forecastingtechniques 2.pdf

Dr. C. Lightner Fayetteville State University
1
FORECASTING TECHNIQUES
Chapter 16
Qualitative Approaches to Forecasting
Quantitative Approaches to Forecasting
The Components of a Time Series
Using Smoothing Methods in Forecasting
Measures of Forecast Accuracy
Using Trend Projection in Forecasting
Using Regression Analysis in Forecasting

2
Forecasting Introduction
An essential aspect of managing any organization is
planning for the future.
Organizations employ forecasting techniques to
determine future inventory, costs, capacities, and
interest rate changes.
There are two basic approaches to forecasting:
-Qualitative
-Quantitative

3
Qualitative Approaches to Forecasting
Delphi Approach
– A panel of experts, each of whom is physically separated from
the others and is anonymous, is asked to respond to a
sequential series of questionnaires.
– After each questionnaire, the responses are tabulated and the
information and opinions of the entire group are made known to
each of the other panel members so that they may revise their
previous forecast response.
– The process continues until some degree of consensus is
achieved.

4
Qualitative Approaches (continued)
Scenario Writing
– Scenario writing consists of developing a conceptual scenario
of the future based on a well defined set of assumptions.
– After several different scenarios have been developed, the
decision maker determines which is most likely to occur in the
future and makes decisions accordingly.

5
Qualitative Approaches (continued)
Subjective or Interactive Approaches
– These techniques are often used by committees or panels
seeking to develop new ideas or solve complex problems.
– They often involve "brainstorming sessions".
– It is important in such sessions that any ideas or opinions be
permitted to be presented without regard to its relevancy and
without fear of criticism.

6
Quantitative Approaches to Forecasting
Quantitative methods are based on an analysis of historical data
concerning one or more time series.
A time series is a set of observations measured at successive
points in time or over successive periods of time.
If the historical data used are restricted to past values of the series
that we are trying to forecast, the procedure is called a time series
method.
If the historical data used involve other time series that are believed
to be related to the time series that we are trying to forecast, the
procedure is called a causal method.
Quantitative approaches are generally preferred. In this chapter we
will focus on quantitative approaches to forecasting.

7
Time Series Data
Time Series Data is usually plotted on a graph to
determine the various characteristics or components of
the time series data.
There are 4 Major Components: Trend, Cyclical,
Seasonal, and Irregular Components.

8
Components of a Time Series
The trend component accounts for the gradual shifting
of the time series over a long period of time.
Any regular pattern of sequences of values above and
below the trend line is attributable to the cyclical
component of the series.
The seasonal component of the series accounts for
regular patterns of variability within certain time periods,
such as over a year.
The irregular component of the series is caused by
short-term, unanticipated and non-recurring factors that
affect the values of the time series. One cannot attempt
to predict its impact on the time series in advance.

9
Time Series Data
We will learn the following Forecasting Approaches:
Smoothing
Trend Projections

10
Excel Instructions for Drawing a Scatter Plot
1. Enter data in the Excel spreadsheet.
2. Click on Insert on the toolbar and then click on the Chart tab. The
Chart Wizard will appear. In step 1 on select the XY (scatter) chart
type and then click next.
3. In step 2 specify the cells where your data is located in the data
range box.
4. In step 3 you can give your chart a title and label your axes. In
step 4 specify where you want the chart to be placed.

11
During the past ten weeks, sales of cases of Comfort brand
headache medicine at Robert's Drugs have been as follows:
Week Sales Week Sales
1 110 6 120
2 115 7 130
3 125 8 115
4 120 9 110
5 125 10 130
Plot this data.
Example: Robert’s Drugs

12
Plot Robert’s Drugs Example
Excel Spreadsheet Showing Input Data. Specify cells A4:B13 as the Data
Range. A B
1 Robert's Drugs
2
3 Week (t ) Salest
4 1 110
5 2 115
6 3 125
7 4 120
8 5 125
9 6 120
10 7 130
11 8 115
12 9 110
13 10 130
14 11

13
Plot Robert’s Drugs Example
Robert's Drug Example
105
110
115
120
125
130
135
0 5 10 15
Week, t
Sales
I labeled
Robert’s Drug
Example as
The Chart title
I labeled
Week, t as
My Value (x)
axis
I labeled
Sales as
My Value (y)
axis

14
Smoothing Methods
In cases in which the time series is fairly stable and
has no significant trend, seasonal, or cyclical effects,
one can use smoothing methods to average out the
irregular components of the time series.
Three common smoothing methods are:
– Moving average
– Weighted moving average
– Exponential smoothing

15
Smoothing Methods: Moving Average
Moving Average Method
The moving average method consists of computing
an average of the most recent n data values for the
series and using this average for forecasting the value
of the time series for the next period.

16
Robert Drug’s Example: Moving Average
Our scatter plot for Robert’s Drug Sales has no
significant trend, seasonal, or cyclical effects. Thus we
should employ a smoothing technique for forecasting
sales.
Forecast the sales for period 11 using a three period
moving average (MA3).

17
Example: Robert’s Drugs: Moving Average
Steps to Moving Average Using Excel
Step 1: Select the Tools pull-down menu.
Step 2: Select the Data Analysis option.
Step 3: When the Data Analysis Tools dialog
appears, choose Moving Average.
Step 4: When the Moving Average dialog box
appears:
Enter B4:B13 in the Input Range box.
Enter 3 in the Interval box.
Enter C5 in the Output Range box.
Select OK.
This specifies
the value of n
This is the column
following our data,
and one row below where
our data begins.

18
Robert’s Drugs: Moving Average
MA3 (Three period Moving average) for Robert’s Drug Example
Ft is the forecast for week t.
F4 (forecast for week 4)=116.7
F11 (forecast for week 11)=118.3
Thus we would forecast the sales
for Week 11 to be 118.3
Robert's Drug
n=3
Week (t ) Yt Ft
1 110
2 115 #N/A
3 125 #N/A
4 120 116.6667
5 125 120
6 120 123.3333
7 130 121.6667
8 115 125
9 110 121.6667
10 130 118.3333
11 118.3333

19
Smoothing Methods: Weighted Moving Average
Weighted Moving Average Method
The weighted moving average method consists of computing a
weighted average of the most recent n data values for the series
and using this weighted average for forecasting the value of the
time series for the next period. The more recent observations are
typically given more weight than older observations. For
convenience, the weights usually sum to 1.
The regular moving average gives equal weight to past data values
when computing a forecast for the next period. The weighted
moving average allows different weights to be allocated to past
data values.
There is no Excel command for computing this so you must do this
manually. You can either manually enter the formulas into excel
and apply to all periods or compute value by hand.

20
Smoothing Methods: Weighted Moving Average
Use a 3 period weighted moving average to forecast the sales for
week 11 giving a weight of 0.6 to the most recent period, 0.3 to the
second most recent period, and 0.1 to the third most recent period.
F11 = (0.6)*130 + (0.3)*110 + (0.1)* 115= 122.5
Thus we would forecast the sales for week 11 to be 122.5.
Sales for the
most recent
period
Sales for 2nd
most recent
period
Sales for 3rd
most recent
period

21
Smoothing Methods: Exponential Smoothing
Exponential Smoothing
– Using exponential smoothing, the forecast for the next
period is equal to the forecast for the current period plus a
proportion (α) of the forecast error in the current period.
– Using exponential smoothing, the forecast is calculated by:
Ft+1=α Yt + (1- α)Ft
where:
α is the smoothing constant (a number between 0 and 1)
Ft is the forecast for period t
Ft+1 is the forecast for period t+1
Yt is the actual data value for period t
This is the same as
Ft+1 = Ft + α (Yt – Ft)

22
Robert’s Drugs: Exponential Smoothing
Forecast the sales for period 11 using Exponential
Smoothing α= 0.1.

23
Steps to Exponential Smoothing Using Excel
Step 1: Select the Tools pull-down menu.
Step 2: Select the Data Analysis option.
Step 3: When the Data Analysis Tools dialog
appears, choose Exponential Smoothing.
Step 4: When the Exponential Smoothing dialog box
appears:
Enter B4:B13 in the Input Range box.
Enter 0.9 (for α = 0.1) in Damping Factor box.
Enter C4 in the Output Range box.
Select OK.
Damping factor
is always 1-α

24
F11 = 0.1 * Y10 + .9 F10
= .1 *130 + .9 * 115.4099
= 116.87
Robert's Drugs
α=0.1
Week (t) Salest
Ft
1 110 #N/A
2 115 110
3 125 110.5
4 120 111.95
5 125 112.755
6 120 113.9795
7 130 114.5816
8 115 116.1234
9 110 116.0111
10 130 115.4099
11
Thus we would
forecast sales for
week 11 to be 116.87

25
Questions That You Should Be Asking
For the Moving Average technique, how do I determine the best
value of n to use for forecasting?
For Exponential Smoothing, how do I determine the best value of α
to use?
If I realize that a smoothing technique should be employed, how do
you know which smoothing technique is best?
In order to answer the above questions, we need criteria for
judging the accuracy of a forecasting technique. Once we select a
criterion, the method (or parameter) which provides the best value
for our criterion is the best method (or parameter) to use for
forecasting our scenario.

26
Measures of Forecast Accuracy
Mean Squared Error (MSE)
The average of the squared forecast errors for the historical
data is calculated. The forecasting method or parameter(s) which
minimize this mean squared error is then selected.
Mean Absolute Deviation (MAD)
The mean of the absolute values of all forecast errors is
calculated, and the forecasting method or parameter(s) which
minimize this measure is selected. The mean absolute deviation
measure is less sensitive to individual large forecast errors than
the mean squared error measure.
You may choose either of the above criteria for evaluating the
accuracy of a method (or parameter).

27
Selecting the best Smoothing Technique for Robert’s Drugs
Determine the smoothing technique that is best for forecasting
Robert’s Drug sales: A two period moving average, a three period
moving average, exponential smoothing (α=0.1), or exponential
smoothing (α=0.2)
Realistically we should have experimented with more values of n
for the moving average, and α for exponential smoothing to
determine the absolute best parameters to use for our technique.
On the next slide we randomly chose to use the MSE criterion to
judge the best technique.

28
Robert’s Drugs :Comparing Smoothing Techniques
Double click on the Excel sheet below to enter actual Excel spreadsheet
that I created. Clicking on individual cells will provide the formulas that were
entered to compute the observed values.
MSE for MA2
Robert's Drug
Sales n=2 Error
Week (t ) Yt Ft (Yt - Ft) (Yt - Ft)
2
1 110
2 115 #N/A
3 125 112.5 12.5 156.25
4 120 120 0 0
5 125 122.5 2.5 6.25
6 120 122.5 -2.5 6.25
7 130 122.5 7.5 56.25
8 115 125 -10 100
9 110 122.5 -12.5 156.25
10 130 112.5 17.5 306.25
11 120
MSE 98.4375

29
MSE for MA3
Robert's Drug
Sales n=3 Error
2
1 110
2 115 #N/A
3 125 #N/A
4 120 116.6667 3.333333 11.11111
5 125 120 5 25
6 120 123.3333 -3.33333 11.11111
7 130 121.6667 8.333333 69.44444
8 115 125 -10 100
9 110 121.6667 -11.6667 136.1111
10 130 118.3333 11.66667 136.1111
11 118.3333
MSE 69.84127

30
MSE for Exponential
Smoothing α=0.1
Sales α=0.1 Error
2
1 110 #N/A
2 115 110 5 25
3 125 110.5 14.5 210.25
4 120 111.95 8.05 64.8025
5 125 112.755 12.245 149.94
6 120 113.9795 6.0205 36.24642
7 130 114.5816 15.41845 237.7286
8 115 116.1234 -1.1234 1.262016
9 110 116.0111 -6.01106 36.13279
10 130 115.4099 14.59005 212.8696
11
MSE 108.248

31
MSE for Exponential
Smoothing α=0.2
Sales α=0.2 Error
2
1 110 #N/A
2 115 110 5 25
3 125 111 14 196
4 120 113.8 6.2 38.44
5 125 115.04 9.96 99.2016
6 120 117.032 2.968 8.809024
7 130 117.6256 12.3744 153.1258
8 115 120.1005 -5.10048 26.0149
9 110 119.0804 -9.08038 82.45337
10 130 117.2643 12.73569 162.1979
11
MSE 87.91584

32
Since the three period moving average technique
(MA3) provides to lowest MSE value, this is the best
smoothing technique to use for forecasting Robert’s
Drug Sales.

33
Trend Projection
If a time series exhibits a linear trend, the method of least
squares may be used to determine a trend line (projection) for
future forecasts.
Least squares, also used in regression analysis, determines the
unique trend line forecast which minimizes the mean square
error between the trend line forecasts and the actual observed
values for the time series.
The independent variable is the time period and the dependent
variable is the actual observed value in the time series.

34
Trend Projection
Using the method of least squares, the formula for the trend
projection is:
Yt = b0 + b1t.
where: Yt = trend forecast for time period t
b1 = slope of the trend line
b0 = trend line projection for time 0
b1 = nΣ tYt - Σt ΣYt
nΣt 2
- (Σt )2
where: Yt = observed value of the time series at time period t
= average of the observed values for Yt
= average time period for the n observations
0 1
b Y b t
= −
t
t
Y
t

35
Example: Auger’s Plumbing Service
The number of plumbing repair jobs performed by Auger's Plumbing
Service in each of the last nine months are listed below.
Month Jobs Month Jobs Month Jobs
March 353 June 374 September 399
April 387 July 396 October 412
May 342 August 409 November 408
Forecast the number of repair jobs Auger's will perform in
December using the least squares method.

36
Auger’s Plumbing Service: Trend Projection
Trend Projection
(month) t Yt tYt t 2
(Mar.) 1 353 353 1
(Apr.) 2 387 774 4
(May) 3 342 1026 9
(June) 4 374 1496 16
(July) 5 396 1980 25
(Aug.) 6 409 2454 36
(Sep.) 7 399 2793 49
(Oct.) 8 412 3296 64
(Nov.) 9 408 3672 81
Sum 45 3480 17844 285

37
Trend Projection (continued)
= 45/9 = 5 = 3480/9 = 386.667
nΣtYt - Σ t Σ Yt (9)(17844) - (45)(3480)
b1 = = = 7.4
n Σ t 2
- (Σ t)2
(9)(285) - (45)2
= 386.667 - 7.4(5) = 349.667
Thus our trend line is Yt = 349.667 + 7.4 t.
Y10 = 349.667 + (7.4)(10) = 423.667
423.667
0 1
b Y b t
= −
Y
t t
For December t=10

38
Auger’s Plumbing Service: Trend Line in Excel
A B C
1 Auger's Plumbing Service
2
3 Month Calls
4 1 353
5 2 387
6 3 342
7 4 374
8 5 396
9 6 409
10 7 399
11 8 412
12 9 408
13
Excel Spreadsheet Showing Input Data

39
Steps to Trend Projection Using Excel
Step 1: Select an empty cell (B13) in the worksheet.
Step 2: Select the Insert pull-down menu.
Step 3: Choose the Function option.
Step 4: When the Select Category dialog box appears:
Choose Statistical in Function Category box.
Choose Forecast in the Function Name box.
Select OK.
Step 5: When the Forecast dialog box appears:
Enter 10 in the x box (for month 10).
Enter B4:B12 in the Known y’s box.
Enter A4:A12 in the Known x’s box.
Select OK.

40
Spreadsheet Showing Trend Projection for Month 10
Auger's Plumbing Service
Month Calls
1 353
2 387
3 342
4 374
5 396
6 409
7 399
8 412
9 408
10 423.667 Projected

41
Roberts Drug Example
Suppose we neglected to plot Robert’s Drug example, and therefore we
do not know that a trend does not exist. Use trend analysis to forecast
the sales for month 11.
Week (t ) Yt
1 110
2 115
3 125
4 120
5 125
6 120
7 130
8 115
9 110
10 130
11 124 Forecast

42
Question????
How could we use the MSE or MAD to verify that the
MA3 is a better smoothing technique than trend analysis
for Robert’s Drug Sales data?

43
Causal Method: Regression Analysis
Regression Analysis is similar to trend analysis, except
the independent variable is not restricted to time. Refer
to Robert’s Drug example. Instead of letting time
represent our independent variable, we could forecast
sales based upon the price of the product. Since
products often go on sale, we could collect data over
several months collecting the weekly price and number
of items sold for the week. For this model, we would
find the regression equation in the same manner in
which we found the trend line except we would call the
independent variable x, instead of t.

44
Regression Equation
Using the method of least squares, the formula for the regression
line is:
Y = b0 + b1x.
where: Y= dependent variable which depends on the value of x
b1 = slope of the regression line
b0 = regression line projection for x= 0
b1 = nΣ XiYi - ΣXi ΣYi
nΣXi
2
- (ΣXi)2
where: Yt = observed value of the time series at time period t
= average of the observed values for Yt
= average time period for the n observations
t
t
Y
t
b y b x
0 1
= −

45
Regression Analysis in Excel
The dependent variable Y can predicted using the
same forecast function in Excel as used to forecast a
trend line. Follow the same steps provided on slide 39.

46
THE END
See your textbook for more
examples and detailed explanations
of all topics discussed in these notes.

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