12-1 Forecasting
CHAPTER
12
Forecasting
Management Mathematics-76.
AHNAF ABBAS
12-2 Forecasting
CHAPTER
12
Objectives
1. How to Classify Forecasts
2. How to Calculate Moving Averages
3. How to Perform Exponential
Smoothing.
Management Mathematics-76.
AHNAF ABBAS
12-3 Forecasting
FORECAST:
A statement about the future value of a variable of
interest such as demand.
Forecasts affect decisions and activities throughout
an organization
Accounting, finance
Human resources
Marketing
MIS
Operations
Product / service design
12-4 Forecasting
Uses of Forecasts
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, workloads
Product/service design New products and services
12-5 Forecasting
Basic Assumptions
Assumes causal system
past ==> future
Past patterns (behavior) will continue into
J
future. O
S
Forecasts rarely perfect because of H
randomness I see that you will
I
get an A this semester.
Forecast accuracy decreases
as time horizon increases
12-6 Forecasting
Elements of a Good Forecast
Timely
Reliable Accurate
Written
12-7 Forecasting
Steps in the Forecasting Process
“The forecast”
Step 6 Monitor the forecast
Step 5 Prepare the forecast
Step 4 Gather and analyze data
Step 3 Select a forecasting technique
Step 2 Establish a time horizon
Step 1 Determine purpose of forecast
12-8 Forecasting
Naive Forecasts
Uh, give me a minute....
We sold 250 wheels last
week.... Now, next week
we should sell....
The forecast for any period equals
the previous period’s actual value.
12-9 Forecasting
Naïve Forecasts
Simple to use
Virtually no cost
Quick and easy to prepare
Data analysis is nonexistent
Easily understandable
Cannot provide high accuracy
12-10Forecasting
Types of Forecasts
Types By lead time
The time between when the forecast is
made and the future point to which it
refers.
Long-term: more than 10 years.
Medium-term: up to 5 years.
short-term: months to a year.
12-11 Forecasting
Types of Forecasts
Univariate :Using past patterns
e.g. Time series which uses historical
data assuming the future will be like the
past.
Multivariate- uses explanatory variables
to predict the future, i.e. Past
relationships between multiple variables.
Qualitative Judgmental - uses subjective
inputs
12-12Forecasting
Judgmental Forecasts (Qualitative)
Executive opinions
Sales force opinions
Consumer surveys
Outside opinion
Delphi method
Opinions of managers and staff
12-13Forecasting
Time Series Forecasts
A time series is a continuous set of observations that
are ordered in equally spaced intervals(e.g one per
month).
Basic concept of univariate forecasting:
Future values = f( Past values )
e.g. Two months average sales :
Forecast for June =
(April sales + May sales ) / 2
Univariate methods includes smoothing (averages)
and exponential smoothing.
12-14Forecasting
Multivariate Forecasts
Known as Causal methods: make projections of the
future by modeling the relationship between a series
and other series.
e.g. A forecast for furniture sales may be based on a
relationship between economic indicators such as
housing starts, personal income ,No. of new
marriages etc… :
Future values =
f( Past values, Values of other variables )
e.g. June demand = 50 + 0.2 MS + 1xAPI +0.5NH
Multivariate methods include multiple regression and
econometric.
12-15Forecasting
Monthly Sales and Forecast
2000
1800
1600
1400
Sales ($1000)
1200
1000
800
600
400
200 Monthly Sales
Forecast
0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Month
12-16Forecasting
Monthly Sales and Forecast
2000
1800
1600
1400
Sales ($1000)
1200
1000
800
600 We’ll guess same as last month
400
200 Monthly Sales
Forecast
0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Month
12-17Forecasting
Monthly Sales and Forecast
2000
1800
1600
1400
Sales ($1000)
1200
1000
800
600
400
200 Monthly Sales
Forecast
0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Month
12-18Forecasting
Monthly Sales and Forecast
2000
1800
1600
1400
Sales ($1000)
1200
1000
We’ll guess same as last month
800 plus a little more for a possible trend
600
400
200 Monthly Sales
Forecast
0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Month
12-19Forecasting
Monthly Sales and Forecast
2000
1800
1600
1400
Sales ($1000)
1200
1000
This is easy, who needs forecasting
800
600
400
200 Monthly Sales
Forecast
0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Month
12-20Forecasting
Monthly Sales and Forecast
2000
1800
1600
1400
Sales ($1000)
1200
1000
Continue with our successful method: guess
800 the same as last month plus a little more
for a possible trend
600
400
200 Monthly Sales
Forecast
0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Month
12-21Forecasting
Monthly Sales and Forecast
2000
1800
1600
1400
Sales ($1000)
1200
1000
800
600
400
200 Monthly Sales
Forecast
0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Month
12-22Forecasting
Monthly Sales and Forecast
2000
1800
1600
1400
Sales ($1000)
1200
1000
Definitely looks like a trend
800
600
400
200 Monthly Sales
Forecast
0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Month
12-23Forecasting
Monthly Sales and Forecast
2000
1800
1600
1400
Sales ($1000)
1200
1000
800
600
400
200 Monthly Sales
Forecast
0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Month
12-24Forecasting
Monthly Sales and Forecast
2000
1800
1600
1400
Sales ($1000)
1200
1000
Trend might be a tad steeper
800 than I thought
600
400
200 Monthly Sales
Forecast
0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Month
12-25Forecasting
Monthly Sales and Forecast
2000
1800
1600
1400
Sales ($1000)
1200
1000
Opps
800
600
400
200 Monthly Sales
Forecast
0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Month
12-26Forecasting
Monthly Sales and Forecast
2000
1800
1600
1400
Sales ($1000)
1200
1000
Momentary deviation,
800 trend will continue
600
400
200 Monthly Sales
Forecast
0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Month
12-27Forecasting
Monthly Sales and Forecast
2000
1800
1600
1400
Sales ($1000)
1200
1000
See, I told you this was easy!
800
600
400
200 Monthly Sales
Forecast
0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Month
12-28Forecasting
Monthly Sales and Forecast
2000
1800
1600
1400
Trend will continue
Sales ($1000)
1200
1000
800
600
400
200 Monthly Sales
Forecast
0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Month
12-29Forecasting
Monthly Sales and Forecast
2000
1800
1600
1400
Sales ($1000)
1200
1000
Opps, another momentary fluctuation:
800
600
400
200 Monthly Sales
Forecast
0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Month
12-30Forecasting
Monthly Sales and Forecast
2000
1800
1600
1400 Trend should continue
Sales ($1000)
1200
1000
800
600
400
200 Monthly Sales
Forecast
0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Month
12-31Forecasting
Monthly Sales and Forecast
2000
1800
1600
1400 Oh oh!
Sales ($1000)
1200
1000
800
600
400
200 Monthly Sales
Forecast
0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Month
12-32Forecasting
Monthly Sales and Forecast
2000
1800
1600
1400
Sales ($1000)
1200
1000 Sales has leveled off:
800
Lets average last few points
600
400
200 Monthly Sales
Forecast
0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Month
12-33Forecasting
Monthly Sales and Forecast
2000
1800
1600
1400
Sales ($1000)
1200
1000 Oh oh, maybe things are
800
going down hill
600
400
200 Monthly Sales
Forecast
0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Month
12-34Forecasting
Monthly Sales and Forecast
2000
1800
1600
1400
Sales ($1000)
1200
Let’s be conservative and
1000
Assume a negative trend
800
600
400
200 Monthly Sales
Forecast
0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Month
12-35Forecasting
Monthly Sales and Forecast
2000
1800
1600
1400
Sales ($1000)
1200
Thank goodness, we are
1000
still basically level
800
600
400
200 Monthly Sales
Forecast
0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Month
12-36Forecasting
Monthly Sales and Forecast
2000
1800
1600
1400
Sales ($1000)
1200
We’ll guess same as
1000 last month
800
600
400
200 Monthly Sales
Forecast
0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Month
12-37Forecasting
Monthly Sales and Forecast
2000
1800
1600
This stuff is easy
1400
Sales ($1000)
1200
1000
800
600
400
200 Monthly Sales
Forecast
0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Month
12-38Forecasting
Monthly Sales and Forecast
2000
1800
1600
We have for sure
1400
leveled off
Sales ($1000)
1200
1000
800
600
400
200 Monthly Sales
Forecast
0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Month
12-39Forecasting
Monthly Sales and Forecast
2000
1800
1600 Big trouble!!!
Chief forecaster Joshi and
1400
CEO Joshi1 fired!
Sales ($1000)
1200
1000
800
600
400
200 Monthly Sales
Forecast
0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Month
12-40Forecasting
Monthly Sales and Forecast
2000
1800
1600
1400 New chief forecaster points
out the obvious trend
Sales ($1000)
1200
1000
800
600
400
200 Monthly Sales
Forecast
0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Month
12-41Forecasting
Monthly Sales and Forecast
2000
1800
1600
Remarkable turnaround in sales.
1400
New CEO Joshi2 given credit
Sales ($1000)
1200
1000
800
600
400
200 Monthly Sales
Forecast
0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Month
12-42Forecasting
Monthly Sales and Forecast
2000
1800
1600
1400
Still looks like a trend to me
Sales ($1000)
1200
1000
800
600
400
200 Monthly Sales
Forecast
0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Month
12-43Forecasting
Monthly Sales and Forecast
2000
1800
1600
1400
Maybe not!
Sales ($1000)
1200
1000
800
600
400
200 Monthly Sales
Forecast
0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Month
12-44Forecasting
Monthly Sales and Forecast
2000
1800
1600
1400
Level except for anomaly
Sales ($1000)
1200
1000
800
600
400
200 Monthly Sales
Forecast
0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Month
12-45Forecasting
Monthly Sales and Forecast
2000
1800
1600
1400
Have things turned around?
Sales ($1000)
1200
1000
800
600
400
200 Monthly Sales
Forecast
0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Month
12-46Forecasting
Monthly Sales and Forecast
2000
1800
1600
1400
I’ll hedge my bets
Sales ($1000)
1200
1000
800
600
400
200 Monthly Sales
Forecast
0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Month
12-47Forecasting
Monthly Sales and Forecast
2000
1800 Things have turned around.
1600 Perhaps Joshi2 truly is a genius
1400
Sales ($1000)
1200
1000
800
600
400
200 Monthly Sales
Forecast
0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Month
12-48Forecasting
Monthly Sales and Forecast
2000
1800
1600
Trend up!
1400
Sales ($1000)
1200
1000
800
600
400
200 Monthly Sales
Forecast
0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Month
12-49Forecasting
Monthly Sales and Forecast
2000
1800
1600
Not bad!
1400
Sales ($1000)
1200
1000
800
600
400
200 Monthly Sales
Forecast
0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Month
12-50Forecasting
Monthly Sales and Forecast
2000
1800
Revise trend a tad
1600
1400
Sales ($1000)
1200
1000
800
600
400
200 Monthly Sales
Forecast
0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Month
12-51Forecasting
Monthly Sales and Forecast
2000
1800 Joshi2 makes cover of Fortune
1600
1400
Sales ($1000)
1200
1000
800
600
400 Joshi2
200
Joshi1 Monthly Sales
Forecast
0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Month
12-52Forecasting
Monthly Sales and Forecast
2000
1800 This is easy!!
1600
1400
Sales ($1000)
1200
1000
800
600
400
200 Monthly Sales
Forecast
0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Month
12-53Forecasting
Monthly Sales and Forecast
2000
1800
No big deal,
1600 trend continues
1400
Sales ($1000)
1200
1000
800
(in an unrelated matter
Joshi2 cashes out
600
stock options)
400
200 Monthly Sales
Forecast
0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Month
12-54Forecasting
Monthly Sales and Forecast
2000
1800
1600
1400
Sales ($1000)
1200
1000
800
600
400
200 Monthly Sales
Forecast
0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Month
12-55Forecasting
Monthly Sales and Forecast
2000
1800
1600
1400
Sales ($1000)
1200
1000
800 Heads will surely
roll soon
600
400
200 Monthly Sales
Forecast
0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Month
12-56Forecasting
Monthly Sales and Forecast
2000
1800
1600
1400
Sales ($1000)
1200
1000
800 Let’s be cautiously
optimistic
600
400
200 Monthly Sales
Forecast
0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Month
12-57Forecasting
Monthly Sales and Forecast
2000
1800
Joshi2 called
1600 before board
1400
Sales ($1000)
1200
1000
800
600
400
200 Monthly Sales
Forecast
0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Month
12-58Forecasting
Monthly Sales and Forecast
2000
1800
1600
1400
Sales ($1000)
1200
1000
800
600
400
200 Monthly Sales
Forecast
0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Month
12-59Forecasting
Monthly Sales and Forecast
2000
1800 Perhaps we over
1600 reacted
1400
Sales ($1000)
1200
1000
800
600
400
200 Monthly Sales
Forecast
0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Month
12-60Forecasting
Monthly Sales and Forecast
2000
1800
1600
1400
Sales ($1000)
1200
1000
800
600 We will guess level
400
200 Monthly Sales
Forecast
0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Month
12-61Forecasting
Monthly Sales and Forecast
2000
1800
1600
1400
Sales ($1000)
1200
1000
800
600 Back to normal!
400
200 Monthly Sales
Forecast
0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Month
12-62Forecasting
Monthly Sales and Forecast
2000
1800
1600
1400
Sales ($1000)
1200
1000
800
600
400
200 Monthly Sales
Forecast
0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Month
12-63Forecasting
Monthly Sales and Forecast
2000
1800 Joshi2 fired!
1600
1400
Sales ($1000)
1200
1000
800
600
400
200 Monthly Sales
Forecast
0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Month
12-64Forecasting
Structure of a Time Series
Trend patterns- general increase or decrease in a
time series that lasts for certain period.
population changes,changes in economic conditions..
Seasonality – results from the events that are
periodic.Common seasonal influences : climate
,human habits ,holidays,….
Cycle – wavelike variations of more than one year’s
duration.
economic and business expansions ,contractions.
Random variations - caused by chance,many
influences that act independently to yield non
repeating patterns.
12-65Forecasting
Forecast Variations
Figure 3.1
Irregular
variatio
n
Trend
Cycles
90
89
88
Seasonal variations
12-66Forecasting
Statistical Fundamentals 4 Forecasting
Importance of Pattern :
Actual value = Pattern + Error
Predicting values using Mean, Median or Mode
Mean : arithmetic average ,measures that value about
which 50% of deviations are above and 50% are
below.i.e. Sum(Deviations) = 0
e.g. Time t = 1 2 3 4 5 6 7 (seven months)
Value X=11 4 5 12 9 2 6; X = sales
Mean Sales = 7
Sum(Deviations) = 0
12-67Forecasting
Statistical Fundamentals 4 Forecasting
The Median : 50% of values are above and 50%
are below.
e.g. 2 4 5 6 9 11 12
Median = 6
When an even number of observations exists,
Median = mean of middle two values.
The Mode : is the number or group of numbers
that occur most often.
12-68Forecasting
Statistical Fundamentals 4 Forecasting
Comparison of Measures:
The Mean : Because it is the center of deviations, the
mean is greatly influenced by the
extreme values.
e.g. A very large deviation (Outlier) will greatly affect
the value of the mean. It is not appropriate without
adjusting the outlier.
The Median : is not affected by extreme values.
Useful in describing highly skewed data.
The Mode: is not affected by extremes.
12-69Forecasting
Statistical Fundamentals 4 Forecasting
Example:
Consider this sales time series for forecasting
Period 9 :
Period t = 1 2 3 4 5 6 7 8
Value X = 100 70 90 110 1200 110 130 80
Mean = 236.25 ; Median = 105 ; Mode = 110.
Best estimate = 130 ;
Mean = 102.5 ; Median = 105 ; Mode = 110
&130
12-70Forecasting
Statistical Fundamentals 4 Forecasting
Measuring Errors-Standard deviation & MAD
Standard Deviation: The square root of the mean of the
squared deviations.
For a population : (RMS)
Known as Root Mean Square Error
( X t ) 2
For a Sample: N
( Xt X ) 2
S
n1
12-71Forecasting
Statistical Fundamentals 4 Forecasting
Mean Absolute Deviation - MAD
MAD =
Xt X
n
Comparison of Error Measures:
MAD and Standard deviation are equivalent measures
of dispersion.
Despite the popularity of MAD , standard deviation is
the preferred measure in forecasting.The more high
the RMS& MAD ,the better the Forecast.
12-72Forecasting
Univariate Methods
Moving average
Weighted moving average
Exponential smoothing
Are effective methods for short term forecasts
(series that do not have cyclical or seasonal
patterns)
12-73Forecasting
Univariate Methods-Moving Averages
Moving averages: Future value will equal an
average of past values.
Useful in random series because it averages
or smoothes the most recent actual values to
remove the unwanted randomness.
Remember :
Forecast error = Actual - Forecast
12-74Forecasting
Univariate Methods-Moving Averages
Example:
Month t Actual MA2 Error MA4 Error
Jan 1 120
Feb 2 124
Mar 3 122 122 0.00
April 4 123 123 0.00
May 5 125 122.5 2.50 122.25 2.75
Jun 6 128 124 4.00 123.5 4.50
Jul 7 129 126.5 2.5 124.5 4.50
Aug 8 127 128.5 -1.5 126.5 0.75
12-75Forecasting
Techniques for Averaging
1. Each new forecast moves ahead one period by
adding the newest actual and dropping the oldest
actual.
MA4(May) = (Jan+Feb+Mar+Apr)/4
MA4(Jun) = (Feb+Mar+Apr+May)/4
2. Response to Recent data:
MA’s Forecasts can be made less responsive to recent
data by increasing the number of past observations.
MA’s Forecasts can be made more responsive to
recent data by decreasing the number of past
observations.
12-76Forecasting
Simple Moving Average
Actual
MA5
47
45
43
41
39
37 MA3
35
1 2 3 4 5 6 7 8 9 10 11 12
n
1 Ai
i=
MAn =
n
12-77Forecasting
Weighted Moving Averages
Weight 0.10 0.20 0.30 0.40
Month 1 2 3 4_ 5
Sales 100 90 105 95 ?
F5 = 0.40(95) + 0.30(105) + 0.20(90) +
0.10(100) = 97.5 units
12-78Forecasting
Exponential Smoothing
Ft At 1 ( 1 )Ft 1
Ft = Exponentially smoothed forecast for period t.
At -1= Actual in the prior period.
Ft -1 = Exponentially smoothed forecast of the prior
period
= Smoothing constant. ( 0 < < 1)
Smoothing constant determines the weight given to
the most recent observations, it controls the rate of
smoothing or averaging.
12-79Forecasting
Exponential Smoothing
Example: suppose a company desires to forecast
demand for a product with = 0.3 .
Last month’s actual = 1000 and the forecast was
900, the forecast for this month:
Ft = (0.3)(1000) + (1-0.3)(900) = 930
Alpha provides the relative weight given to each
term of the equation. With alpha = 0.3 ,the
forecast is 30% of the most recent Actual and
70% of the most recent Forecasted value.
12-80Forecasting
Forecast Accuracy
The fitted region is where we assume the data is known and
we fit the model to this data.
The forecast region is where we assume the data is not
known and has to be forecast using the model derived from
the fitted region.
Mean Absolute Deviation (MAD)
Average absolute error
Mean Squared Error (MSE)
Average of squared error
Mean Absolute Percent Error (MAPE)
Average absolute percent error
12-81Forecasting
MAD, MSE, and MAPE
Actual forecast
MAD =
n
2
( Actual forecast)
MSE =
n-1
( Actual forecas / Actual*100)
MAPE =
t
n
12-82Forecasting
Absolute Error Measures
et = At - Ft
Month Actual Forec. Error. |Error| Error2 St. Dev.
Jan. 10 15 -5 5 25 6.25
Feb. 12 14 -2 2 4 4.38
Mar. 14 13.6 0.4 0.4 0.16 3.09
Apr. 13 13.68 -0.68 0.68 0.46 2.53
49 56.28 -7.28 8.08 29.62
et et
ME : mean error = = -1.82; MAD = = 0.5
n n
SSE : sum of square errors = et2= 29.62
12-83Forecasting
Exponential Smoothing
Steps in Using Exponential smoothing:
1. Choice of a smoothing constant:The best alphas should
be chosen on the basis of Minimal sum of squared
errors.
2. An initial forecast: the first actual value is chosen as
the forecast for the second period.
Example : Period Actual Forecast =0.3
1 900
2 1000 900
F3 = A2 +(1 - )F2 = (0.3)(1000) + (1 -0.3)(900)=930
12-84Forecasting
Example - Exponential Smoothing
Period Actual Alpha = 0.1 Error Alpha = 0.4 Error
1 42
2 40 42 -2.00 42 -2
3 43 41.8 1.20 41.2 1.8
4 40 41.92 -1.92 41.92 -1.92
5 41 41.73 -0.73 41.15 -0.15
6 39 41.66 -2.66 41.09 -2.09
7 46 41.39 4.61 40.25 5.75
8 44 41.85 2.15 42.55 1.45
9 45 42.07 2.93 43.13 1.87
10 38 42.36 -4.36 43.88 -5.88
11 40 41.92 -1.92 41.53 -1.53
12 41.73 40.92
12-85Forecasting
Picking a Smoothing Constant
Actual
50
.4
.1
Demand
45
40
35
1 2 3 4 5 6 7 8 9 10 11 12
Period
12-86Forecasting
Example
Period Actual Forecast (A-F) |A-F| (A-F)^2 (|A-F|/Actual)*100
1 217 215 2 2 4 0.92
2 213 216 -3 3 9 1.41
3 216 215 1 1 1 0.46
4 210 214 -4 4 16 1.90
5 213 211 2 2 4 0.94
6 219 214 5 5 25 2.28
7 216 217 -1 1 1 0.46
8 212 216 -4 4 16 1.89
-2 22 76 10.26
MAD= 2.75
MSE= 10.86
MAPE= 1.28
12-87Forecasting
The Smoothing Constant
1. The weights of the past Actuals are determined
by alpha:
Most recent :
One period old : (1 )1
Two periods old : (1 ) 2
etc…
2. The alpha that yields the most accurate forecast
is the one that achieves the lowest MSE.
12-88Forecasting
The Smoothing Constant
3. If = 1 ,then F = A
t t – 1 (zero smoothing)
4. Relation with number of periods :
2
N 1
e.g. N = 19 , then 0.1
Useful when converting from or to MA’s
Response to recent data:
More responsive : higher alpha.
Less responsive : lower alpha.
12-89Forecasting
Exercises
12-90Forecasting
Exercises
12-91Forecasting
Exercises