New Forecasting Techniques

8/10/2019 New Forecasting Techniques

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Dr. C. LightnerFayetteville State University

1

FORECASTING TECHNIQUES

Chapter 16Qualitative 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


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2

Forecasting Introduction

An essential aspect of managing any organization isplanning 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


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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 toeach of the other panel members so that they may revise their

previous forecast response.

The process continues until some degree of consensus is

achieved.


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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.


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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.


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6

Quantitative Approaches to Forecasting

Quantitative methods are based on an analysis of historical dataconcerning one or more time series.

A time series is a set of observations measured at successivepoints in time or over successive periods of time.

If the historical data used are restricted to past values of the seriesthat we are trying to forecast, the procedure is called a time seriesmethod.

If the historical data used involve other time series that are believedto 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 wewill focus on quantitative approaches to forecasting.


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8

Components of a Time Series

The trend component accounts for the gradual shiftingof the time series over a long period of time.

Any regular pattern of sequences of values above andbelow the trend line is attributable to the cyclical

component of the series.The seasonal component of the series accounts forregular patterns of variability within certain time periods,such as over a year.

The irregular component of the series is caused byshort-term, unanticipated and non-recurring factors thataffect the values of the time series. One cannot attemptto predict its impact on the time series in advance.


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9

Time Series Data

We will learn the following Forecasting Approaches:Smoothing

Trend Projections


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10

Excel Instructions for Drawing a Scatter Plot

1. Enter data in the Excel spreadsheet.2. Click on Inserton 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 datarange 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.


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11

During the past ten weeks, sales of cases of Comfort brandheadache medicine at Robert's Drugs have been as follows:

Week Sales Week Sales

1 110 6 120

2 115 7 1303 125 8 115

4 120 9 110

5 125 10 130

Plot this data.

Example: Roberts Drugs


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12

Plot Roberts Drugs Example

Excel Spreadsheet Showing Input Data. Specify cells A4:B13 as the DataRange.

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


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13

Plot Roberts Drugs Example

Robert's Drug Example

105

110

115

120

125

130

135

0 5 10 15

Week, t

Sales

I labeledRoberts Drug

Example as

The Chart title

I labeledWeek, t as

My Value (x)

axis

I labeled

Sales asMy Value (y)

axis


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14

Smoothing Methods

In cases in which the time series is fairly stable andhas 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


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15

Smoothing Methods: Moving Average

Moving Average MethodThe moving average method consists of computing

an average of the most recent ndata values for the

series and using this average for forecasting the value

of the time series for the next period.


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16

Robert Drugs Example: Moving Average

Our scatter plot for Roberts Drug Sales has nosignificant 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).


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17

Example: Roberts Drugs: Moving Average

Steps to Moving Average Using Excel

Step 1: Select the Toolspull-down menu.

Step 2: Select the Data Analysisoption.

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 Rangebox.

Enter 3 in the Intervalbox.Enter C5 in the Output Rangebox.

Select OK.

This specifies

the value of n

This is the column

following our data,

and one row below where

our data begins.


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18

Roberts Drugs: Moving Average

MA3(Three period Moving average) for Roberts 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 Drugn=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 1259 110 121.6667

10 130 118.3333

11 118.3333


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Smoothing Methods: Weighted Moving Average

Weighted Moving Average MethodThe weighted moving average method consists of computing a

weighted average of the most recent ndata 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. Forconvenience, 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.


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Smoothing Methods: Weighted Moving Average

Use a 3 period weighted moving average to forecast the sales forweek 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


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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 () of the forecast error in the current period.

Using exponential smoothing, the forecast is calculated by:

Ft+1= Yt + (1- )Ft

where:

is the smoothing constant (a number between 0 and 1)

Ft is the forecast for period tFt +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+ (YtFt)


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22

Roberts Drugs: Exponential Smoothing

Forecast the sales for period 11 using ExponentialSmoothing = 0.1.


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Dr. C. LightnerFayetteville State University 23


Steps to Exponential Smoothing Using Excel

Step 1: Select the Toolspull-down menu.

Step 2: Select the Data Analysisoption.

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 Rangebox.

Enter 0.9 (for = 0.1) in Damping Factorbox.

Enter C4 in the Output Rangebox.

Select OK.

Damping factor

is always 1-


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F11 = 0.1 * Y10 + .9 F10= .1 *130 + .9 * 115.4099

= 116.87

Robert's Drugs

=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


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Questions That You Should Be Asking

For the Moving Average technique, how do I determine the bestvalue of n to use for forecasting?

For Exponential Smoothing, how do I determine the best value of

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 forforecasting our scenario.


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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).


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Selecting the best Smoothing Technique for Roberts Drugs

Determine the smoothing technique that is best for forecastingRoberts Drug sales: A two period moving average, a three period

moving average, exponential smoothing (=0.1), or exponential

smoothing (=0.2)

Realistically we should have experimented with more values of n

for the moving average, and 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 tojudge the best technique.


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Roberts Drugs :Comparing Smoothing Techniques

MSE for MA3

Robert's Drug

Sales n=3 Error

Week (t ) Yt Ft (Yt- Ft) (Yt- Ft)2

1 110

2 115 #N/A

3 125 #N/A

4 120 116.6667 3.333333 11.111115 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


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MSE for Exponential

Smoothing =0.1

Sales =0.1 Error


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


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MSE for Exponential

Smoothing =0.2

Sales =0.2 Error


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


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Since the three period moving average technique(MA3) provides to lowest MSE value, this is the best

smoothing technique to use for forecasting Roberts

Drug Sales.


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Trend Projection

If a time series exhibits a linear trend, the method of leastsquares 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 observedvalues for the time series.

The independent variable is the time period and the dependent

variable is the actual observed value in the time series.


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Trend Projection

Using the method of least squares, the formula for the trendprojection is:Y

t= b0+ b1t.

where: Yt= trend forecast for time period t

b1 = slope of the trend line

b0= trend line projection for time 0

b1= n tYt- tYt

nt 2- (t )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 1b Y b t

t

t Y

t


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Example: Augers 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 412May 342 August 409 November 408

Forecast the number of repair jobs Auger's will perform in

December using the least squares method.


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Augers Plumbing Service: Trend Projection

Trend Projection

(month) t Yt tYt t2

(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


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Trend Projection (continued)

= 45/9 = 5 = 3480/9 = 386.667

ntYt- t Yt (9)(17844) - (45)(3480)b

1= = = 7.4n t 2- (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

0 1b Y b t

Yt t

For December t=10


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Augers Plumbing Service: Trend Line in Excel

A B C

1 Auger's Plumbing Service

2

3 Month Calls

4 1 3535 2 387

6 3 342

7 4 374

8 5 396

9 6 40910 7 399

11 8 412

12 9 408

13

Excel Spreadsheet Showing Input Data


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Steps to Trend Projection Using ExcelStep 1: Select an empty cell (B13) in the worksheet.

Step 2: Select the Insertpull-down menu.

Step 3: Choose the Functionoption.

Step 4: When the Select Category dialog box appears:

Choose Statisticalin Function Category box.

Choose Forecastin the Function Name box.

Select OK.

Step 5: When the Forecast dialog box appears:

Enter 10 in the xbox (for month 10).Enter B4:B12 in the Known ysbox.

Enter A4:A12 in the Known xsbox.

Select OK.


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Spreadsheet Showing Trend Projection for Month 10Auger's Plumbing Service

Month Calls

1 353

2 3873 342

4 374

5 396

6 409

7 3998 412

9 408

10 423.667 Projected


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Roberts Drug Example

Suppose we neglected to plot Roberts Drug example, and therefore wedo not know that a trend does not exist. Use trend analysis to forecast

the sales for month 11.

Week (t) Yt1 110

2 115

3 125

4 120

5 125

6 120

7 130

8 115

9 110

10 130

11 124 Forecast


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Dr. C. Lightner

Fayetteville State University

42

Question????

How could we use the MSE or MAD to verify that theMA3is a better smoothing technique than trend analysis

for Roberts Drug Sales data?


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Dr. C. Lightner


43

Causal Method: Regression Analysis

Regression Analysis is similar to trend analysis, exceptthe independent variable is not restricted to time. Refer

to Roberts 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 theindependent variable x, instead of t.


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Dr. C. Lightner


44

Regression Equation

Using the method of least squares, the formula for the regressionline 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= n XiYi- XiYi

nXi2- (Xi)

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 x0 1


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Dr. C. Lightner


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Regression Analysis in Excel

The dependent variable Y can predicted using thesame forecast function in Excel as used to forecast a

trend line. Follow the same steps provided on slide 39.


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Dr. C. Lightner 46

THE END

See your textbook for moreexamples and detailed explanations

of all topics discussed in these notes.

New Forecasting Techniques

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