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

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t

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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

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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

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where

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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

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where

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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