSelf Service Gas Stations
Oil company wants to expand itsnetwork of self-service gas stations
We’ll use historical data for fivestations to calculate average trafficflow and sales
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Traffic flow: average # of cars / hour
Sales: average dollar sales / hour
Plot the averages in a scatterplot.
Figure 1, p274
Sales & Traffic Data
-
50
100
150
200
250
300
0 50 100 150 200 250
Cars/hour
S
a l e s / h o u r ( $ )
Figure 2, p274
Scatter Plot of Sales & Traffic Data
-
50
100
150
200
250
300
0 50 100 150 200 250
Cars/hour
S
a l e s / h o u r ( $ ) y = a + bx
Method of Least Squares
Figure 3, p275
Use Regression to fit a Linear Function
Figure 5, p277
TSS = ESS + RSS
TSS = Σi=1
n
(Y i – Y )2 –
ESS = Σi=1
n
(Y i – Y i )2^
Σi=1
n
(Y i – Y )2^ –RSS =
R2 =RSSTSS
Regression computes three types of errors
Total
Residual
Regression
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Should we build a gas station atBuffalo Grove where traffic is 183cars/hour?
y = a + b * x ^
Sales/hour = 57.104 + 0.92997 * 183 cars/hr
= $227.29
How confident are we in thisforecast?
Confidence intervals use the following statistics:
1.00 =68% 1.96 = 95.0% 3.00 = 99.7%
+- 2 * Standard Error (Se)Y Se =
Σi=1
n
(Y i – Y i )2^
n – k -1=
n – k -1
ESS
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Excel calculates the Standard Errorfor us. [227.29 – 2(44.18); 227.29 + 2(44.18)]
[$138.93; $315.65]
The 95% confidence interval is:
Other important information:
T-statistic and its p-valueUpper & Lower 95%F significanceR2 and Adjusted R2
Figure 5, p277
Fitting a QuadraticFunction
-
50
100
150
200
250
300
0 50 100 150 200 250
Cars/hour
S a l e s / h o u r ( $ )
Fitting a Quadratic Function
Figure 10, p283
y = a0 + a1x + a2x 2
y = a0 + a1x + a2x 2 Figure 7, p281
Use Solver to fit a Quadratic Function
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We could create a formula that exactlypasses through every data point…..
But, why wouldn’t we want to do that?
Which curve to fit?Goodness of fit statistics:Sum of Squared Errors (SSE)
n
SSE = Σi=1
(Y i – Y i )2
^ Goodness of fit statistics:Mean Squared Error (MSE)
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MSE =Sum of Squared Errors
(# of points – # of parameters)
Regression: SSE = 5854Quadratic: SSE = 4954
Regression: MSE = 5854 / (5 - 2) = 1951.3Quadratic: MSE = 4954 / (5 - 3) = 2477.0
y = 5x + 5
0
20
40
60
80
100
120
140
1 3 5 7 9 1 1 1 3 1 5 1 7 1 9 2 1 2 3 2 5
Time
P r o f i t
y = -5x + 135
0
20
40
60
80
100
120
140
1 3 5 7 9 1 1 1 3 1 5 1 7 1 9 2 1 2 3 2 5
Time
C u s t o m e r s
Causal Forecasting Models
Positive Slopeindicates upwardtrend
Negative Slopeindicatesdownward trend
Time-Series Forecasting Models
Time is the independent variable
1. Curve Fitting:a) Linearb) Quadratic
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2. Moving Averages (Naive)a) Simple n-Period Moving Avgb) Weighted n-Period Moving Avg
3. Exponential Smoothinga) Basic modelb) Holt’s Model (trend)
Seasonality
Curve Fitting
Plot historical values as function oftime and draw a linear “trend line”.
Use trend line to predict futurevalue.
The Bank of Laramie
Moving Averages (Naïve):
Use previous period’s actual valueto forecast the current period (i.e.,use 12th value to predict 13th value).
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Moving Averages:
Use average of past 12 values asbest forecast for 13th value.
Simple n-Period Moving Averages:
Use average of the most recent 6values to predict 13th value.
Steco: asimple n-periodmovingaveragesforecastingmodel
MONTH
ACTUAL
SALES
($000s)
THREE-MONTH
SIMPLE MOVING
AVERAGE FORECAST
FOUR-MONTH SIMPLE
MOVING AVERAGE
FORECAST
Jan. 20
Feb. 24
Mar. 27
Apr. 31 (20 + 24 + 27)/3 = 23.67
May 37 (24 + 27 + 31)/ 3 = 27. 33 (20 + 24 + 27 + 31)/ 4 = 25. 50
June 47 (27 + 31 + 37)/ 3 = 31. 67 (24 + 27 + 31 + 37)/ 4 = 29. 75
July 53 (31 + 37 + 47)/ 3 = 38. 33 (27 + 31 + 37 + 47)/ 4 = 35. 50
A ug. 62 (37 + 47 + 53)/ 3 = 45. 67 (31 + 37 + 47 + 53)/ 4 = 42. 00
S ep. 54 (47 + 53 + 62)/ 3 = 54. 00 (37 + 47 + 53 + 62)/ 4 = 49. 75
Oc t. 36 (53 + 62 + 54)/ 3 = 56. 33 (47 + 53 + 62 + 54)/ 4 = 54. 00
Nov. 32 (62 + 54 + 36)/ 3 = 50. 67 (53 + 62 + 54 + 36)/ 4 = 51. 25
Dec . 29 (54 + 36 + 32)/ 3 = 40. 67 (62 + 54 + 36 + 32)/ 4 = 46. 00
Three- and Four- Month Simple Moving Averages
Table 1, p2904
12131415
16ˆ
y y y y y
+++=
Goodness of fit statistics
forecastsofnumber
salesforecastsalesactual
MADforecastsall
−
=
∑
forecastsofnumber
%100salesactual
salesforecastsalesactual
MAPEforecastsall
∑ ∗−
=
STECO: Simple n-Period Moving Average
MONTH
ACTUAL
SALES
($000s)
THREE-MONTH
SIMPLE MOVING
AVERAGE
FORECAST
ABSOLUTE
ERROR
FOUR-MONTH
SIMPLE MOVING
AVERAGE
FORECAST
ABSOLUTE
ERROR
Jan. 20
Feb. 24
Mar. 27Apr. 31 23.67$ 7.33
May 37 27.33$ 9.67 25.50$ 11.50
June 47 31.67$ 15.33 29.75$ 17.25
July 53 38.33$ 14.67 35.50$ 17.50
Aug. 62 45.67$ 16.33 42.00$ 20.00
Sep. 54 54.00$ 0.00 49.75$ 4.25
Oct. 36 56.33$ 20.33 54.00$ 18.00
Nov. 32 50.67$ 18.67 51.25$ 19.25
Dec. 29 40.67$ 11.67 46.00$ 17.00
SUM = 114.00 SUM = 124.75
MAD = 12.67 MAD = 15.59
Figure 14, p291
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Simple n-Period Moving Averageforecasting models have twoshortcomings
Philosophical ShortcomingMost recent observations receive nomore weight or importance thanolder observations.
Operational ShortcomingAll historical data used to makeforecast must be stored in someway to calculate the forecast.
Weighted n-Period MovingAverages:
Resolves philosophical
shortcoming of simple periodmoving average forecasting
Weighted n-Period MovingAverages:
Use weighted average of previousvalues & assign higher weights tomore recent observations
Recent data is more importantthan old data
425160ˆ y y y y α α α ++=
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Constraints:
The (weights) are positivenumbers
s'α
Constraints:
Smaller weights are assigned toolder data
Constraints:
All the weights sum to 1
alpha2 = 0.167 Month Actual Sales (000)3month WMA Fcst Absolute Error
alpha1 = 0.333 January 20
alpha0 = 0.500 February 24
SUM OF WTS= 1.00 March 27
April 31 24.83 6.17
May 37 28.50 8.50
June 47 33.33 13.67
July 53 41.00 12.00
August 62 48.33 13.67
September 54 56.50 2.50
October 36 56.50 20.50
November 32 46.34 14.34
December 29 37.01 8.01
Sum = 99.35
MAD = 11.04
Use Solver to find the optimal
weightsFigure 16, p293
Weighted n-Period MovingAverages resolves philosophicalshortcoming of simple periodmoving average forecasting
Exponential Smoothing resolvesoperational shortcoming ofsimple period moving averageforecasting
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Exponential Smoothing Exponential Smoothing
tt1t y)1(yy α−+α=+
Forecast for t + 1 Observed in t Forecast for t
Where is a user-specified constantα
Resolves operational shortcoming of theMoving Averages Model:
10,001:40,000:
5,000 * 8
5,000
ExponentialSmoothing
Model
8-period MovingAverage Model
Number ofInventory Items
to Forecast
ty000,5
ty000,5
α1
Saving alpha and the last forecasts stores all the previous forecasts.
When t = 1, the expression becomes:
tt2 y)1(yy α−+α=tt1t y)1(yy α−+α=+
alpha = 0.500 Month Actual Sales (000)Fcst Sales Absolute Error
January 20 20.00
February 24 20.00 4.00
March 27 22.00 5.00
April 31 24.50 6.50
May 37 27.75 9.25
June 47 32.38 14.63
July 53 39.69 13.31
August 62 46.34 15.66
September 54 54.17 0.17
October 36 54.09 18.09
November 32 45.04 13.04
December 29 38.52 9.52
Sum = 109.17
MAD = 9.92
Does exponential smoothing
produce a better forecast?
The value of alpha affects theperformance of the model
VARIABLE COEFFICIENT α = 0.1 α = 0.3 α = 0.5
y t α 0.1 0.3 0.5
y t-1 α(1-α) 0.09 0.21 0.25
y t-2 α(1-α)20.081 0.147 0.125
y t-3 α(1-α)30.07290 0.10290 0.06250
y t-4 α(1-α)40.06561 0.07203 0.03125
y t-5 α(1-α)50.05905 0.05042 0.01563
y t-6 α(1-α)6
0.05314 0.03529 0.00781y t-7 α(1-α)7
0.04783 0.02471 0.00391
y t-8 α(1-α)80.04305 0.01729 0.00195
y t-9 α(1-α)90.03874 0.01211 0.00098
y t-10 α(1-α)100.03487 0.00847 0.00049
Sum of the Weights 0.68619 0.98023 0.99951
Case 1: Response to Sudden Change
System Change when t = 100
-1
0
1
1
2
94 95 96 97 98 99 100 101 102 103
t
yt
A forecasting system with alpha = 0.5responds quickly to changes in the data.
Response to a Unit Change in yt
00.10.20.30.40.5
0.6
0.70.80.9
11.11.2
100 105 110 115 120 125
t
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Exponential smoothing is not a goodforecasting tool in a rapidly growing or adeclining market.
Steadily Increasing Values of yt
(Linear Ramp)
0
1
2
3
4
5
6
0 2 4 6 8 10
t
yt
Case 2: Response to Steady Change
Steadily Increasing Values of yt
(Linear Ramp)
0
1
2
3
4
5
6
0 2 4 6 8 10
t
yt
Case 2: Response to Steady Change
But the model can be adjusted (Holt’smodel / exponential smoothing w/trend)
Exponential smoothing is not a good
model to use here because it ignores theseasonal pattern.
Seasonal Pattern in y t
-0.1
0.1
0.3
0.5
0.7
0.9
1.1
1.3
1.5
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
t
y t
Case 3: Response to Seasonal Change
Seasonality
Takes into consideration and adjustsfor the seasonal patterns in data
1. Look at original data to see seasonalpattern. Examine the data &hypothesize an m-period seasonalpattern.
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2. Deseasonalize the Data 3. Forecast using deseasonalized data
4. Seasonalize the forecast to accountfor the seasonal pattern
Gillett Coal Mine
Coal Receipts Over a Nine-Year Period
0
500
1,000
1,500
2,000
2,500
3,000
1 - 1
1 - 3
2 - 1
2 - 3
3 - 1
3 - 3
4 - 1
4 - 3
5 - 1
5 - 3
6 - 1
6 - 3
7 - 1
7 - 3
8 - 1
8 - 3
9 - 1
9 - 3
Time (Year and Quarter)
C o a l ( 0 0 0 T o n s )
1. Look at original data to see seasonalpattern. Examine the data &hypothesize an m-period seasonalpattern. Figure 27, p303
Deseasonalized Data
-
500.0
1,000.0
1,500.0
2,000.0
2,500.0
3,000.0
1-
1
1-
2
1-
3
1-
4
2-
1
2-
2
2-
3
2-
4
3-
1
3-
2
3-
3
3-
4
4-
1
4-
2
4-
3
4-
4
5-
1
5-
2
5-
3
5-
4
6-
1
6-
2
6-
3
6-
4
7-
1
7-
2
7-
3
7-
4
8-
1
8-
2
8-
3
8-
4
9-
1
9-
2
9-
3
9-
4
Time (Year & Qtr)
C o a l ( 0 0 0 T o n s )
2. Deseasonalize the Data
Figure 32, p306
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2.Deseasonalize the Data
a) Calculate a series of m -period movingaverages, where m is the length of the
seasonal pattern.b) Center the moving average in the middle of
the data from which it was calculated.c) Divide the actual data at a given point in the
series by the centered moving averagecorresponding to the same point.
d) Develop seasonal index
e) Divide actual data by the seasonal index
a)Calculate a series of m -period movingaverages, where m is the length of theseasonal pattern.
Time Coal 4 Period
Year-Qtr Receipts Moving Average
1-1 2,159 -----
1-2 1,203 -----
1-3 1,094 1,613
1-4 1,996 1,594
2-1 2,081 1,626
2-2 1,332 1,721
2-3 1,476 1,856
2-4 2,533 1,898
3-1 2,249 1,948
3-2 1,533 2,063
3-3 1,935 2,060
3-4 2,523 2,050
4-1 2,208 2,066
(2,159+1,203+1,094+1,996)/4 = 1,613
Figure 28, p304
Time Coal 4 Period Centered
Year-Qtr Receipts Moving Average Moving Average
1-1 2,159
1-2 1,203
1-3 1,094 1,613 1,603
1-4 1,996 1,594 1,610
2-1 2,081 1,626 1,674
2-2 1,332 1,721 1,788
2-3 1,476 1,856 1,877
2-4 2,533 1,898 1,923
3-1 2,249 1,948 2,005
3-2 1,533 2,063 2,061
3-3 1,935 2,060 2,055
3-4 2,523 2,050 2,058
4-1 2,208 2,066 2,064
4-2 1,597 2,061 2,087
4-3 1,917 2,112 2,163
4-4 2,726 2,213 2,255
(1613 + 1594)/2 =1603
b)Center the moving average in themiddle of the data from which it was
calculated.Figure 28, p304
Data & Centered Moving Average
0
500
1,000
1,500
2,000
2,500
3,000
1-
1
1-
2
1-
3
1-
4
2-
1
2-
2
2-
3
2-
4
3-
1
3-
2
3-
3
3-
4
4-
1
4-
2
4-
3
4-
4
5-
1
5-
2
5-
3
5-
4
6-
1
6-
2
6-
3
6-
4
7-
1
7-
2
7-
3
7-
4
8-
1
8-
2
8-
3
8-
4
9-
1
9-
2
9-
3
9-
4
Time (Year & Qtr)
C o a l ( 0 0 0 T o n s )
Receipts
Centered
Moving
Average
b)Center the moving average in themiddle of the data from which it was
calculated.Figure 29, p305
c) Divide the actual data at a given pointin the series by the centered movingaverage corresponding to the samepoint.
Time Coal 4 Period Centered Ratio of Coal Receipts to
Year-Qtr Receipts Moving Average Moving Average Centered Moving Average
1-1 2,159
1-2 1,203
1-3 1,094 1,613 1,603 0.682
1-4 1,996 1,594 1,610 1.240
2-1 2,081 1,626 1,674 1.244
2-2 1,332 1,721 1,788 0.745
2-3 1,476 1,856 1,877 0.787
2-4 2,533 1,898 1,923 1.317
3-1 2,249 1,948 2,005 1.122
3-2 1,533 2,063 2,061 0.744
3-3 1,935 2,060 2,055 0.942
3-4 2,523 2,050 2,058 1.226
1,094 / 1,603 = 0.682
Figure 28, p304
d)Develop seasonal index for eachquarter• Group ratios by quarter• Average all of the ratios to moving
averages quarter by quarter• Add Seasonal Indices data to table• Normalize the seasonal index
T im e C oa l 4 P er io d C en te re d R at io o f C oa l R ec ei pt s t o S ea so na l
Year-Qtr Receipts Moving Average Moving Average Centered Moving Average Indices
1-1 2,159 1.112
1-2 1,203 0.786
1-3 1,094 1,613 1,603 0.682 0.863
1-4 1,996 1,594 1,610 1.240 1.238
2-1 2,081 1,626 1,674 1.244 1.112
2-2 1,332 1,721 1,788 0.745 0.786
2-3 1,476 1,856 1,877 0.787 0.863
2-4 2,533 1,898 1,923 1.317 1.238
3-1 2,249 1,948 2,005 1.122 1.112
3-2 1,533 2,063 2,061 0.744 0.786
3-3 1,935 2,060 2,055 0.942 0.863
3-4 2,523 2,050 2,058 1.226 1.238
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e)Divide actual data by the seasonalindex
T im e C o al 4 P er io d C en te r ed R at i o o f C o al R e ce ip t s t o S e as on a l D es ea s on a li ze d
Y e ar -Q t r R e ce i pt s M o vi ng A v er ag e M o vi ng A v er ag e C en t er ed M o vi n g Av e ra ge I n di ce s D at a
1-1 2,159 1.112 1,941.0
1-2 1,203 0.786 1,529.8
1-3 1,094 1,613 1,603 0.682 0.863 1,267.7
1-4 1,996 1,594 1,610 1.240 1.238 1,611.9
2-1 2,081 1,626 1,674 1.244 1.112 1,870.9
2-2 1,332 1,721 1,788 0.745 0.786 1,693.8
2-3 1,476 1,856 1,877 0.787 0.863 1,710.3
2-4 2,533 1,898 1,923 1.317 1.238 2,045.6
3-1 2,249 1,948 2,005 1.122 1.112 2,021.9
3-2 1,533 2,063 2,061 0.744 0.786 1,949.4
3-3 1,935 2,060 2,055 0.942 0.863 2,242.2
3-4 2,523 2,050 2,058 1.226 1.238 2,037.5
Figure 31, p306
Deseasonalized Data
-
500.0
1,000.0
1,500.0
2,000.0
2,500.0
3,000.0
1 - 1
1 - 3
2 - 1
2 - 3
3 - 1
3 - 3
4 - 1
4 - 3
5 - 1
5 - 3
6 - 1
6 - 3
7 - 1
7 - 3
8 - 1
8 - 3
9 - 1
9 - 3
Time (Year & Qtr)
C o a
l ( 0 0 0 T o n s )
DeseasonalizedData
e)Divide actual data by the seasonalindex
Figure 32, p306
3. Forecast method in deseasonalizedterms• Review the graphed deseasonalized data to
reveal pattern• Use forecasting method that accounts for
the pattern in the deseasonalized data• Use Excel’s Solver to minimize the error
Time Coal 4 Period Centered Ratio of Coal Receipts to Seasonal Deseasonalized
Y ea r- Qt r R ec ei pt s M ov in g A ve ra ge M ov in g A ve ra ge C en te re d M ov in g A ve ra ge I nd ic es D at a F or ec as t
1-1 2,159 1.108 1,948.1 1,948.1
1-2 1,203 0.784 1,535.4 1,948.1
1-3 1,094 1,613 1,603 0.682 0.860 1,272.3 1,678.5
1-4 1,996 1,594 1,610 1.240 1.234 1,617.8 1,413.1
2-1 2,081 1,626 1,674 1.244 1.108 1,877.8 1,546.8
2-2 1,332 1,721 1,788 0.745 0.784 1,700.0 1,763.0
2-3 1,476 1,856 1,877 0.787 0.860 1,716.6 1,721.9
2-4 2,533 1,898 1,923 1.317 1.234 2,053.1 1,718.4
3-1 2,249 1,948 2,005 1.122 1.108 2,029.3 1,937.1
3-2 1,533 2,063 2,061 0.744 0.784 1,956.5 1,997.4
3-3 1,935 2,060 2,055 0.942 0.860 2,250.4 1,970.7
3-4 2,523 2,050 2,058 1.226 1.234 2,045.0 2,153.4
Figure 33, p307
4. Reseasonalize the forecast to account forthe seasonal pattern• Multiply the deseasonalized forecast by the
seasonal index for the appropriate period.• Graph the actual Coal Receipts and
Seasonalized Forecast
T im e C oa l 4 P er io d C en te re d R at io o f C oa l R ec ei pt s t o S ea so na l D es ea so na li ze d S ea so na li ze
Y ea r- Qt r R ec ei pt s M ov in g A ve ra ge M ov in g A ve ra ge C en te re d M ov in g A ve ra ge I nd ic es D at a F or ec as t F or ec as t
1-1 2,159 ----- ----- ----- 1.108 1,948.1 1,948.1 2,159.000
1-2 1,203 ----- ----- ----- 0.784 1,535.4 1,948.1 1,526.409
1-3 1,094 1,613 1,603 0.682 0.860 1,272.3 1,678.5 1,443.212
1-4 1,996 1,594 1,610 1.240 1.234 1,617.8 1,413.1 1,743.439
2-1 2,081 1,626 1,674 1.244 1.108 1,877.8 1,546.8 1,714.276
2-2 1,332 1,721 1,788 0.745 0.784 1,700.0 1,763.0 1,381.390
2-3 1,476 1,856 1,877 0.787 0.860 1,716.6 1,721.9 1,480.540
2-4 2,533 1,898 1,923 1.317 1.234 2,053.1 1,718.4 2,120.128
3-1 2,249 1,948 2,005 1.122 1.108 2,029.3 1,937.1 2,146.723
3-2 1,533 2,063 2,061 0.744 0.784 1,956.5 1,997.4 1,564.974
3-3 1,935 2,060 2,055 0.942 0.860 2,250.4 1,970.7 1,694.495
3-4 2,523 2,050 2,058 1.226 1.234 2,045.0 2,153.4 2,656.854
Actual & Forecast
0
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Year-Quarter
C o a l ( 0 0 0 T o n s )
Coal Receipts
Seasonalized Forecast
4. Reseasonalize the forecast to account forthe seasonal pattern
1. Look at original data to see seasonal pattern. Examine thedata & hypothesize an m-period seasonal pattern.
2. Deseasonalize the data.
a) Calculate a series of m -period moving averages, where m
is the length of the seasonal pattern.b) Center the moving average in the middle of the data from
which it was calculated.
c) Divide the actual data at a given point in the series by thecentered moving average corresponding to the same point.
d) Develop seasonal indexe) Divide actual data by the seasonal index
3. Forecast method in deseasonalized terms.
4. Reseasonalize the forecast to account for the seasonalpattern.
8/14/2019 Chapter 13 Forecasting
http://slidepdf.com/reader/full/chapter-13-forecasting 19/21
Returns the sum of squares of differences ofcorresponding values in two arrays.
Syntax: SUMXMY2(array_x,array_y), whereArray_x is the first array or range of values.Array_y is the second array or range of values.
The equation for the sum of squared differences is:
( )∑ −=2
yx2SUMXMY
SUMXMY2( ) Measures of Comparison
forecastsof number
sales forecast salesactual
MADforecastsall
−
=
∑
forecastsof number
salesactual
sales forecast salesactual
MAPE forecastsall
∑ ∗−
=
%100
forecastsof number
sales forecast salesactual
MSE
n
t
∑=
−
= 1
2)(
Model Validation Create experience by simulating thepast.
Create the model with a portion of thehistorical data.
Use remaining data to see how wellthe model would have performed.
8/14/2019 Chapter 13 Forecasting
http://slidepdf.com/reader/full/chapter-13-forecasting 20/21
QualitativeForecasting
Models
ExpertJudgment
ConsensusPanel
DelphiMethod
Coordinator requests forecasts
Coordinator receivesIndividual forecasts
Coordinator determines(a) Median response(b) Range of middle
50% of answers
Coordinator requestsexplanations from any
expert whose estimateis not in the middle
50%
Coordinator sends to all experts(a) Median response
(b) Range of middle 50%(c) Explanations
Delphi
Method
Grassroots Forecasting
8/14/2019 Chapter 13 Forecasting
http://slidepdf.com/reader/full/chapter-13-forecasting 21/21
Market Research