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I see that you will get an A this semester. Department of Business Administration. Chapter 3: Forecasting. FALL 20 10 - 2011. Outline: What You Will Learn. List the elements of a good forecast. Outline the steps in the forecasting process.

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Chapter 3 forecasting

I see that you willget an A this semester.

Department of Business Administration

Chapter 3: Forecasting

FALL 2010-2011


Outline: What You Will Learn . . .

  • List the elements of a good forecast.

  • Outline the steps in the forecasting process.

  • Describe at least three qualitative forecasting techniques and the advantages and disadvantages of each.

  • Compare and contrast qualitative and quantitative approaches to forecasting.

  • Briefly describe averaging techniques, trend and seasonal techniques, and regression analysis, and solve typical problems.

  • Describe two measures of forecast accuracy.

  • Describe two ways of evaluating and controlling forecasts.

  • Identify the major factors to consider when choosing a forecasting technique


What is meant by Forecasting and Why?

  • Forecasting is the process of estimating a variable, such as the sale of the firm at some future date.

  • Forecasting is important to business firm, government, and non-profit organization as a method of reducing the risk and uncertainty inherent in most managerial decisions.

  • A firm must decide how much of each product to produce, what price to charge, and how much to spend on advertising, and planning for the growth of the firm.


The aim of forecasting
The aim of forecasting

  • The aim of forecasting is to reduce the risk or uncertainty that the firm faces in its short-term operational decision making and in planning for its long term growth.

  • Forecasting the demand and sales of the firm’s product usually begins with macroeconomic forecast of general level of economic activity for the economy as a whole or GNP.


The aim of forecasting

  • The firm uses the macro-forecasts of general economic activity as inputs for their micro-forecasts of the industry’s and firm’s demand and sales.

  • The firm’s demand and sales are usually forecasted on the basis of its historical market share and its planned marketing strategy (i.e., forecasting by product line and region).

  • The firm uses long-term forecasts for the economy and the industry to forecast expenditure on plant and equipment to meet its long-term growth plan and strategy.


Forecasting process map

Sales

Marketing

Product

Management

& Finance

Executive

Management

Production &

Inventory

Control

Forecasting Process Map

Causal

Factors

Demand

History

Statistical Model

Consensus

Process

Consensus

Forecast



I see that you willget an A this semester.

Features of Forecasts

  • Assumes causal systempast ==> future

  • Forecasts rarely perfect because of randomness

  • Forecasts more accurate forgroups vs. individuals

  • Forecast accuracy decreases as time horizon increases


Elements of a good forecast

Timely

Accurate

Reliable

Easy to use

Written

Meaningful

Elements of a Good Forecast


Steps in the forecasting process

“The forecast”

Step 6 Monitor the forecast

Step 5 Make the forecast

Step 4 Obtain, clean and analyze data

Step 3 Select a forecasting technique

Step 2 Establish a time horizon

Step 1 Determine purpose of forecast

Steps in the Forecasting Process


Forecasting techniques
Forecasting Techniques

  • A wide variety of forecasting methods are available to management. These range from the most naïve methods that require little effort to highly complex approaches that are very costly in terms of time and effort such as econometric systems of simultaneous equations.

  • Mainly these techniques can break down into three parts:Qualitative approaches (Judgmental forecasts) and Quantitative approaches (Time-series forecasts) and Associative model forecasts).


Forecasting techniques1
Forecasting Techniques

  • Judgmental - uses subjective inputs such as opinion from consumer surveys, sales staff etc..

  • Time series - uses historical data assuming the future will be like the past

  • Associative models - uses explanatory variables to predict the future


Qualitative forecasts or judgmental forecasts
Qualitative Forecasts or Judgmental Forecasts

  • Survey Techniques

  • Some of the best-know surveys

    • Planned Plant and Equipment Spending

    • Expected Sales and Inventory Changes

    • Consumers’ Expenditure Plans

  • Opinion Polls

    • Business Executives

    • Sales Force

    • Consumer Intentions


What are qualitative forecast
What are qualitative forecast ?

  • Qualitative forecast estimate variables at some future date using the results of surveys and opinion polls of business and consumer spending intentions.

  • The rational is that many economic decisions are made well in advance of actual expenditures.

  • For example, businesses usually plan to add to plant and equipment long before expenditures are actually incurred.


Qualitative Forecasts or Judgmental Forecasts

  • Surveys and opinion pools are often used to make short-term forecasts when quantitative data are not available

  • Usually based on judgments about causal factors that underlie the demand of particular products or services

  • Do not require a demand history for the product or service, therefore are useful for new products/services

  • Approaches vary in sophistication from scientifically conducted surveys to intuitive hunches about future events

  • The approach/method that is appropriate depends on a product’s life cycle stage


Qualitative Forecasts or Judgmental Forecasts

  • Polls can also be very useful in supplementing quantitative forecasts, anticipating changes in consumer tastes or business expectations about future economic conditions, and forecasting the demand for a new product.

  • Firms conduct opinion polls for economic activities based on the results of published surveys of expenditure plans of businesses, consumers and governments.


Qualitative Forecasts or Judgmental Forecasts

  • Survey Techniques– The rationale for forecasting based on surveys of economic intentions is that many economic decisions are made in advance of actual expenditures (Ex: Consumer’s decisions to purchase houses, automobiles, TV sets, furniture, vocation, education etc. are made months or years in advance of actual purchases)

  • Opinion Polls– The firm’s sales are strongly dependent on the level of economic activity and sales for the industry as a whole, but also on the policies adopted by the firm. The firm can forecast its sales by pooling experts within and outside the firm.


Qualitative Forecasts or Judgmental Forecasts

  • Executive Polling- Firm can poll its top management from its sales, production, finance for the firm during the next quarter or year.

  • Bandwagon effect (opinions of some experts might be overshadowed by some dominant personality in their midst).

  • Delphi Method – experts are polled separately, and then feedback is provided without identifying the expert responsible for a particular opinion.


Qualitative Forecasts or Judgmental Forecasts

  • Consumers intentions polling-

  • Firms selling automobiles, furniture, etc. can pool a sample of potential buyers on their purchasing intentions. By using results of the poll a firm can forecast its sales for different levels of consumer’s future income.

  • Sales force polling –

  • Forecast of the firm’s sales in each region and for each product line, it is based on the opinion of the firm’s sales force in the field (people working closer to the market and their opinion about future sales can provide essential information to top management).


Quantitative forecasting approaches
Quantitative Forecasting Approaches

  • Based on the assumption, the “forces” that generated the past demand will generate the future demand, i.e., history will tend to repeat itself.

  • Analysis of the past demand pattern provides a good basis for forecasting future demand.

  • Majority of quantitative approaches fall in the category of time series analysis.


Time series analysis
Time Series Analysis

  • A time series (naive forecasting) is a set of numbers where the order or sequence of the numbers is important, i.e., historical demand

  • Attempts to forecasts future values of the time series by examining past observations of the data only. The assumption is that the time series will continue to move as in the past

  • Analysis of the time series identifies patterns

  • Once the patterns are identified, they can be used to develop a forecast


Forecast horizon
Forecast Horizon

  • Short term

    • Up to a year

  • Medium term

    • One to five years

  • Long term

    • More than five years


Reasons for fluctuations in time series data
Reasons for Fluctuations in Time Series Data

  • Secular Trend are noted by an upward or downward sloping line- long-term movement in data (e.g. Population shift, changing income and cultural changes).

  • Cycle fluctuations is a data pattern that may cover several years before it repeats itself- wavelike variations of more than one year’s duration (e.g. Economic, political and agricultural conditions).

  • Seasonality is a data pattern that repeats itself over the period of one year or less- short-term regular variations in data (e.g. Weekly or daily restaurant and supermarket experiences).

  • Irregular variationscaused by unusual circumstances(e.g. Severe weather conditions, strikes or major changes in a product or service).

  • Random influences (noise) orvariationsresults from random variation or unexplained causes. (e.g. residuals)


Forecast variations
Forecast Variations

Irregularvariation

Trend

Cycles

90

89

88

Seasonal variations


Uses for na ve forecasts
Uses for Naïve Forecasts

  • Stable time series data

    • F(t) = A(t-1)

  • Seasonal variations

    • F(t) = A(t-n)

  • Data with trends

    • F(t) = A(t-1) + (A(t-1) – A(t-2))


Techniques for averaging
Techniques for Averaging

  • Moving average

  • Weighted moving average

  • Exponential smoothing


Moving averages
Moving Averages

  • Moving average – A technique that averages a number of recent actual values, updated as new values become available.

At-n+ … At-2 + At-1

Ft = MAn=

n

n= number of period

  • Weighted moving average – More recent values in a series are given more weight in computing the forecast.

wnAt-n + … wn-1At-2 + w1At-1

Ft = WMAn=

n

n=total amount of number of weights


Simple moving average
Simple Moving Average

Actual

MA5

MA3

At-n+ … At-2 + At-1

Ft = MAn=

n


Simple moving average1
Simple Moving Average

  • An averaging period (AP) is given or selected

  • The forecast for the next period is the arithmetic average of the AP most recent actual demands

  • It is called a “simple” average because each period used to compute the average is equally weighted

  • It is called “moving” because as new demand data becomes available, the oldest data is not used

  • By increasing the AP, the forecast is less responsive to fluctuations in demand (low impulse response and high noise dampening)

  • By decreasing the AP, the forecast is more responsive to fluctuations in demand (high impulse response and low noise dampening)


Exponential smoothing
Exponential Smoothing

Ft = Ft-1 + (At-1 - Ft-1)

  • Premise--The most recent observations might have the highest predictive value.Therefore, we should give more weight to the more recent time periods when forecasting.

  • Weighted averaging method based on previous forecast plus a percentage of the forecast error

  • A-F is the error term,  is the % feedback

Ft = forecast for period t

Ft-1 = forecast for the previous period

= smoothing constant

At-1 = actual data for the previous period


Exponential smoothing forecasts
Exponential SmoothingForecasts

  • The weights used to compute the forecast (moving average) are exponentially distributed.

  • The forecast is the sum of the old forecast and a portion (a) of the forecast error (A t-1 - Ft-1).

  • The smoothing constant, , must be between 0.0 and 1.0.

  • A large  provides a high impulse response forecast.

  • A small  provides a low impulse response forecast.


Example moving average
Example-Moving Average

  • Central Call Center (CCC) wishes to forecast the number of incoming calls it receives in a day from the customers of one of its clients, BMI.

  • CCC schedules the appropriate number of telephone operators based on projected call volumes.

  • CCC believes that the most recent 12 days of call volumes (shown on the next slide) are representative of the near future call volumes.


Example moving average1
Example-Moving Average

  • Moving Average

  • Use the moving average method with an AP = 3

  • days to develop a forecast of the call volume in Day 13 (The 3 most recent demands)

  • compute a three-period average forecast given scenario above:

  • F13 = (168 + 198 + 159)/3 = 175.0 calls


Example weighted moving average
Example-Weighted Moving Average

  • Weighted Moving Average (Central Call Center )

  • Use the weighted moving average method with an AP = 3 days and weights of .1 (for oldest datum), .3, and .6 to develop a forecast of the call volume in Day 13.

  • compute a weighted average forecast given scenario above:

  • F13 = .1(168) + .3(198) + .6(159) = 171.6 calls

  • Note: The WMA forecast is lower than the MA forecast because Day 13’s relatively low call volume carries almost twice as much weight in the WMA (.60) as it does in the MA (.33).

1


Example exponential smoothing
Example-Exponential Smoothing

  • Exponential Smoothing (Central Call Center)

  • Suppose a smoothing constant value of .25 is used and the exponential smoothing forecast for Day 11 was 180.76 calls.

  • what is the exponential smoothing forecast for Day 13?

  • F12 = 180.76 + .25(198 – 180.76) = 185.07

  • F13 = 185.07 + .25(159 – 185.07) = 178.55


Example 2 exponential smoothing
Example 2-Exponential Smoothing

  • Exponential Smoothing (Actual Demand forecasting )

  • Suppose a smoothing constant value of .10 is used and the exponential smoothing forecast for the previous period was 42 units (actual demand was 40 units).

  • what is the exponential smoothing forecast for the nextperiods?

  • F3 = 42 + .10(40 – 42) = 41.8

  • F4 = 41.8 + .10(43 – 41.8) = 41.92


Example 2 exponential smoothing graphical presentation

Actual

.4

 .1

Example 2-Exponential SmoothingGraphical presentation


Trend projection
Trend Projection

  • The simplest form of time series is projecting the past trend by fitting a straight line to the data either visually or more precisely by regression analysis.

  • Linear regression analysis establishes a relationship between a dependent variable and one or more independent variables.

  • In simple linear regression analysis there is only one independent variable.

  • If the data is a time series, the independent variable is the time period.

  • The dependent variable is whatever we wish to forecast.


Linear trend equation

Ft

Ft = a + bt

0 1 2 3 4 5 t

Linear Trend Equation

  • Ft = Forecast for period t

  • t = Specified number of time periods

  • a = Value of Ft at t = 0

  • b = Slope of the line


Trend projection1
Trend Projection

  • Linear Trend:St = S0 + b tb = Growth per time period

  • Constant Growth RateSt = S0 (1 + g)t g = Growth rate

  • Estimation of Growth Rate ln St = ln S0 + t ln (1 + g)


Trend projection simple linear regression
Trend Projection- Simple Linear Regression

  • Regression Equation

  • This model is of the form:

  • Y = a + bX

  • Y = dependent variable (the value of time series to be forecasted for period t)

  • X = independent variable ( time period in which the time series is to be forecasted)

  • a = y-axis intercept (estimated value of the time series, the constant of the regression)

  • b = slope of regression line (absolute amount of growth per period)


Trend projection calculating a and b

Constants a and b

The constants a and b are computed using the equations given:

Once the a and b values are computed, a future value of X can be entered into the regression equation and a corresponding value of Y (the forecast) can be calculated.

Trend Projection- Calculating a and b


Trend projection calculating a and b1
Trend Projection- Calculating a and b

Or If formula b is used first, it may be used formula a in the following format:


Example 1 for trend projection e lectricity sales
Example 1 for Trend Projection- Electricity sales

  • Suppose we have the data show electricity sales in a city between 1997.1 and 2000.4. The data are shown in the following table. Use time series regression to forecast the electricity consumption (mn kilowatt) for the next four quarters.

  • Do not forget to use the formulae a and b


Example 1 for trend projection
Example1 for Trend Projection


Example 1 for trend projection1
Example1 for Trend Projection

Y = 11.90 + 0.394X

  • Y17 = 11.90 + 0.394(17) = 18.60 in the first quarter of 2001

  • Y18 = 11.90 + 0.394(18) = 18.99 in the second quarter of 2001

  • Y19 = 11.90 + 0.394(19) = 19.39 in the third quarter of 2001

  • Y20 = 11.90 + 0.394(20) = 19.78 in the fourth quarter of 2001

  • Note: Electricity sales are expected to increase by 0.394 mn kilowatt-hours per quarter.


Example 2 for Trend Projection

  • Estimate a trend line using regression analysis

  • Use time (t) as the independent variable:


Example 2 for Trend Projection

(continued)

  • The linear trend model is:


Example 2 for Trend Projection

(continued)

  • Forecast for time period 7:


Example for trend projection using non linear form s t s 0 1 g t
Example for Trend Projection using-Non linear form St = S0 (1 + g)t

  • Running the regression above in the form of logarithms: ln St = ln S0 + t ln (1 + g) to construct the equation which has coefficients a and b.

  • Antilog of 2.49 is 12.06 and Antilog of 0.026 is 1.026.

St = 12.06(1.026)t


Example for trend projection using st s 0 1 g t
Example for Trend Projection using St = S0 (1 + g)t

  • S17= 12.06(1.026)17 = 18.66 in the first quarter of 2001

  • S18= 12.06(1.026)18 = 19.14 in the second quarter of 2001

  • S19= 12.06(1.026)19 = 19.64 in the third quarter of 2001

  • S20= 12.06(1.026)20= 20.15 in the fourth quarter of 2001

These forecasts are similar to those obtained by fitting a linear trend


Evaluating forecast model performance
Evaluating Forecast-Model Performance

  • Accuracy

    • Accuracy is the typical criterion for judging the performance of a forecasting approach

    • Accuracy is how well the forecasted values match the actual values

  • Accuracy of a forecasting approach needs to be monitored to assess the confidence you can have in its forecasts and changes in the market may require reevaluation of the approach

  • Accuracy can be measured in several ways

    • Standard error of the forecast (SEF)

    • Mean absolute deviation (MAD)

    • Mean squared error (MSE)

    • Mean absolute percenterror (MAPE)

    • Root mean squared error (RMSE)


Forecast accuracy
Forecast Accuracy

  • Error - difference between actual value and predicted value

  • Mean Absolute Deviation (MAD)

    • Average absolute error

  • Mean Squared Error (MSE)

    • Average of squared error

  • Mean Absolute Percent Error (MAPE)

    • Average absolute percent error

  • Root Mean Squared Error (RMSE)

    • Root Average of squared error


Mad mse and mape

2

(

Actual

forecast)

MSE

=

n

-

1

(

Actual

forecast

/ Actual*100)

MAPE

=

n

MAD, MSE, and MAPE

Actual

forecast

=

MAD

n


Mad mse and mape1
MAD, MSE and MAPE

  • MAD

    • Easy to compute

    • Weights errors linearly

  • MSE

    • Squares error

    • More weight to large errors

  • MAPE

    • Puts errors in perspective

  • RMSE

    • Root of Squares error

    • More weight to large errors


Example-MAD, MSE, and MAPECompute MAD, MSE and MAP for the following data showing actual and the predicted numbers of account serviced.

22/8=2.75

76/8-1=10.86

10.26/8=1.28 %


Example central call center forecast accuracy mad
Example: Central Call Center-Forecast Accuracy - MAD

  • Which forecasting method (the AP = 3 moving average or the a = .25 exponential smoothing) is preferred, based on the MAD over the most recent 9 days? (Assume that the exponential smoothing forecast for Day 3 is the same as the actual call volume.)


  • E AP4 = 161-187.3=26.3

  • EEXP4 = 161-186=25.0

Example: Central Call Center-Forecast Accuracy - MAD

  • MADMA = 20.5/9 = 2.27

  • F4MA = (186 + 217 + 159)/3 = 187.33 calls

  • F4EXP = 186 + .25(186 – 186) = 186.00 calls

  • MADEXP = 18.0/9= 2.0


Example for ma techniques electricity sales data from 2000 1 to 2002 4 t 12 forecast accuracy rmse
Example-For MA TechniquesElectricity sales data from 2000.1 to 2002.4 (t=12)-Forecast Accuracy - RMSE

AP = 3 moving average

AP = 5 moving average


Example for ma techniques electricity sales data from 2000 1 to 2002 4 t 12 forecast accuracy rmse1
Example-For MA TechniquesElectricity sales data from 2000.1 to 2002.4 (t=12)-Forecast Accuracy - RMSE

Sqroot of 78.33/9=2.95

RMSE for 3-qma=2.95

RMSE for 5-qma=2.99

Sqroot of 62.48/7=2.98

Thus three-quarter moving average forecast is marginally better than the corresponding five- moving average forecast.


Example exponential smoothing forecast accuracy rmse

(20+22+...23)/12=21=F1

Example-Exponential Smoothing Forecast Accuracy - RMSE

F2= 0.3 (20)+(1-0.3) 21=20.7 with w=0.3

F2= 0.5 (20)+(1-0.5) 21=20.5 with w=0.5


Example exponential smoothing forecast accuracy rmse1
Example-Exponential Smoothing Forecast Accuracy - RMSE

F2= 0.3 (20)+(1-0.3) 21=20.7 with w=0.3

F2= 0.5 (20)+(1-0.5) 21=20.5 with w=0.5

RMSE with w=0.3 is 2.70

RMSE with w=0.5 is 2.91

Both exponential forecasts are better than the previous techniques in terms of average values.



Seasonal variation1

Actual

Trend Forecast

Ratio =

SeasonalAdjustment

Average of Ratios forEach Seasonal Period

=

Seasonal Variation

Ratio to Trend Method

AdjustedForecast

TrendForecast

SeasonalAdjustment

=


Seasonal variation2
Seasonal Variation

Ratio to Trend Method:Example Calculation for Quarter 1

Trend Forecast for 2001.1 = 11.90 + (0.394)(17) = 18.60

Seasonally Adjusted Forecast for 2001.1 = (18.60)(0.887) = 16.50

Deseasonalize data=actual sales/seasonal relative (index)


Seasonal variation3
Seasonal Variation

  • Select a representative historical data set.

  • Develop a seasonal index for each season.

  • Use the seasonal indexes to deseasonalize the data.

  • Perform linear regression analysis on the deseasonalized data.

  • Use the regression equation to compute the forecasts.

  • Use the seasonal indexes to reapply the seasonal patterns to the forecasts.


Example computer products corp
Example: Computer Products Corp.

  • Seasonalized Times Series Regression Analysis

  • An analyst at CPC wants to develop next year’s quarterly forecasts of sales revenue for CPC’s line of Epsilon Computers. The analyst believes that the most recent 8 quarters of sales (shown on the next slide) are representative of next year’s sales. Calculate the seasonal indexes





Deflating a Time Series

  • Observed values can be adjusted to base year equivalent

  • Allows uniform comparison over time

  • Deflation formula:

where

= adjusted time series value at time t

yt = value of the time series at time t

It = index value at time t


Deflating a Time Series: Example

  • Which movie made more money (in real terms)?

(Total Gross $ = Total domestic gross ticket receipts in $millions)


Deflating a Time Series: Example

  • GWTW made about twice as much as Star Wars, and about 4 times as much as Titanic when measured in equivalent dollars



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