forecasting_ch5 till deseasonalize

7/29/2019 Forecasting_Ch5 Till Deseasonalize

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Forecasting


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Application Areas

MEDICAL

MILITARY

TELECOM

SCM

MANAGEMENT

FINANCE

WEATHER

POLITICS

ASTRONOMY

DEMOGRAPHY


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8 Steps to Forecasting

1.Use or Objective?

2.What items/Quantities to be forecasted?

3.Time Horizon?

1 month (short term) 1 year (mid term) > 1 year (long term)

4.Select the forecasting Model

5.Gather Data

6.Validate the Forecasting Model

7.Make the forecast

8.Implement the results


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Qualitative Models

Decision Making Group

Staff Personal

Respondents

Surveys/Ques

High Level Managers

(Small Group)

Statistical

Models

Group

Estimate

Demand


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Qualitative Models

Regional Salesperson

Forecast

Nationwide Level Forecast

all regions forecasts

Overall Forecast

Customer

ForecastsAlso helps i

improving p

F E


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Forecast ErrorsMeasures of forecast accuracy include:

Mean Absolute Deviation (MAD)

Mean Squared Error (MSE)

Mean Absolute Percent Error (MAPE)

= |forecast errors|n

= (errors)n

=actualn

100%

error

2

4th One is Bias i.e. a


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Forecast Accuracy

Forecast Error Actual Value Forecast Value

Mean Absolute Deviation

(MAD)Forecast Error

n

YearForecasted

Traffic (Erl)

Actual

Traffic (Erl)

|Actual-Forecast|

2005 2045000 3027900 982900

2006 4294500 5582850 1288350

2007 11165700 16190265 5024565

2008 32380530 46951768.5 14571238.5

2009 35618583 53994533.8 18375950.775Total Sum of Forecast rrors ------> 40243004.275 n

Onfo

the 8.0


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Forecast Accuracy...Contd

Forecast Error Actual Value Forecast Value

Mean Squared Error

(MSE)

(Error)

n

YearForecasted

Traffic (Erl)

Actual

Traffic (Erl)

(Error)

2005 2045000 3027900 9.66092E+11

2006 4294500 5582850 1.65985E+12

2007 11165700 16190265 2.52463E+13

2008 32380530 46951768.5 2.12321E+14

2009 35618583 53994533.8 3.37676E+14Sum of S uared Errors ------> 5.77869E+14 n

2

2


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Mean Absolute Percent Error

(MAPE)

(Error/actual)

n

YearForecasted

Traffic (Erl)

Actual

Traffic (Erl)

|(Error/actual)|

2005 2045000 3027900 0.324614419234453

2006 4294500 5582850 0.230769230769231

2007 11165700 16190265 0.310344827586207

2008 32380530 46951768.5 0.310344827586207

2009 35618583 53994533.8 0.340329835082459Sum of S uared Errors ------> 1.51640314025856 n

MAPE =

X


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Bias (Error)

n

YearForecasted

Traffic (Erl)

Actual

Traffic (Erl)

Error

2005 2045000 3027900 982900

2006 4294500 5582850 1288350

2007 11165700 16190265 5024565

2008 32380530 46951768.5 14571238.5

2009 35618583 53994533.8 18375950.775Sum of S uared Errors ------> 40243004.275 n

Bia

i.e

Biasmeas

errors c

p


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F t E


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Forecast Errors

Ms. Smith forecasted

total hospital

inpatient days last

year. Now that the

actual data are

known, she is

reevaluating

her forecasting

model. Compute the

MAD, MSE, and

MAPE for her

forecast.

Month Forecast ActualJAN 250 243FEB 320 315MAR 275 286APR 260 256MAY 250 241JUN 275 298JUL 300 292AUG 325 333SEP 320 326OCT 350 378NOV 365 382DEC 380 396


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Forecast Errors

Forecast Actual |error| error^2 |error/actual|

JAN 250 243 7 49 0.03

FEB 320 315 5 25 0.02

MAR 275 286 11 121 0.04

APR 260 256 4 16 0.02

MAY 250 241 9 81 0.04

JUN 275 298 23 529 0.08

JUL

300 292 8 64 0.03AUG 325 333 8 64 0.02

SEP 320 326 6 36 0.02

OCT 350 378 28 784 0.07

NOV 365 382 17 289 0.04

DEC 380 396 16 256 0.04

AVERAGE

11.83 192.83 3.68

MAD = MSE = MAPE= .0368*100

=


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Time Series Models


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Composition of Time SeriesTrend (T):

Gradual up or down movement over time

Seasonality (S):

Pattern of fluctuations above or below trend line that occurIn weekly or monthly data, the seasonal component, oftenseasonality, is the component of variation in a time series wh

dependent on the time of year.

It describes any regular fluctuations with a period of less thFor example, the costs of various types of fruits and vegetab

unemployment figures and average daily rainfall, all show ma

seasonal variation.


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Composition of Time Series

Cycles(C):

Patterns in data that occur every several years.In weekly or monthly data, the cyclical component describfluctuations.

It is a non-seasonal component which varies in a recogniza

Random variations (R):

blipsin the data caused by chance and unusual situations

Ti S i & F ti


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Time Series & Forecasting

Q: What is Time Series?

A: Data collected at regular intervals of time.Q: What is Time Series & Forecasting?

A: Using Time Series to detect patterns in data collover time to cope with uncertainty about the future.

Q: Why we use Time Series & Forecasting?

A: To cope with uncertainty about the future.

Example: Inventory Requirements for a local shoe store or the grocery store

Predict Annual Sales of the Video Games


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Moving Averages

If all variations in a time series are due to random variations, withseasonal, or cyclical component, some type of averaging or smo

model would be appropriate.

M i A


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Moving Averages

n

Simple moving average =

demand in previous nperiods

Moving average methods consist of

computing an average of the most recentn data values for the time series and

using this average for the forecast of the

next period.

Month Actual

Shed

Sales

Three-

Moving

January 10

February 12

March 13

April 16

May 19

June 23

July 26

(10+12+13

(12+13+16

(13+16+19

(16+19+23


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Weighted Moving Averag

WeightsApplied

3

2

1

3*Sales last m

2*Sales

6

Month Actual

Shed

Sales

Three-Month Weighted

Moving Average

10

12

13

16

19

23

January

February

March

April

May

June

July 26

[3*13+2*12+1*10]/6 = 12 1/6

[3*16+2*13+1*12]/6 =14 1/3

[3*19+2*16+1*13]/6 = 17

[3*23+2*19+1*16]/6 = 20 1/2

Weighted moving averages use weights to

put more emphasis on certain recent

periods.

(weigh

tforpe

riodn)

(dem

andin

perio

dn)

weigh

ts

E i l S hi


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Exponential SmoothingExponential smoothing is a type of

moving average technique that involves

little record keeping of past data.

New forecast

= previous forecast + (previous actual previous

forecast)

Mathematically this is expressed as:

Ft = Ft-1 + (Yt-1 - Ft-1)

Ft-1 = previous forecast

= smoothing constant

Ft = new forecast

Yt-1 = previous period actual

Qtr Actual

Tonnage

Unloaded

Roun

1 180 175

2 168 176=

3 159 175 =

4 175 173 =

5 190 173 =

6 205 175 =

7 180 178 =

8 182 178 =

9 ? 179=

the larger thesmoothing parameter ,

the greater the weight

given to the most

recent value

E i l S hi


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Exponential Smoothing

Qtr Actual

Tonnage

Unloaded

Rounded Forecast using =0

1 180 175

2 168 176= 175.00+0.10(180-175)

3 159 175 =175.50+0.10(168-175.50)

4 175 173 =174.75+0.10(159-174.75)

5 190 173 =173.18+0.10(175-173.18)

6 205 175 =173.36+0.10(190-173.36)

7 180 178 =175.02+0.10(205-175.02)

8 182 178 =178.02+0.10(180-178.02)

9 ? 179= 178.22+0.10(182-178.22)

Qtr Actual

Tonnage

Unloaded

Rounded Forecast using =0.50

1 180 175

2 168 178 =175.00+0.50(180-175)

3 159 173 =177.50+0.50(168-177.50)

4 175 166 =172.75+0.50(159-172.75)

5 190 170 =165.88+0.50(175-165.88)

6 205 180 =170.44+0.50(190-170.44)

7 180 193 =180.22+0.50(205-180.22)

8 182 186 =192.61+0.50(180-192.61)

9 ?184 =186.30+0.50(182-186.30)

E ti l S thi


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Exponential Smoothing

ActualForecast with

a = 0.10Absolute

DeviationsForecast with

a = 0.50Absolute

Deviations

180 175 5 175 5

168 176 8 178 10

159 175 16 173 14

175 173 2 166 9

190 173 17 170 20

205 175 30 180 25

180 178 2 193 13

182 178 4 186 4

MAD 10.0 12

To select the best smoothing constant,

evaluate the accuracy of each forecasting

model.

The lowest MAD results from = 0.10


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Cl E l


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Class Example

PM Computer assembles customizedpersonal computers from generic parts.

The owners purchase generic computerparts in volume at a discount from a

variety of sources whenever they see a

good deal.

It is important that they develop a goodforecast of demand for their computers

so they can purchase component parts

efficiently.

Period month actual demand

1 Jan 37

2 Feb 40

3 Mar 41

4 Apr 37

5 May 45

6 June 50

7 July 43

8 Aug 47

9 Sept 56

Compute a 2-month moving average Compute a 3-month weighted average using

weights of 4,2,1 for the past three months of

data

Compute an exponential smoothing forecastusing = 0.7

Using MAD, what forecast is most accurate?

Cl E l S l ti


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Class Example Solutio

MAD

Exponential smoothing resulted in the lowest MAD.

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