McGraw-Hill/Irwin Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.
2.22.2
Forecasting
OUTLINEOUTLINE
Introduction Steps in forecasting process Types of forecasting Naïve Forecasts Averaging Forecasts Linear Trend Forecasts Associative Forecasts Forecast Accuracy
3-2
Learning ObjectivesLearning Objectives
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.
Learning ObjectivesLearning Objectives
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.
3-5
FORECAST: A statement about the future value of a
variable of interest such as demand. Forecasting is used to make informed
decisions. Long-range Short-range
3-6
ForecastsForecasts
Forecasts affect decisions and activities throughout an organization Accounting, finance Human resources Marketing MIS Operations Product/service design
Accounting Cost/profit estimates
Finance Cash flow and funding
Human resources Hiring/recruiting/training
Marketing Pricing, promotion, strategy
MIS IT/IS systems, services
Operations Schedules, MRP, workloads
Product/service design New products and services
Uses of ForecastsUses of Forecasts
I see that you willget an A this semester.
Assumes causal systempast ==> future
Forecasts rarely perfect because of randomness
Forecasts more accurate forgroups vs. individuals
Forecast accuracy decreases as time horizon increases
Features of ForecastsFeatures of Forecasts
3-9
Elements of a Good ForecastElements of a Good Forecast
Timely
AccurateReliable
Mea
ningfu
l
Written
Easy
to u
se
Steps in the Forecasting ProcessSteps in the Forecasting Process
Step 1 Determine purpose of forecast
Step 2 Establish a time horizon
Step 3 Select a forecasting technique
Step 4 Obtain, clean and analyze data
Step 5 Make the forecast
Step 6 Monitor the forecast
“The forecast”
Types of ForecastsTypes of Forecasts
Judgmental: uses subjective inputs
Time series: uses historical data, assuming the future will be like the past
Associative models: uses explanatory variables to predict the future
Judgmental ForecastsJudgmental Forecasts
Executive opinions
Sales force opinions
Consumer surveys
Outside opinion
Delphi method Opinions of managers and staff Achieves a consensus forecast
Time Series ForecastsTime Series Forecasts
Trend: long-term movement in data Seasonality: short-term regular
variations in data Cycles: wavelike variations of more than
one year’s duration Irregular variations: caused by unusual
circumstances Random variations: caused by chance
Forecast VariationsForecast Variations
Trend
Irregularvariation
Seasonal variations
908988
Figure 3.1
Cycles
Naive ForecastsNaive Forecasts
Uh, give me a minute.... We sold 250 wheels lastweek.... Now, next week we should sell....
The forecast for any period equals the previous period’s actual value.
Simple to use Virtually no cost Quick and easy to prepare Data analysis is nonexistent Easily understandable Cannot provide high accuracy Can be a standard for accuracy
Naive ForecastsNaive 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))
Uses of Naive ForecastsUses of Naive Forecasts
Techniques for AveragingTechniques for Averaging
Moving average
Weighted moving average
Exponential smoothing
Moving AveragesMoving Averages
Moving average: A technique that averages a number of recent actual values, updated as new values become available.
Weighted moving average: More recent values in a series are given more weight in computing the forecast.
Ft = MAn= n
At-n + … At-2 + At-1
Ft = WMAn= n
wnAt-n + … wn-1At-2 + w1At-1
Simple Moving AverageSimple Moving Average
35
37
39
41
43
45
47
1 2 3 4 5 6 7 8 9 10 11 12
Actual
MA3
MA5
Ft = MAn= n
At-n + … At-2 + At-1
Exponential SmoothingExponential Smoothing
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.
Ft = Ft-1 + (At-1 - Ft-1)
Exponential SmoothingExponential Smoothing
Weighted averaging method based on previous forecast plus a percentage of the forecast error
A-F is the error term, is the % feedback
Ft = Ft-1 + (At-1 - Ft-1)
Period Actual Alpha = 0.1 Error Alpha = 0.4 Error1 422 40 42 -2.00 42 -23 43 41.8 1.20 41.2 1.84 40 41.92 -1.92 41.92 -1.925 41 41.73 -0.73 41.15 -0.156 39 41.66 -2.66 41.09 -2.097 46 41.39 4.61 40.25 5.758 44 41.85 2.15 42.55 1.459 45 42.07 2.93 43.13 1.87
10 38 42.36 -4.36 43.88 -5.8811 40 41.92 -1.92 41.53 -1.5312 41.73 40.92
Example 3: Exponential SmoothingExample 3: Exponential Smoothing
Picking a Smoothing ConstantPicking a Smoothing Constant
35
40
45
50
1 2 3 4 5 6 7 8 9 10 11 12
Period
Dem
and .1
.4
Actual
Common Nonlinear TrendsCommon Nonlinear Trends
Parabolic
Exponential
Growth
Figure 3.5
Linear Trend EquationLinear 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
Ft = a + bt
0 1 2 3 4 5 t
Ft
Calculating a and bCalculating a and b
b = n (ty) - t y
n t2 - ( t)2
a = y - b t
n
Linear Trend Equation ExampleLinear Trend Equation Example
t yW e e k t 2 S a l e s t y
1 1 1 5 0 1 5 02 4 1 5 7 3 1 43 9 1 6 2 4 8 64 1 6 1 6 6 6 6 45 2 5 1 7 7 8 8 5
t = 1 5 t 2 = 5 5 y = 8 1 2 t y = 2 4 9 9( t ) 2 = 2 2 5
Linear Trend CalculationLinear Trend Calculation
y = 143.5 + 6.3t
a = 812 - 6.3(15)
5 =
b = 5 (2499) - 15(812)
5(55) - 225 =
12495-12180
275 -225 = 6.3
143.5
Techniques for SeasonalityTechniques for Seasonality
Seasonal variations Regularly repeating movements in series values
that can be tied to recurring events
Seasonal relative Percentage of average or trend
Centered moving average A moving average positioned at the center of the
data that were used to compute it
Associative ForecastingAssociative Forecasting
Predictor variables: used to predict values of variable interest
Regression: technique for fitting a line to a set of points
Least squares line: minimizes sum of squared deviations around the line
Linear Model Seems ReasonableLinear Model Seems Reasonable
A straight line is fitted to a set of sample points.
0
10
20
30
40
50
0 5 10 15 20 25
X Y7 152 106 134 15
14 2515 2716 2412 2014 2720 4415 347 17
Computedrelationship
Linear Regression AssumptionsLinear Regression Assumptions
Variations around the line are random Deviations around the line normally distributed Predictions are being made only within the
range of observed values For best results:
Always plot the data to verify linearity Check for data being time-dependent Small correlation may imply that other variables
are important
Forecast AccuracyForecast 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
MAD, MSE, and MAPEMAD, MSE, and MAPE
MAD = Actual forecast
n
MSE = Actual forecast)
-1
2
n
(
MAPE = Actual forecas
t
n
/ Actual*100)
MAD, MSE, and MAPEMAD, MSE, and MAPE
MAD Easy to compute Weights errors linearly
MSE Squares error More weight to large errors
MAPE Puts errors in perspective
Example 10Example 10
Period Actual Forecast (A-F) |A-F| (A-F)^2 (|A-F|/Actual)*1001 217 215 2 2 4 0.922 213 216 -3 3 9 1.413 216 215 1 1 1 0.464 210 214 -4 4 16 1.905 213 211 2 2 4 0.946 219 214 5 5 25 2.287 216 217 -1 1 1 0.468 212 216 -4 4 16 1.89
-2 22 76 10.26
MAD= 2.75MSE= 10.86
MAPE= 1.28
Controlling the ForecastControlling the Forecast
Control chart A visual tool for monitoring forecast errors Used to detect non-randomness in errors
Forecasting errors are in control if All errors are within the control limits No patterns, such as trends or cycles, are
present
Sources of Forecast ErrorsSources of Forecast Errors
Model may be inadequate Irregular variations Incorrect use of forecasting technique