Chapter 12 - Forecasting

Forecasting is important in the business decision-making process in which a current choice or decision has future implications:

Routine decisions very near in the futuresmall gains or lossesassume future is like the past

Business is the main user of Forecasting Methods, but other areas such as State and Federal governments and non-profit organizations (university, hospital, services) use forecasting.

Marketing and operations management is the most obvious function in business to use forecasting. A valid strategy depends on demand expectations.

Introduction to Forecasting

As business majors, you operate and make decisions within the framework of a complex, interrelated, social, economic, and competitive structure.

The success of a firm depends on its ability to compete with firms producing similar products or services from the same market.

Firms must secure information concerning potential market sales to plan effectively.

Introduction to Forecasting

Sales forecasts become the primary information input depicting the state of the environment.

The better and more complete the data, the better the decision will be.

Introduction to Forecasting

Forecasting alleviates uncertainty:Long and short term forecastsForecasts relating to industry trendsMarket research relating to consumer

surveysAdvertising & Sales promotionsDemand Anticipation Inventory levels

Introduction to Forecasting

Horizontal PatternNo trend, stationaryEqually likely chance that the next value will

be above the mean or below itStable sales, # of defects in production

process

Introduction to Forecasting

Horizontal Pattern

1 2 3 4 5 6 7 8 9 10

SeasonalFluctuations occur in certain months/quarter

during the year. Examples: weather, holidays

Introduction to Forecasting

Seasonal

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Introduction to Forecasting

Cyclical Similar to seasonal, but the length of cycle is longer

than one year: Housing starts, GNP Difficult to predict because it does not repeat itself

at constant intervals

Cyclical

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Introduction to Forecasting

TrendGeneral increase or decrease in value over

timeExamples: sales, stock

Trend

0 5 10 15 20

Accuracy of Techniques & Measurement Error

There will always be some deviation between actual and forecasted values. Our objective is to minimize the deviations with sound analysis

Errors are squared to eliminate signs and emphasize the extreme errors

Predict Actual Error Error2

3 2 1 14 2 2 4

Types of Models

Time Series Identify historical patterns and forecast into

the future. If we know that sales are 20% above average each January, the forecast for next January should be upward 20%.

This is an inappropriate method for weekly sales fluctuations that are the result of price and advertising changes.

Types of Models

Causal Assumes that the value of a certain variable is a

function of several other variables. Time Series could be considered causal since

actual values are assumed to be a function of the time period. Usually, variables other than time are used. For example, sales as a function of price and advertising.

This is a more complex method than time series.

Types of Models

Statistical Models Statistical analysis can be used to identify

patterns in the variables and in making statements about the reliability of the forecast. Confidence Intervals, R2, Test of Significance

Non-Statistical Models These models do not follow rules of statistical

analysis and probability theory. Usually, they are easy to understand and apply. They are limited because they lack guidelines.

Qualitative models

• Once a linear relationship is defined, the independent variable can be used to forecast the dependent variable.

Y^ = bo + bX

• bo is called the Y intercept - represents the value of Y when X = 0. But be cautious - this interpretation may be incorrect and difficult to estimate - many times our data does not include 0. Think of this value as representing the influences of the many other independent variables that are not included in the equation.

• bX is called the slope - represents the amount of change in Y when X increases by one unit.

Regression Analysis

Sales Advertising27 2023 2031 2545 2847 2942 2839 3145 3457 3559 3673 4184 45

Regression StatisticsMultiple R 0.964212R Square 0.929705Adjusted R Square 0.922675Standard Error 5.039375Observations 12

Tools, Data Analysis, Regression - Hint: Include labels in the input ranges to help with the interpretation! Can also include plots (not shown here)

ANOVAdf SS MS F Significance F

Regression 1 3358.714 3358.714 132.2573 4.35E-07Residual 10 253.953 25.3953Total 11 3612.667

Coefficients

Standard Error t Stat P-value

Lower 95%

Upper 95%

Intercept -23.0191 6.316228 -3.64444 0.004504 -37.0925 -8.94566Advertising 2.280186 0.198272 11.50032 4.35E-07 1.838409 2.721962

Regression Analysis

Averages

Naive models3 and 5 month moving averages

• Continually revising a forecast in light of more recent experiences. Averaging (smoothing) past values of a series in a decreasing (exponential) manner. The observations are weighted with more weight being given to the more recent observations

tF

tD

newF

FDFF

t

t

t

tttt

at valuesmoothed forecasted

periodin n observatio new

1)(0constant smoothing

periodnext for valuesmoothed

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Exponential Smoothing Methods

Forecast Errors

MAD measures forecast accuracy by averaging the absolute value of the forecast errors (n = number of errors and not sample size). Magnitude of errors.

MSE (Mean Squared Error) - each error is squared, then summed and divided by the number of observations (errors). Identifies large forecasting errors because of the squares

MAPE (Mean absolute percentage error) - percentages. Find the MAD for EACH period then divide by actual of that period and dividing the sum by the number of errors. How large the forecast errors are in comparison to the actual values.

Forecast Errors

n

CFEE

ECFE

FDE

t

ttt

n

DEMAPE

n

EMAD

n

EE

n

EMSE

tt

t

t

t

100]/||[

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2

Tracking Signals

Indicate whether a forecast method is accurately predicting.

Tracking Signal = CFE / MADIt is actually a control chart (see table

12.2 for limits)Hold-out sample – used to test forecast

before applying to practice

OMS 335 - Forecasting

Averages, Regression, Multiple Regression, Smoothing

SeasonalityMeasuring Forecast ErrorsCombining ForecastsGreat course! Lots of computer

experience in Excel and Mini-tab. 2nd Six Weeks – MW 6-9 pm