Time-Series Forecasting Learning Objectives 1.Describe What Forecasting Is 2. Forecasting Methods...

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Time-Series Time-Series Forecasting Forecasting

Transcript of Time-Series Forecasting Learning Objectives 1.Describe What Forecasting Is 2. Forecasting Methods...

Page 1: Time-Series Forecasting Learning Objectives 1.Describe What Forecasting Is 2. Forecasting Methods 3.Explain Time Series & Components 4.Smooth a Data.

Time-Series ForecastingTime-Series Forecasting

Page 2: Time-Series Forecasting Learning Objectives 1.Describe What Forecasting Is 2. Forecasting Methods 3.Explain Time Series & Components 4.Smooth a Data.

Learning Objectives

1.Describe What Forecasting Is

2. Forecasting Methods

3.Explain Time Series & Components

4.Smooth a Data Series

5.Forecast Using Smoothing Methods, & Trend

6.Use MAD to Measure Forecast Error

Page 3: Time-Series Forecasting Learning Objectives 1.Describe What Forecasting Is 2. Forecasting Methods 3.Explain Time Series & Components 4.Smooth a Data.

What Is Forecasting?

1.Process of Predicting a Future Event

2.Underlying Basis of All Business PlanningProduction

Inventory

Personnel

Facilities

Sales will be $200 Million!

Page 4: Time-Series Forecasting Learning Objectives 1.Describe What Forecasting Is 2. Forecasting Methods 3.Explain Time Series & Components 4.Smooth a Data.

Forecasting Methods

1.Qualitative MethodsExpert Opinion

Delphi Method

Surveys

2.Quantitative MethodsTime Series

CausalRegression

Page 5: Time-Series Forecasting Learning Objectives 1.Describe What Forecasting Is 2. Forecasting Methods 3.Explain Time Series & Components 4.Smooth a Data.

Quantitative Forecasting Steps

1.Select Several Forecasting Methods

2.‘Forecast’ the Past

3.Evaluate Forecasts

4.Select Best Method

5.Forecast the Future

6.Monitor Continuously Forecast Accuracy

Page 6: Time-Series Forecasting Learning Objectives 1.Describe What Forecasting Is 2. Forecasting Methods 3.Explain Time Series & Components 4.Smooth a Data.

What’s a Time Series?

1. Set of Numerical Data

2. Obtained by Observing Response Variable at Regular Time Periods

3. Assumes that Factors Influencing Past & Present Will Continue

4. ExampleYear: 1990 1991 1992 19931994

Sales: 78.7 63.5 89.7 93.292.1

Page 7: Time-Series Forecasting Learning Objectives 1.Describe What Forecasting Is 2. Forecasting Methods 3.Explain Time Series & Components 4.Smooth a Data.

Time Series Components

Trend

Seasonal

Cyclical

Irregular

Page 8: Time-Series Forecasting Learning Objectives 1.Describe What Forecasting Is 2. Forecasting Methods 3.Explain Time Series & Components 4.Smooth a Data.

Trend Component

1. Persistent, Overall Upward or Downward Pattern

2. Due to Population, Technology, etc.

3. 15 to 20 Years Duration

Mo., Qtr., Yr.

Response

Page 9: Time-Series Forecasting Learning Objectives 1.Describe What Forecasting Is 2. Forecasting Methods 3.Explain Time Series & Components 4.Smooth a Data.

Linear Increasing Trend Linear Decreasing Trend

Nonlinear Trend No Trend

Examples of Some Time Series Trend Patterns

Page 10: Time-Series Forecasting Learning Objectives 1.Describe What Forecasting Is 2. Forecasting Methods 3.Explain Time Series & Components 4.Smooth a Data.

Toaster Sales in Hundreds, By Quarter, 1990-1998

TIME QUARTER1 QUARTER2 QUARTER3 QUARTER4 ------------------------------------------- 1990 187 243 209 291 1991 198 263 270 297 1992 274 363 294 336 1993 232 273 241 289 1994 206 295 239 317 1995 237 366 300 429 1996 282 424 383 478 1997 375 429 393 560 1998 373 423 387 433

Page 11: Time-Series Forecasting Learning Objectives 1.Describe What Forecasting Is 2. Forecasting Methods 3.Explain Time Series & Components 4.Smooth a Data.

Long-Term Trend in Toaster Sales

YEAR

199119901989198819871986198519841983

Mea

n S

ALE

S

600

500

400

300

200

100

Page 12: Time-Series Forecasting Learning Objectives 1.Describe What Forecasting Is 2. Forecasting Methods 3.Explain Time Series & Components 4.Smooth a Data.

Cyclical Component

1. Repeating Up & Down Movements

2. Due to Interactions of Factors Influencing Economy

3. Usually 2-15 Years Duration

Mo., Qtr., Yr.

ResponseCycle Prosperity

Recession Depression Recovery

Page 13: Time-Series Forecasting Learning Objectives 1.Describe What Forecasting Is 2. Forecasting Methods 3.Explain Time Series & Components 4.Smooth a Data.

Cycles in Toaster Sales

YEAR

199119901989198819871986198519841983

SA

LES

600

500

400

300

200

100

Page 14: Time-Series Forecasting Learning Objectives 1.Describe What Forecasting Is 2. Forecasting Methods 3.Explain Time Series & Components 4.Smooth a Data.

Seasonal Component

1. Regular Pattern of Up & Down Fluctuations

2. Due to Weather, Customs,etc.

3. Occurs Within 1 Year

Mo., Qtr.

Response

Summer

Page 15: Time-Series Forecasting Learning Objectives 1.Describe What Forecasting Is 2. Forecasting Methods 3.Explain Time Series & Components 4.Smooth a Data.

The Seasonal Pattern of Toaster Sales

YEAR

1983

1985

1987

1989

19914321

SA

LES

500

400

300

200

100

QUARTER

Page 16: Time-Series Forecasting Learning Objectives 1.Describe What Forecasting Is 2. Forecasting Methods 3.Explain Time Series & Components 4.Smooth a Data.

Irregular Component

1. Erratic, Unsystematic, ‘Residual’ Fluctuations

2. Due to Random Variation or Unforeseen Events

Union Strike Tornado

3. Short Duration & Nonrepeating

Page 17: Time-Series Forecasting Learning Objectives 1.Describe What Forecasting Is 2. Forecasting Methods 3.Explain Time Series & Components 4.Smooth a Data.

Irregular Fluctuations in Toaster Sales

Quarters

Page 18: Time-Series Forecasting Learning Objectives 1.Describe What Forecasting Is 2. Forecasting Methods 3.Explain Time Series & Components 4.Smooth a Data.

Multiplicative Time-Series Model

1. Any Observed Value in a Time Series Is the Product of Time Series Components

2. If Annual Data Y = T x C x I

3. If Quarterly or Monthly Data Yi = T x S x C x I

Page 19: Time-Series Forecasting Learning Objectives 1.Describe What Forecasting Is 2. Forecasting Methods 3.Explain Time Series & Components 4.Smooth a Data.

Time Series Forecasting

Linear

Time SeriesForecasting

Trend?Smoothing

Methods

TrendModels

YesNo

ExponentialSmoothing

Quadratic ExponentialHolt-

WintersAuto-

Regressive

MovingAverage

Page 20: Time-Series Forecasting Learning Objectives 1.Describe What Forecasting Is 2. Forecasting Methods 3.Explain Time Series & Components 4.Smooth a Data.

Moving Average Method

1. Series of Arithmetic Means

2. Used Only for SmoothingProvides Overall Impression of Data Over

Time

3. Equation

L = Averaging Period (Odd # Years)MA (L)

Y

Li

i t

(L-1)/2

T=(1-L)/2

Page 21: Time-Series Forecasting Learning Objectives 1.Describe What Forecasting Is 2. Forecasting Methods 3.Explain Time Series & Components 4.Smooth a Data.

TimeResponse

Yi

Moving Total(L=3)

MovingAvg (L=3)

1991 4 NA NA

1992 6 4 + 6 + 5 = 15 15/3 = 5.0

1993 5 6 + 5 + 3 = 14 14/3 = 4.7

1994 3 5 + 3 + 7 = 15 15/3 = 5.0

1995 7 3 + 7 + 6 = 16 16/3 = 5.3

1996 6 NA NA

Moving Average Calculation

Page 22: Time-Series Forecasting Learning Objectives 1.Describe What Forecasting Is 2. Forecasting Methods 3.Explain Time Series & Components 4.Smooth a Data.

Moving Average Graph

Year

Sales

0

2

4

6

8

91 92 93 94 95 96

Page 23: Time-Series Forecasting Learning Objectives 1.Describe What Forecasting Is 2. Forecasting Methods 3.Explain Time Series & Components 4.Smooth a Data.

Moving Average with Even Number of Periods

Average of Four-YearElectricity Four-Year Four-Year Centered

Year Purchases Moving Total Moving Totals Moving Average1974 6851975 688

1976 7542913

2975.0 743.75

1977 7863037

3114.0 778.50

1978 8093191

3221.5 805.38

1979 8423252

3272.0 818.00

divide by 4

Page 24: Time-Series Forecasting Learning Objectives 1.Describe What Forecasting Is 2. Forecasting Methods 3.Explain Time Series & Components 4.Smooth a Data.

Time Series Forecasting

Linear

Time SeriesForecasting

Trend?Smoothing

Methods

TrendModels

YesNo

ExponentialSmoothing

Quadratic ExponentialHolt-

WintersAuto-

Regressive

MovingAverage

Page 25: Time-Series Forecasting Learning Objectives 1.Describe What Forecasting Is 2. Forecasting Methods 3.Explain Time Series & Components 4.Smooth a Data.

Exponential Smoothing Method

1. Form of Weighted Moving Average Weights Decline Exponentially Most Recent Data Weighted Most

2. Used for Smoothing & Forecasting Assumes No Trend

3. Requires Smoothing Coefficient (W) Subjectively Chosen Ranges from 0 to 1

Page 26: Time-Series Forecasting Learning Objectives 1.Describe What Forecasting Is 2. Forecasting Methods 3.Explain Time Series & Components 4.Smooth a Data.

Exponential Smoothing Equations

1. Smoothing Equations

Ei = W·Yi + (1 - W)·Ei-1

2. Forecasting Equation

Yi+1 = EiEi = Smoothed

Value

Yi = Actual Value

W = Smoothing Coefficient

Page 27: Time-Series Forecasting Learning Objectives 1.Describe What Forecasting Is 2. Forecasting Methods 3.Explain Time Series & Components 4.Smooth a Data.

Time YiSmoothed Value, Ei

(W = .2)Forecast

Yi+1

1991 4 4.0 NA

1992 6 (.2)(6) + (1-.2)(4.0) = 4.4 4.0

1993 5 (.2)(5) + (1-.2)(4.4) = 4.5 4.4

1994 3 (.2)(3) + (1-.2)(4.5) = 4.2 4.5

1995 7 (.2)(7) + (1-.2)(4.2) = 4.8 4.2

1996 NA NA 4.8

Exponential Smoothing Calculation

^

Ei = W·Yi + (1 - W)·Ei-1

Page 28: Time-Series Forecasting Learning Objectives 1.Describe What Forecasting Is 2. Forecasting Methods 3.Explain Time Series & Components 4.Smooth a Data.

Exponential Smoothing Graph

Year

Sales

0

2

4

6

8

91 92 93 94 95

Page 29: Time-Series Forecasting Learning Objectives 1.Describe What Forecasting Is 2. Forecasting Methods 3.Explain Time Series & Components 4.Smooth a Data.

Exponential Smoothing Thinking Challenge

You’re an economist for GM. You want to get a feel for the long-term trend in car sales. You want to smooth cyclical & random fluctuations using exponential smoothing with W = .25. Yearly sales (million units) are 2, 4, 1, 3.

Page 30: Time-Series Forecasting Learning Objectives 1.Describe What Forecasting Is 2. Forecasting Methods 3.Explain Time Series & Components 4.Smooth a Data.

To obtain starting values: 1.E1 = Y1 = 2

2. E2 = W·Y2 + (1 - W)·E1 = (.25)(4) + (1.00 - .25)(2) = 2.5

3. E3 = W·Y3 + (1 - W)·E2

= (.25)(1) + (1.00 - .25)(2.5) = 2.125

4. E4 = W·Y4 + (1 - W)·E3

= (.25)(3)+(1.00 - .25)(2.125)=2.34

Exponential Smoothing Solution*

Page 31: Time-Series Forecasting Learning Objectives 1.Describe What Forecasting Is 2. Forecasting Methods 3.Explain Time Series & Components 4.Smooth a Data.

Selecting Smoothing Coefficient (W)

1. Subjectively Chosen Computer Search Routines Available

2. To Smooth Cyclical & Irregular, Small W Reveals Long-Term Pattern

3. To Forecast, Large W Forecast Will Reflect Prior Period Data Most

4. Recent Data Weighted Most for All W


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