Chapter 7 Forecasting n Quantitative Approaches to Forecasting n The Components of a Time Series n...

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Chapter 7 Forecasting Quantitative Approaches to Forecasting The Components of a Time Series Measures of Forecast Accuracy Using Smoothing Methods in Forecasting Using Seasonal Components in Forecasting Qualitative Approaches to Forecasting

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Page 1: Chapter 7 Forecasting n Quantitative Approaches to Forecasting n The Components of a Time Series n Measures of Forecast Accuracy n Using Smoothing Methods.

Chapter 7Forecasting

Quantitative Approaches to Forecasting The Components of a Time Series Measures of Forecast Accuracy Using Smoothing Methods in Forecasting Using Seasonal Components in Forecasting Qualitative Approaches to Forecasting

Page 2: Chapter 7 Forecasting n Quantitative Approaches to Forecasting n The Components of a Time Series n Measures of Forecast Accuracy n Using Smoothing Methods.

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.

Page 3: Chapter 7 Forecasting n Quantitative Approaches to Forecasting n The Components of a Time Series n Measures of Forecast Accuracy n Using Smoothing Methods.

Time Series D

eman

d fo

r pr

oduc

t or

ser

vice

| | | |1 2 3 4

Year

Average demand over

four years

Seasonal peaks

Trend component

Actual demand

Random variation

Page 4: Chapter 7 Forecasting n Quantitative Approaches to Forecasting n The Components of a Time Series n Measures of Forecast Accuracy n Using Smoothing Methods.

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.

0 5 10 15 20

Page 5: Chapter 7 Forecasting n Quantitative Approaches to Forecasting n The Components of a Time Series n Measures of Forecast Accuracy n Using Smoothing Methods.

Components of a Time 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.

M T W T F

Page 6: Chapter 7 Forecasting n Quantitative Approaches to Forecasting n The Components of a Time Series n Measures of Forecast Accuracy n Using Smoothing Methods.

Measures of Forecast Accuracy

Mean Squared ErrorThe 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 DeviationThe 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.

Page 7: Chapter 7 Forecasting n Quantitative Approaches to Forecasting n The Components of a Time Series n Measures of Forecast Accuracy n Using Smoothing Methods.

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.

Four common smoothing methods are:• Moving averages• Centered moving averages• Weighted moving averages

Page 8: Chapter 7 Forecasting n Quantitative Approaches to Forecasting n The Components of a Time Series n Measures of Forecast Accuracy n Using Smoothing Methods.

Smoothing Methods

Moving Average MethodThe 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.

Page 9: Chapter 7 Forecasting n Quantitative Approaches to Forecasting n The Components of a Time Series n Measures of Forecast Accuracy n Using Smoothing Methods.

Sales of Comfort brand headache medicine forthe past ten weeks at Rosco Drugsare shown on the next slide. If Rosco Drugs uses a 3-periodmoving average to forecast sales,what is the forecast for Week 11?

Example: Rosco Drugs

Page 10: Chapter 7 Forecasting n Quantitative Approaches to Forecasting n The Components of a Time Series n Measures of Forecast Accuracy n Using Smoothing Methods.

Past Sales

Week Sales Week Sales 1 110 6 120 2 115 7 130 3 125 8 115 4 120 9 110 5 125 10 130

Example: Rosco Drugs

Page 11: Chapter 7 Forecasting n Quantitative Approaches to Forecasting n The Components of a Time Series n Measures of Forecast Accuracy n Using Smoothing Methods.

Example: Rosco Drugs

Excel Spreadsheet Showing Input DataA B C

1 Robert's Drugs2

3 Week (t ) Salest Forect+1

4 1 1105 2 1156 3 1257 4 1208 5 1259 6 120

10 7 13011 8 11512 9 11013 10 130

Page 12: Chapter 7 Forecasting n Quantitative Approaches to Forecasting n The Components of a Time Series n Measures of Forecast Accuracy n Using Smoothing Methods.

Example: Rosco Drugs

Steps to Moving Average Using ExcelStep 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 C4 in the Output Range box.Select OK.

Page 13: Chapter 7 Forecasting n Quantitative Approaches to Forecasting n The Components of a Time Series n Measures of Forecast Accuracy n Using Smoothing Methods.

Example: Rosco Drugs

Spreadsheet Showing Results Using n = 3

A B C1 Robert's Drugs2

3 Week (t ) Salest Forect+1

4 1 110 #N/A5 2 115 #N/A6 3 125 #N/A7 4 120 116.78 5 125 120.09 6 120 123.3

10 7 130 121.711 8 115 125.012 9 110 121.713 10 130 118.3

Page 14: Chapter 7 Forecasting n Quantitative Approaches to Forecasting n The Components of a Time Series n Measures of Forecast Accuracy n Using Smoothing Methods.

Smoothing Methods

Centered Moving Average Method

The centered moving average method consists of computing an average of n periods' data and associating it with the midpoint of the periods. For example, the average for periods 5, 6, and 7 is associated with period 6. This methodology is useful in the process of computing season indexes.

Page 15: Chapter 7 Forecasting n Quantitative Approaches to Forecasting n The Components of a Time Series n Measures of Forecast Accuracy n Using Smoothing Methods.

Example: Rosco Drugs

Spreadsheet Showing Results Using n = 3

A B C1 Robert's Drugs2

3 Week (t ) Salest Forect+1

4 1 110 #N/A5 2 115 116.76 3 125 120.07 4 120 123.38 5 125 121.79 6 120 125.0

10 7 130 121.711 8 115 118.612 9 110 118.313 10 130 #N/A

Page 16: Chapter 7 Forecasting n Quantitative Approaches to Forecasting n The Components of a Time Series n Measures of Forecast Accuracy n Using Smoothing Methods.

Trend Projection

Using the method of least squares, the formula for the trend projection is: Tt = b0 + b1t.

where: Tt = trend forecast for time period t

b1 = slope of the trend line

b0 = trend line projection for time 0

b1 = ntYt - t Yt

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

Yt

Page 17: Chapter 7 Forecasting n Quantitative Approaches to Forecasting n The Components of a Time Series n Measures of Forecast Accuracy n Using Smoothing Methods.

The number of plumbing repair jobs performed byAuger's Plumbing Service in each of the last ninemonths is listed on the next slide. Forecastthe number of repair jobs Auger's willperform in December using the leastsquares method.

Example: Auger’s Plumbing Service

Page 18: Chapter 7 Forecasting n Quantitative Approaches to Forecasting n The Components of a Time Series n Measures of Forecast Accuracy n Using Smoothing Methods.

Month Jobs Month Jobs Month Jobs

March 353 June 374 September 399

April 387 July 396 October 412

May 342 August 409 November 408

Example: Auger’s Plumbing Service

Page 19: Chapter 7 Forecasting n Quantitative Approaches to Forecasting n The Components of a Time Series n Measures of Forecast Accuracy n Using Smoothing Methods.

Example: Auger’s Plumbing Service

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

Page 20: Chapter 7 Forecasting n Quantitative Approaches to Forecasting n The Components of a Time Series n Measures of Forecast Accuracy n Using Smoothing Methods.

Example: Auger’s Plumbing Service

Trend Projection (continued)

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

ntYt - t Yt (9)(17844) - (45)(3480) b1 = = =

7.4 nt 2 - (t)2 (9)(285) - (45)2

= 386.667 - 7.4(5) = 349.667

T10 = 349.667 + (7.4)(10) =

423.667423.667

0 1b Y b t

Yt

Page 21: Chapter 7 Forecasting n Quantitative Approaches to Forecasting n The Components of a Time Series n Measures of Forecast Accuracy n Using Smoothing Methods.

Example: Auger’s Plumbing Service

Excel Spreadsheet Showing Input DataA B C

1 Auger's Plumbing Service23 Month Calls4 1 3535 2 3876 3 3427 4 3748 5 3969 6 409

10 7 39911 8 41212 9 40813

Page 22: Chapter 7 Forecasting n Quantitative Approaches to Forecasting n The Components of a Time Series n Measures of Forecast Accuracy n Using Smoothing Methods.

Example: Auger’s Plumbing Service

Steps to Trend Projection Using ExcelStep 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 Paste Function dialog box

appears:Choose Statistical in Function

Category box.Choose Forecast in the Function

Name box.Select OK.

more . . . . . . .

Page 23: Chapter 7 Forecasting n Quantitative Approaches to Forecasting n The Components of a Time Series n Measures of Forecast Accuracy n Using Smoothing Methods.

Example: Auger’s Plumbing Service

Steps to Trend Projecting Using Excel (continued)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.

Page 24: Chapter 7 Forecasting n Quantitative Approaches to Forecasting n The Components of a Time Series n Measures of Forecast Accuracy n Using Smoothing Methods.

Example: Auger’s Plumbing Service

Spreadsheet with Trend Projection for Month 10 A B C

1 Auger's Plumbing Service23 Month Calls4 1 3535 2 3876 3 3427 4 3748 5 3969 6 409

10 7 39911 8 41212 9 40813 10 423.667 Projected

Page 25: Chapter 7 Forecasting n Quantitative Approaches to Forecasting n The Components of a Time Series n Measures of Forecast Accuracy n Using Smoothing Methods.

Forecasting with Trendand Seasonal Components

Steps of Multiplicative Time Series Model1. Calculate the centered moving averages

(CMAs).2. Center the CMAs on integer-valued periods.3. Determine the seasonal and irregular factors

(StIt ).

4. Determine the average seasonal factors.5. Scale the seasonal factors (St ).

6. Determine the deseasonalized data.7. Determine a trend line of the

deseasonalized data.8. Determine the deseasonalized predictions.9. Take into account the seasonality.

Page 26: Chapter 7 Forecasting n Quantitative Approaches to Forecasting n The Components of a Time Series n Measures of Forecast Accuracy n Using Smoothing Methods.

Example: Terry’s Tie Shop

Business at Terry's Tie Shop can be viewed asfalling into three distinct seasons:(1) Christmas (November-December);(2) Father's Day (late May - mid-June);and (3) all other times. Average weeklysales ($) during each of the three seasonsduring the past four years are shown onthe next slide.

Determine a forecast for the average weekly salesin year 5 for each of the three seasons.

Page 27: Chapter 7 Forecasting n Quantitative Approaches to Forecasting n The Components of a Time Series n Measures of Forecast Accuracy n Using Smoothing Methods.

Example: Terry’s Tie Shop

Past Sales ($)

Year Season 1 2 3 4 1 1856 1995 2241 2280 2 2012 2168 2306 2408 3 985 1072 1105 1120

Page 28: Chapter 7 Forecasting n Quantitative Approaches to Forecasting n The Components of a Time Series n Measures of Forecast Accuracy n Using Smoothing Methods.

Example: Terry’s Tie Shop

Dollar Moving Scaled

Year Season Sales (Yt) Average StIt St Yt/St

1 1 1856 1.178 1576

2 2012 1617.67 1.244 1.236 1628

3 985 1664.00 .592 .586 1681

2 1 1995 1716.00 1.163 1.178 1694

2 2168 1745.00 1.242 1.236 1754

3 1072 1827.00 .587 .586 1829

3 1 2241 1873.00 1.196 1.178 1902

2 2306 1884.00 1.224 1.236 1866

3 1105 1897.00 .582 .586 1886

4 1 2280 1931.00 1.181 1.178 1935

2 2408 1936.00 1.244 1.236 1948

3 1120 .586 1911

Page 29: Chapter 7 Forecasting n Quantitative Approaches to Forecasting n The Components of a Time Series n Measures of Forecast Accuracy n Using Smoothing Methods.

1. Calculate the centered moving averages.There are three distinct seasons in each

year. Hence, take a three-season moving average to eliminate seasonal and irregular factors. For example:

1st MA = (1856 + 2012 + 985)/3 = 1617.67

2nd MA = (2012 + 985 + 1995)/3 = 1664.00

etc.

Example: Terry’s Tie Shop

Page 30: Chapter 7 Forecasting n Quantitative Approaches to Forecasting n The Components of a Time Series n Measures of Forecast Accuracy n Using Smoothing Methods.

Example: Terry’s Tie Shop

2. Center the CMAs on integer-valued periods.The first moving average computed in

step 1 (1617.67) will be centered on season 2 of year 1. Note that the moving averages from step 1 center themselves on integer-valued periods because n is an odd number.

Page 31: Chapter 7 Forecasting n Quantitative Approaches to Forecasting n The Components of a Time Series n Measures of Forecast Accuracy n Using Smoothing Methods.

Example: Terry’s Tie Shop

3. Determine the seasonal & irregular factors (St It ). Isolate the trend and cyclical components. For each period t, this is given by:

St It = Yt /(Moving Average for period t )

Page 32: Chapter 7 Forecasting n Quantitative Approaches to Forecasting n The Components of a Time Series n Measures of Forecast Accuracy n Using Smoothing Methods.

Example: Terry’s Tie Shop

4. Determine the average seasonal factors. Averaging all St It values corresponding to

that season:

Season 1: (1.163 + 1.196 + 1.181) /3 = 1.180

Season 2: (1.244 + 1.242 + 1.224 + 1.244) /4 = 1.238

Season 3: (.592 + .587 + .582) /3 = .587

Page 33: Chapter 7 Forecasting n Quantitative Approaches to Forecasting n The Components of a Time Series n Measures of Forecast Accuracy n Using Smoothing Methods.

Example: Terry’s Tie Shop

5. Scale the seasonal factors (St ).

Average the seasonal factors = (1.180 + 1.238 + .587)/3 = 1.002. Then, divide each seasonal factor by the average of the seasonal factors.

Season 1: 1.180/1.002 = 1.178 Season 2: 1.238/1.002 = 1.236 Season 3: .587/1.002 = .586

Total = 3.000

Page 34: Chapter 7 Forecasting n Quantitative Approaches to Forecasting n The Components of a Time Series n Measures of Forecast Accuracy n Using Smoothing Methods.

Example: Terry’s Tie Shop

6. Determine the deseasonalized data.Divide the data point values, Yt , by St .

7. Determine a trend line of the deseasonalized data.

Using the least squares method for t = 1, 2, ..., 12, gives:

Tt = 1580.11 + 33.96t

Page 35: Chapter 7 Forecasting n Quantitative Approaches to Forecasting n The Components of a Time Series n Measures of Forecast Accuracy n Using Smoothing Methods.

Example: Terry’s Tie Shop

8. Determine the deseasonalized predictions.Substitute t = 13, 14, and 15 into the

least squares equation:

T13 = 1580.11 + (33.96)(13) = 2022

T14 = 1580.11 + (33.96)(14) = 2056

T15 = 1580.11 + (33.96)(15) = 2090

Page 36: Chapter 7 Forecasting n Quantitative Approaches to Forecasting n The Components of a Time Series n Measures of Forecast Accuracy n Using Smoothing Methods.

Example: Terry’s Tie Shop

9. Take into account the seasonality.Multiply each deseasonalized prediction

by its seasonal factor to give the following forecasts for year 5:

Season 1: (1.178)(2022) = Season 2: (1.236)(2056) = Season 3: ( .586)(2090) =

23822382

25412541

12251225

Page 37: Chapter 7 Forecasting n Quantitative Approaches to Forecasting n The Components of a Time Series n Measures of Forecast Accuracy n Using Smoothing Methods.

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.

Page 38: Chapter 7 Forecasting n Quantitative Approaches to Forecasting n The Components of a Time Series n Measures of Forecast Accuracy n Using Smoothing Methods.

Qualitative Approaches to Forecasting

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.

Page 39: Chapter 7 Forecasting n Quantitative Approaches to Forecasting n The Components of a Time Series n Measures of Forecast Accuracy n Using Smoothing Methods.

Qualitative Approaches to Forecasting

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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