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Chapter 3
Forecasting
Instructor Slides
You should be able to:1. List the elements of a good forecast
2. Outline the steps in the forecasting process
3. Describe at least three qualitative forecasting techniques and the advantages and disadvantages of each
4. Compare and contrast qualitative and quantitative approaches to forecasting
5. Know definition of time-series behaviors.
6. Describe averaging techniques (moving average, weighted moving average, and exponential smoothing) and linear regression analysis, and solve typical problems
7. Explain and calculate three measures of forecast accuracy (MAD, MSE, MAPE)
8. Assess the major factors and trade-offs to consider when choosing a forecasting technique
Chapter 3: Learning Objectives
3-2
You don’t need to prepare following topics for exam 1. Trend-adjusted exponential smoothing
2. Techniques for seasonality (knowing definition of seasonality is enough)
3. Techniques for cycles (knowing definition of cycles is enough)
4. For linear regression calculation (a and b, correlation), formula will be provided in exam (if there’re questions), but you need to memorize three accuracy measures, and three averaging technique formula.
5. Monitoring the forecast (just ignore this)
Instructor Slides 3
Forecast
Forecast – a statement about the future value of a variable of interest
We make forecasts about such things as weather, demand, and resource availability
Forecasts are an important element in making informed decisions
Instructor Slides 3-4
Two Important Aspects of Forecasts
Expected level of demand (or other variable)
The level of demand may be a function of some structural variation such as trend or seasonal variation
Accuracy
Related to the potential size of forecast error
Instructor Slides 3-5
Features Common to All Forecasts
Instructor Slides
1. Techniques assume some underlying causal system that existed in the past will persist into the future
2. Forecasts are not perfect
3. Forecasts for groups of items are more accurate than those for individual items (cancelling effect)
4. Forecast accuracy decreases as the forecasting horizon increases
3-6
Elements of a Good Forecast
Instructor Slides
The forecast should be timely should be accurate should be reliable should be expressed in meaningful units should be in writing technique should be simple to understand and use should be cost effective
3-7
Steps in the Forecasting Process
Instructor Slides
1. Determine the purpose of the forecast
2. Establish a time horizon
3. Obtain, clean, and analyze appropriate data
4. Select a forecasting technique
5. Make the forecast
6. Monitor the forecast
3-8
Forecast Accuracy and Control
Forecasters want to minimize forecast errors
It is nearly impossible to correctly forecast real-world variable values on a regular basis
So, it is important to provide an indication of the extent to which the forecast might deviate from the value of the variable that actually occurs
Forecast accuracy should be an important forecasting technique selection criterion
Error = Actual – Forecast
If errors fall beyond acceptable bounds, corrective action may be necessary
Instructor Slides 3-9
Forecast Accuracy Metrics
n
100
Actual
ForecastActual
MAPE t
tt
Instructor Slides
n
tt ForecastActualMAD
2
tt
1
ForecastActualMSE
n
MAD weights all errors evenly
MSE weights errors according to their squared values
MAPE weights errors according to relative error
3-10
Forecast Error Calculation
PeriodActual
(A)Forecast
(F)(A-F) Error |Error| Error2 [|Error|/Actual]x100
1 107 110 -3 3 9 2.80%
2 125 121 4 4 16 3.20%
3 115 112 3 3 9 2.61%
4 118 120 -2 2 4 1.69%
5 108 109 1 1 1 0.93%
Sum 13 39 11.23%
n = 5 n-1 = 4 n = 5
MAD MSE MAPE
= 2.6 = 9.75 = 2.25%Instructor Slides3-11
Forecasting Approaches
Instructor Slides
Qualitative Forecasting Qualitative techniques permit the inclusion of soft information such as:
Human factors
Personal opinions
Hunches
These factors are difficult, or impossible, to quantify
Quantitative Forecasting
Quantitative techniques involve either the projection of historical data or the development of associative methods that attempt to use causal variables to make a forecast
These techniques rely on hard data
3-12
Forecasting Approaches (another classification)*
Judgmental forecasts: forecast that use subjective inputs such as opinions from consumer surveys, sales staff, managers, executives, and experts.
Time-series forecasts: forecasts that project patterns identified in recent time-series observations.
Associative model: forecasting technique that uses explanatory variables to predict future demand.
Instructor Slides 13
Time-Series Forecasts
Forecasts that project patterns identified in recent time-series observations
Time-series - a time-ordered sequence of observations taken at regular time intervals
Assume that future values of the time-series can be estimated from past values of the time-series
Instructor Slides 3-14
Time-Series Behaviors
Instructor Slides
Trend-long-term upward of downward movement
Seasonality-short-term regular variations related to the calendar or time of day
Cycles-wavelike variations lasting more than one year
Irregular variations-caused by unusual circumstances, not reflective of typical behavior
Random variation-residual variations after all other behaviors are accounted for
3-15
Time-Series Behaviors
Instructor Slides 3-16
Time-Series Forecasting - Naïve Forecast
Instructor Slides
Naïve Forecast
Uses a single previous value of a time series as the basis for a forecast
The forecast for a time period is equal to the previous time period’s value
Can be used with
a stable time series
seasonal variations
trend
3-17
Time-Series Forecasting – Averaging (Smoothing)
Instructor Slides
These techniques work best when a series tends to vary about an average
Averaging techniques smooth variations in the data
They can handle step changes or gradual changes in the level of a series
Techniques
1. Moving average
2. Weighted moving average
3. Exponential smoothing
3-18
Moving Average
Technique that averages a number of the most recent actual values in generating a forecast
Instructor Slidesaverage moving in the periods ofNumber
1 periodin valueActual
average moving period MA
period for timeForecast
where
MA
1
1
n
tA
n
tF
n
AF
t
n
t
n
iit
nt
3-19
Moving Average
Instructor Slides
As new data become available, the forecast is updated by adding the newest value and dropping the oldest and then re-computing the average
The number of data points included in the average determines the model’s sensitivity
Fewer data points used-- more responsive
More data points used-- less responsive
3-20
Weighted Moving Average
The most recent values in a time series are given more weight in computing a forecast
The choice of weights, w, is somewhat arbitrary and involves some trial and error
Instructor Slides
etc. ,1 periodfor valueactual the , periodfor valueactual the
etc. ,1 periodfor weight , periodfor weight
where
)(...)()(
1
1
11
tAtA
twtw
AwAwAwF
tt
tt
ntntttttt
3-21
Exponential Smoothing
A weighted averaging method that is based on the previous forecast plus a percentage of the forecast error
Instructor Slides
period previous thefrom salesor demand Actual
constant Smoothing=
period previous for theForecast
periodfor Forecast
where
)(
1
1
111
t
t
t
tttt
A
F
tF
FAFF
3-22
Techniques for Trend
Instructor Slides
Linear trend equation
Non-linear trends
3-23
Linear Trend
A simple data plot can reveal the existence and nature of a trend
Linear trend equation
Instructor Slides
Ft a bt
where
Ft Forecast for period t
a Value of Ft at t 0
b Slope of the line
t Specified number of time periods from t 0
3-24
Estimating slope and intercept
Instructor Slides
Slope and intercept can be estimated from historical data
b n ty t yn t 2 t
2
a y b t
n or y bt
where
n Number of periods
y Value of the time series
3-25
Techniques for Seasonality*
Instructor Slides
Seasonality – regularly repeating movements in series values that can be tied to recurring events
Expressed in terms of the amount that actual values deviate from the average value of a series
Models of seasonality Additive
Seasonality is expressed as a quantity that gets added to or subtracted from the time-series average in order to incorporate seasonality
Multiplicative
Seasonality is expressed as a percentage of the average (or trend) amount which is then used to multiply the value of a series in order to incorporate seasonality
3-26
Models of Seasonality
Instructor Slides 3-27
Seasonal Relatives
Seasonal relatives The seasonal percentage used in the multiplicative
seasonally adjusted forecasting model
Using seasonal relatives To deseasonalize data
Done in order to get a clearer picture of the nonseasonal (e.g., trend) components of the data series
Divide each data point by its seasonal relative
To incorporate seasonality in a forecast
1. Obtain trend estimates for desired periods using a trend equation
2. Add seasonality by multiplying these trend estimates by the corresponding seasonal relative
Instructor Slides3-28
Techniques for Cycles*
Instructor Slides
Cycles are similar to seasonal variations but are of longer duration
Explanatory approach Search for another variable that relates to, and leads, the
variable of interest
Housing starts precede demand for products and services directly related to construction of new homes
If a high correlation can be established with a leading variable, an equation can be developed that describes the relationship, enabling forecasts to be made
3-29
Associative Forecasting Techniques
Instructor Slides
Associative techniques are based on the development of an equation that summarizes the effects of predictor variables
Predictor variables - variables that can be used to predict values of the variable of interest
Home values may be related to such factors as home and property size, location, number of bedrooms, and number of bathrooms
3-30
Simple Linear Regression
Instructor Slides
Regression - a technique for fitting a line to a set of data points
Simple linear regression - the simplest form of regression that involves a linear relationship between two variables
The object of simple linear regression is to obtain an equation of a straight line that minimizes the sum of squared vertical deviations from the line (i.e., the least squares criterion)
3-31
Least Squares Line
Instructor Slides
nsobservatio paired ofNumber
where
or
and
intercept) at the line theofheight the(i.e., 0 when of Value
line theof Slope
variablent)(independePredictor
variable)(dependent Predicted
where
22
n
xbyn
xbya
xxn
yxxynb
yxya
b
x
y
bxay
c
c
c
3-32
Correlation Coefficient
Correlation, r A measure of the strength and direction of relationship
between two variables
Ranges between -1.00 and +1.00
r2, square of the correlation coefficient (only in 2 variable case) A measure of the percentage of variability in the values
of y that is “explained” by the independent variable
Ranges between 0 and 1.00Instructor Slides
2222
yynxxn
yxxynr
3-33
Simple Linear Regression Assumptions
1. Variations around the line are random
2. Deviations around the average value (the line) should be (approximately) normally distributed
3. Predictions are made only within the range of observed values
Instructor Slides 3-34
Issues to consider*
Instructor Slides
Always plot the line to verify that a linear relationship is appropriate
The data may be time-dependent.
If they are
use analysis of time series
use time as an independent variable in a multiple regression analysis
A small correlation may indicate that other variables are important
3-35
Choosing a Forecasting Technique
Factors to consider
Cost
Accuracy
Availability of historical data
Availability of forecasting software
Time needed to gather and analyze data and prepare a forecast
Forecast horizon
Instructor Slides 3-36
Using Forecast Information
Instructor Slides
Reactive approach View forecasts as probable future demand
React to meet that demand
Proactive approach Seeks to actively influence demand
Advertising
Pricing
Product/service modifications
Generally requires either an explanatory model or a subjective assessment of the influence on demand
3-37
Excel Demo
Instructor Slides 38