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Forecasting Prediction is very difficult, especially if it's about
Forecasting Prediction is very difficult, especially if it's about
Forecasting Prediction is very difficult, especially if it's about
Forecasting Prediction is very difficult, especially if it's about
Objectives
Objectives
What is forecasting
What is forecasting
Why is forecasting important
Why is forecasting important
What is forecasting all about
What is forecasting all about
Whats Forecasting All About
Whats Forecasting All About
Some general characteristics of forecasts
Some general characteristics of forecasts
Key issues in forecasting
Key issues in forecasting
Example: Mercedes E-class vs
Example: Mercedes E-class vs
What should we consider when looking at past demand data
What should we consider when looking at past demand data
Some Important Questions
Some Important Questions
Types of forecasting methods
Types of forecasting methods
Qualitative forecasting methods
Qualitative forecasting methods
Quantitative forecasting methods
Quantitative forecasting methods
How should we pick our forecasting model
How should we pick our forecasting model
Time Series: Moving average
Time Series: Moving average
Time series: simple moving average
Time series: simple moving average
Example: forecasting sales at Kroger
Example: forecasting sales at Kroger
What if we use a 3-month simple moving average
What if we use a 3-month simple moving average
5-month average smoothes data more; 3-month average more responsive
5-month average smoothes data more; 3-month average more responsive
Stability versus responsiveness in moving averages
Stability versus responsiveness in moving averages
Time series: weighted moving average
Time series: weighted moving average
Why do we need the WMA models
Why do we need the WMA models
Example: Kroger sales of bottled water
Example: Kroger sales of bottled water
6-month simple moving average
6-month simple moving average
What if we use a weighted moving average
What if we use a weighted moving average
How do we choose weights
How do we choose weights
Time Series: Exponential Smoothing (ES)
Time Series: Exponential Smoothing (ES)
Why use exponential smoothing
Why use exponential smoothing
Exponential smoothing: the method
Exponential smoothing: the method
Example: bottled water at Kroger
Example: bottled water at Kroger
Example: bottled water at Kroger
Example: bottled water at Kroger
Impact of the smoothing constant
Impact of the smoothing constant
Trend
Trend
Impact of trend
Impact of trend
Exponential smoothing with trend
Exponential smoothing with trend
Example: bottled water at Kroger
Example: bottled water at Kroger
Exponential Smoothing with Trend
Exponential Smoothing with Trend
Linear regression in forecasting
Linear regression in forecasting
Example: do people drink more when its cold
Example: do people drink more when its cold
The best line is the one that minimizes the error
The best line is the one that minimizes the error
Least Squares Method of Linear Regression
Least Squares Method of Linear Regression
What does that mean
What does that mean
Least Squares Method of Linear Regression
Least Squares Method of Linear Regression
How can we compare across forecasting models
How can we compare across forecasting models
Measuring Accuracy: MFE
Measuring Accuracy: MFE
Measuring Accuracy: MAD
Measuring Accuracy: MAD
MFE & MAD: A Dartboard Analogy
MFE & MAD: A Dartboard Analogy
An Analogy (contd)
An Analogy (contd)
MFE & MAD: An Analogy
MFE & MAD: An Analogy
Key Point
Key Point
Measuring Accuracy: Tracking signal
Measuring Accuracy: Tracking signal
Example: bottled water at Kroger
Example: bottled water at Kroger
Bottled water at Kroger: compare MAD and TS
Bottled water at Kroger: compare MAD and TS
Which Forecasting Method Should You Use
Which Forecasting Method Should You Use

: Forecasting. : dcom. : Forecasting.ppt. zip-: 221 .

Forecasting

Forecasting.ppt
1 Forecasting Prediction is very difficult, especially if it's about

Forecasting Prediction is very difficult, especially if it's about

the future. Nils Bohr

2 Forecasting Prediction is very difficult, especially if it's about
3 Objectives

Objectives

Give the fundamental rules of forecasting Calculate a forecast using a moving average, weighted moving average, and exponential smoothing Calculate the accuracy of a forecast

4 What is forecasting

What is forecasting

Forecasting is a tool used for predicting future demand based on past demand information.

5 Why is forecasting important

Why is forecasting important

Demand for products and services is usually uncertain. Forecasting can be used for Strategic planning (long range planning) Finance and accounting (budgets and cost controls) Marketing (future sales, new products) Production and operations

6 What is forecasting all about

What is forecasting all about

We try to predict the future by looking back at the past

Actual demand (past sales) Predicted demand

7 Whats Forecasting All About

Whats Forecasting All About

From the March 10, 2006 WSJ: Ahead of the Oscars, an economics professor, at the request of Weekend Journal, processed data about this year's films nominated for best picture through his statistical model and predicted with 97.4% certainty that "Brokeback Mountain" would win. Oops. Last year, the professor tuned his model until it correctly predicted 18 of the previous 20 best-picture awards; then it predicted that "The Aviator" would win; "Million Dollar Baby" won instead. Sometimes models tuned to prior results don't have great predictive powers.

8 Some general characteristics of forecasts

Some general characteristics of forecasts

Forecasts are always wrong Forecasts are more accurate for groups or families of items Forecasts are more accurate for shorter time periods Every forecast should include an error estimate Forecasts are no substitute for calculated demand.

9 Key issues in forecasting

Key issues in forecasting

A forecast is only as good as the information included in the forecast (past data) History is not a perfect predictor of the future (i.e.: there is no such thing as a perfect forecast)

REMEMBER: Forecasting is based on the assumption that the past predicts the future! When forecasting, think carefully whether or not the past is strongly related to what you expect to see in the future

10 Example: Mercedes E-class vs

Example: Mercedes E-class vs

M-class Sales

Question: Can we predict the new model M-class sales based on the data in the the table?

Answer: Maybe... We need to consider how much the two markets have in common

Month

E-class Sales

M-class Sales

Jan

23,345

-

Feb

22,034

-

Mar

21,453

-

Apr

24,897

-

May

23,561

-

Jun

22,684

-

Jul

?

?

11 What should we consider when looking at past demand data

What should we consider when looking at past demand data

Trends Seasonality Cyclical elements Autocorrelation Random variation

12 Some Important Questions

Some Important Questions

What is the purpose of the forecast? Which systems will use the forecast? How important is the past in estimating the future? Answers will help determine time horizons, techniques, and level of detail for the forecast.

13 Types of forecasting methods

Types of forecasting methods

Qualitative methods

Quantitative methods

Rely on subjective opinions from one or more experts.

Rely on data and analytical techniques.

14 Qualitative forecasting methods

Qualitative forecasting methods

Grass Roots: deriving future demand by asking the person closest to the customer. Market Research: trying to identify customer habits; new product ideas. Panel Consensus: deriving future estimations from the synergy of a panel of experts in the area. Historical Analogy: identifying another similar market. Delphi Method: similar to the panel consensus but with concealed identities.

15 Quantitative forecasting methods

Quantitative forecasting methods

Time Series: models that predict future demand based on past history trends Causal Relationship: models that use statistical techniques to establish relationships between various items and demand Simulation: models that can incorporate some randomness and non-linear effects

16 How should we pick our forecasting model

How should we pick our forecasting model

Data availability Time horizon for the forecast Required accuracy Required Resources

17 Time Series: Moving average

Time Series: Moving average

The moving average model uses the last t periods in order to predict demand in period t+1. There can be two types of moving average models: simple moving average and weighted moving average The moving average model assumption is that the most accurate prediction of future demand is a simple (linear) combination of past demand.

18 Time series: simple moving average

Time series: simple moving average

In the simple moving average models the forecast value is

At + At-1 + + At-n

Ft+1 =

n

t is the current period. Ft+1 is the forecast for next period n is the forecasting horizon (how far back we look), A is the actual sales figure from each period.

19 Example: forecasting sales at Kroger

Example: forecasting sales at Kroger

Kroger sells (among other stuff) bottled spring water

What will the sales be for July?

Month

Bottles

Jan

1,325

Feb

1,353

Mar

1,305

Apr

1,275

May

1,210

Jun

1,195

Jul

?

20 What if we use a 3-month simple moving average

What if we use a 3-month simple moving average

AJun + AMay + AApr

FJul =

= 1,227

3

What if we use a 5-month simple moving average?

AJun + AMay + AApr + AMar + AFeb

FJul =

= 1,268

5

21 5-month average smoothes data more; 3-month average more responsive

5-month average smoothes data more; 3-month average more responsive

What do we observe?

5-month MA forecast

3-month MA forecast

22 Stability versus responsiveness in moving averages

Stability versus responsiveness in moving averages

23 Time series: weighted moving average

Time series: weighted moving average

We may want to give more importance to some of the data

Ft+1 =

wt At + wt-1 At-1 + + wt-n At-n

wt + wt-1 + + wt-n = 1

t is the current period. Ft+1 is the forecast for next period n is the forecasting horizon (how far back we look), A is the actual sales figure from each period. w is the importance (weight) we give to each period

24 Why do we need the WMA models

Why do we need the WMA models

Because of the ability to give more importance to what happened recently, without losing the impact of the past.

25 Example: Kroger sales of bottled water

Example: Kroger sales of bottled water

What will be the sales for July?

Month

Bottles

Jan

1,325

Feb

1,353

Mar

1,305

Apr

1,275

May

1,210

Jun

1,195

Jul

?

26 6-month simple moving average

6-month simple moving average

AJun + AMay + AApr + AMar + AFeb + AJan

FJul =

= 1,277

6

In other words, because we used equal weights, a slight downward trend that actually exists is not observed

27 What if we use a weighted moving average

What if we use a weighted moving average

Make the weights for the last three months more than the first three months

The higher the importance we give to recent data, the more we pick up the declining trend in our forecast.

6-month SMA

WMA 40% / 60%

WMA 30% / 70%

WMA 20% / 80%

July Forecast

1,277

1,267

1,257

1,247

28 How do we choose weights

How do we choose weights

Depending on the importance that we feel past data has Depending on known seasonality (weights of past data can also be zero).

WMA is better than SMA because of the ability to vary the weights!

29 Time Series: Exponential Smoothing (ES)

Time Series: Exponential Smoothing (ES)

Main idea: The prediction of the future depends mostly on the most recent observation, and on the error for the latest forecast.

Denotes the importance of the past error

Smoothing constant alpha ?

30 Why use exponential smoothing

Why use exponential smoothing

Uses less storage space for data Extremely accurate Easy to understand Little calculation complexity There are simple accuracy tests

31 Exponential smoothing: the method

Exponential smoothing: the method

Assume that we are currently in period t. We calculated the forecast for the last period (Ft-1) and we know the actual demand last period (At-1)

The smoothing constant ? expresses how much our forecast will react to observed differences If ? is low: there is little reaction to differences. If ? is high: there is a lot of reaction to differences.

32 Example: bottled water at Kroger

Example: bottled water at Kroger

Month

Actual

Forecasted

? = 0.2

Jan

1,325

1,370

Feb

1,353

1,361

Mar

1,305

1,359

Apr

1,275

1,349

May

1,210

1,334

Jun

?

1,309

33 Example: bottled water at Kroger

Example: bottled water at Kroger

Month

Actual

Forecasted

? = 0.8

Jan

1,325

1,370

Feb

1,353

1,334

Mar

1,305

1,349

Apr

1,275

1,314

May

1,210

1,283

Jun

?

1,225

34 Impact of the smoothing constant

Impact of the smoothing constant

35 Trend

Trend

What do you think will happen to a moving average or exponential smoothing model when there is a trend in the data?

36 Impact of trend

Impact of trend

Sales

Regular exponential smoothing will always lag behind the trend. Can we include trend analysis in exponential smoothing?

Month

Actual Data

Forecast

37 Exponential smoothing with trend

Exponential smoothing with trend

FIT: Forecast including trend ?: Trend smoothing constant

The idea is that the two effects are decoupled, (F is the forecast without trend and T is the trend component)

38 Example: bottled water at Kroger

Example: bottled water at Kroger

? = 0.8

At

Ft

Tt

FITt

? = 0.5

Jan

1325

1380

-10

1370

Feb

1353

1334

-28

1306

Mar

1305

1344

-9

1334

Apr

1275

1311

-21

1290

May

1210

1278

-27

1251

Jun

1218

-43

1175

39 Exponential Smoothing with Trend

Exponential Smoothing with Trend

40 Linear regression in forecasting

Linear regression in forecasting

Linear regression is based on Fitting a straight line to data Explaining the change in one variable through changes in other variables.

dependent variable = a + b ? (independent variable)

By using linear regression, we are trying to explore which independent variables affect the dependent variable

41 Example: do people drink more when its cold

Example: do people drink more when its cold

Alcohol Sales

Which line best fits the data?

Average Monthly Temperature

42 The best line is the one that minimizes the error

The best line is the one that minimizes the error

The predicted line is

So, the error is

Where: ? is the error y is the observed value Y is the predicted value

43 Least Squares Method of Linear Regression

Least Squares Method of Linear Regression

The goal of LSM is to minimize the sum of squared errors

44 What does that mean

What does that mean

Alcohol Sales

So LSM tries to minimize the distance between the line and the points!

Average Monthly Temperature

45 Least Squares Method of Linear Regression

Least Squares Method of Linear Regression

Then the line is defined by

46 How can we compare across forecasting models

How can we compare across forecasting models

We need a metric that provides estimation of accuracy

Forecast Error

Errors can be: biased (consistent) random

Forecast error = Difference between actual and forecasted value (also known as residual)

47 Measuring Accuracy: MFE

Measuring Accuracy: MFE

MFE = Mean Forecast Error (Bias) It is the average error in the observations

1. A more positive or negative MFE implies worse performance; the forecast is biased.

48 Measuring Accuracy: MAD

Measuring Accuracy: MAD

MAD = Mean Absolute Deviation It is the average absolute error in the observations

1. Higher MAD implies worse performance. 2. If errors are normally distributed, then ??=1.25MAD

49 MFE & MAD: A Dartboard Analogy

MFE & MAD: A Dartboard Analogy

Low MFE & MAD: The forecast errors are small & unbiased

50 An Analogy (contd)

An Analogy (contd)

Low MFE but high MAD: On average, the arrows hit the bullseye (so much for averages!)

51 MFE & MAD: An Analogy

MFE & MAD: An Analogy

High MFE & MAD: The forecasts are inaccurate & biased

52 Key Point

Key Point

Forecast must be measured for accuracy! The most common means of doing so is by measuring the either the mean absolute deviation or the standard deviation of the forecast error

53 Measuring Accuracy: Tracking signal

Measuring Accuracy: Tracking signal

If TS > 4 or < -4, investigate!

The tracking signal is a measure of how often our estimations have been above or below the actual value. It is used to decide when to re-evaluate using a model.

Positive tracking signal: most of the time actual values are above our forecasted values Negative tracking signal: most of the time actual values are below our forecasted values

54 Example: bottled water at Kroger

Example: bottled water at Kroger

Question: Which one is better?

Exponential Smoothing (? = 0.2)

Forecasting with trend (? = 0.8) (? = 0.5)

Month

Actual

Forecast

Month

Actual

Forecast

Jan

1,325

1370

Jan

1,325

1,370

Feb

1,353

1306

Feb

1,353

1,361

Mar

1,305

1334

Mar

1,305

1,359

Apr

1,275

1290

Apr

1,275

1,349

May

1,210

1251

May

1,210

1,334

Jun

1,195

1175

Jun

1,195

1,309

55 Bottled water at Kroger: compare MAD and TS

Bottled water at Kroger: compare MAD and TS

We observe that FIT performs a lot better than ES

Conclusion: Probably there is trend in the data which Exponential smoothing cannot capture

MAD

TS

Exponential Smoothing

70

- 6.0

Forecast Including Trend

33

- 2.0

56 Which Forecasting Method Should You Use

Which Forecasting Method Should You Use

Gather the historical data of what you want to forecast Divide data into initiation set and evaluation set Use the first set to develop the models Use the second set to evaluate Compare the MADs and MFEs of each model

Forecasting
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