Forecasting for statistics for management

7/30/2019 Forecasting for statistics for management

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Time Series Data and Forecasting


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Eight Steps to Forecasting

Determine the use of the forecast

What objective are we trying to obtain?

Select the items or quantities that are to be forecasted.

Determine the time horizon of the forecast.

Short time horizon

1 to 30 days Medium time horizon 1 to 12 months

Long time horizon more than 1 year

Select the forecasting model or models

Gather the data to make the forecast. Validate the forecasting model

Make the forecast

Implement the results


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Forecasting Models

Forecasting

TechniquesQualitative

Models Time Series

Methods

CausalMethods

Delphi

Method

Jury of Executive

Opinion

Sales Force

Composite

Consumer Market

Survey

NaiveMovingAverage

Weighted

Moving AverageExponential

Smoothing

Trend Analysis

Seasonality

Analysis

Simple

Regression

Analysis


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Model Differences

Qualitative incorporates judgmental &

subjective factors into forecast.

Time-Series Any statistical data arrange

chronologically is time series. Attempts to

predict the future by using historical data.


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Causal incorporates factors that mayinfluence the quantity being forecasted

into the

Predict sales of cola: temperature,season, day of week, humidity etc.


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Qualitative Forecasting Models

Delphi method

Iterative group process allows experts to make forecasts

Participants:

decision makers: 5 -10 experts who make the forecast

staff personnel: assist by preparing, distributing, collecting, and

summarizing a series of questionnaires and survey results

respondents: group with valued judgments who provide input to

decision makers


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Qualitative Forecasting Models (cont)

Jury of executive opinion Opinions of a small group of high level managers, often in combination

with statistical models.

Result is a group estimate.

Sales force composite

Each salesperson estimates sales in his region.

Forecasts are reviewed to ensure realistic.

Combined at higher levels to reach an overall forecast.

Consumer market survey.

Solicits input from customers and potential customers regardingfuture purchases.

Used for forecasts and product design & planning


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Forecast Error

Bias - Bias is difference betweenthe actual value and theforecasted value. It can becompute by taking the arithmeticsum of the errors

Mean Square Error - Similar tosimple sample variance

Variance - Sample variance(adjusted for degrees of freedom)

Standard Error - Standarddeviation of the samplingdistribution

MAD - Mean Absolute Deviation MAPE Mean Absolute

Percentage Error

tt FAErrorForecast

TFAMAD tt

T

t

/||/T|errorforecast|1

T

1t

TAFAMAPEttt

T

t

/]/|[|1001

TFA

MSE

tt

T

t

/)(

/T|errorforecast|

2

1

T

1t

2


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Quantitative Forecasting Models

Time Series Method

Nave

Whatever happenedrecently will happen again

this time (same timeperiod)

The model is simple andflexible

Provides a baseline to

measure other models Attempts to capture

seasonal factors at theexpense of ignoring trend

dataMonthly:

dataQuarterly:

12

4

tt

tt

YF

YF

1

ttYF


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Nave Forecast

Wallace Garden SupplyForecasting

Period

Actual

Value

Nave

Forecast Error

Absolute

Error

Percent

Error

Squared

Error

January 10 N/A

February 12 10 2 2 16.67% 4.0

March 16 12 4 4 25.00% 16.0

April 13 16 -3 3 23.08% 9.0

May 17 13 4 4 23.53% 16.0

June 19 17 2 2 10.53% 4.0

July 15 19 -4 4 26.67% 16.0

August 20 15 5 5 25.00% 25.0

September 22 20 2 2 9.09% 4.0October 19 22 -3 3 15.79% 9.0

November 21 19 2 2 9.52% 4.0

December 19 21 -2 2 10.53% 4.0

0.818 3 17.76% 10.091

BIAS MAD MAPE MSE

Standard Error (Square Root of MSE) = 3.176619

Storage Shed Sales


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Nave Forecast Graph

0

5

10

15

20

25

February March April May June July August September October November December

Sheds

Period

Wallace Garden - Naive Forecast

Actual Value

Nave Forecast


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Time Series Method

Moving Averages

Assumes item forecasted

will stay steady over time. Technique will smooth

out short-term

irregularities in the time

series.

/kperiods)kpreviousinvalue(Actualaveragemovingperiod-kk

1

k


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Moving Averages


Period

Actual

Value Three-Month Moving AveragesJanuary 10

February 12

March 16

April 13 10 + 12 + 16 / 3 = 12.67

May 17 12 + 16 + 13 / 3 = 13.67

June 19 16 + 13 + 17 / 3 = 15.33

July 15 13 + 17 + 19 / 3 = 16.33August 20 17 + 19 + 15 / 3 = 17.00

September 22 19 + 15 + 20 / 3 = 18.00

October 19 15 + 20 + 22 / 3 = 19.00

November 21 20 + 22 + 19 / 3 = 20.33

December 19 22 + 19 + 21 / 3 = 20.67

Storage Shed Sales


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Moving Averages Forecast

Wallace Garden SupplyForecasting 3 period moving average

Input Data Forecast Error Analysis

Period Actual Value Forecast Error

Absolute

error

Squared

error

Absolute

% errorMonth 1 10

Month 2 12

Month 3 16

Month 4 13 12.667 0.333 0.333 0.111 2.56%

Month 5 17 13.667 3.333 3.333 11.111 19.61%

Month 6 19 15.333 3.667 3.667 13.444 19.30%

Month 7 15 16.333 -1.333 1.333 1.778 8.89%

Month 8 20 17.000 3.000 3.000 9.000 15.00%

Month 9 22 18.000 4.000 4.000 16.000 18.18%

Month 10 19 19.000 0.000 0.000 0.000 0.00%

Month 11 21 20.333 0.667 0.667 0.444 3.17%

Month 12 19 20.667 -1.667 1.667 2.778 8.77%

Average 12.000 2.000 6.074 10.61%

Next period 19.667 BIAS MAD MSE MAPE

Actual Value - Forecast


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Moving Averages Graph

0

5

10

15

20

25

1 2 3 4 5 6 7 8 9 10 11 12

Value

Time

Three Period Moving Average

Actual Value

Forecast


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Time Series Method

Weighted Moving Averages

Assumes data from some periods are more important

than data from other periods (e.g. earlier periods).

Use weights to place more emphasis on some

periods and less on others.

(weights)/periods)kpreviousinvaluei)(Actualperiodeachfor(Weight

averagemovingweightedperiod-k

k

1i

k

1

i


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Weighted Moving AverageWallace Garden SupplyForecasting

Period

Actual

Value Weights Three-Month Weighted Moving Averages

January 10 0.200

February 12 0.300March 16 0.500

April 13 2 + 3.6 + 8 / 1 = 13.600

May 17 2.4 + 4.8 + 6.5 / 1 = 13.700

June 19 3.2 + 3.9 + 8.5 / 1 = 15.600

July 15 2.6 + 5.1 + 9.5 / 1 = 17.200

August 20 3.4 + 5.7 + 7.5 / 1 = 16.600

September 22 3.8 + 4.5 + 10 / 1 = 18.300

October 19 3 + 6 + 11 / 1 = 20.000November 21 4 + 6.6 + 9.5 / 1 = 20.100

December 19 4.4 + 5.7 + 11 / 1 = 20.600

Next period 19.600

Sum of weights = 1.000

Storage Shed Sales


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Weighted Moving Average

Wallace Garden Supply Forecasting 3 period weighted moving average


Period Actual value Weights Forecast Error

Absolute

error

Squared

error

Absolute

% error

Month 1 10 0.200Month 2 12 0.300

Month 3 16 0.500

Month 4 13 13.600 -0.600 0.600 0.360 4.62%

Month 5 17 13.700 3.300 3.300 10.890 19.41%

Month 6 19 15.600 3.400 3.400 11.560 17.89%

Month 7 15 17.200 -2.200 2.200 4.840 14.67%

Month 8 20 16.600 3.400 3.400 11.560 17.00%

Month 9 22 18.300 3.700 3.700 13.690 16.82%Month 10 19 20.000 -1.000 1.000 1.000 5.26%

Month 11 21 20.100 0.900 0.900 0.810 4.29%

Month 12 19 20.600 -1.600 1.600 2.560 8.42%

Average 2.233 6.363 6.363 12.04%

Next period 19.600 BIAS MAD MSE MAPE

Sum of weights = 1.000


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Time Series Method

Exponential Smoothing

Moving average technique that requires little record

keeping of past data.

Uses a smoothing constant with a value between 0

and 1. (Usual range 0.1 to 0.3)

)-tperiodforforecast--tperiodinvalue(actual-tperiodforforecast

tperiodforForecast

111


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Exponential Smoothing Data



Period

Ac tual

Value Ft

At

Ft

Ft+1

January 10 10 0.1

February 12 10 + 0.1 *( 10 - 10 ) = 10.000

March 16 10 + 0.1 *( 12 - 10 ) = 10.200

April 13 10 + 0.1 *( 16 - 10 ) = 10.780

May 17 11 + 0.1 *( 13 - 11 ) = 11.002

June 19 11 + 0.1 *( 17 - 11 ) = 11.602

July 15 12 + 0.1 *( 19 - 12 ) = 12.342August 20 12 + 0.1 *( 15 - 12 ) = 12.607

September 22 13 + 0.1 *( 20 - 13 ) = 13.347

October 19 13 + 0.1 *( 22 - 13 ) = 14.212

November 21 14 + 0.1 *( 19 - 14 ) = 14.691

December 19 15 + 0.1 *( 21 - 15 ) = 15.322

Storage Shed Sales


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0

5

10

15

20

25

January

Febr

uaryM

arch April

May June JulyAu

gust

Septembe

r

Octobe

r

Nove

mber

Decembe

r

Sheds Actual value

Forecast


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Trend & Seasonality

Trend analysis

technique that fits a trend equation (or curve) to a series of historicaldata points.

projects the curve into the future for medium and long termforecasts.

Seasonality analysis

adjustment to time series data due to variations at certain periods.

adjust with seasonal index ratio of average value of the item in aseason to the overall annual average value.

example: demand for coal & fuel oil in winter months.


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Scatter Diagram

Actual value (or)

Y

Period number

(or) X

74 1995

79 1996

80 1997

90 1998105 1999

142 2000

122 2001

Midwestern Manufacturing Sales


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Linear Trend Analysis

Midwestern Manufacturing Sales

0

20

40

60

80

100

120

140

160

1994 1996 1998 2000 2002

Sales(in units) vs. Time

Period number (or) X


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Least Squares for Linear Regression

Midwestern Manufacturing

Least Squares Method

Time

ValuesofDependentVaria

bles


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Least Squares Method

bXaY^

Where

Y^

= predicted value of the dependent variable (demand)

X = value of the independent

variable (time)

a = Y-axis intercept

b = slope of the regression line

]Xn-XY[__

Y

_22 Xn-X

b =


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Linear Trend Data & Error Analysis

Midwestern Manufacturing CompanyForecasting Linear trend analysis


Period

Actual value

(or) Y

Period number

(or) X Forecast Error

Absolute

error

Squared

error

Absolute

% errorYear 1 74 1 67.250 6.750 6.750 45.563 9.12%

Year 2 79 2 77.786 1.214 1.214 1.474 1.54%

Year 3 80 3 88.321 -8.321 8.321 69.246 10.40%

Year 4 90 4 98.857 -8.857 8.857 78.449 9.84%

Year 5 105 5 109.393 -4.393 4.393 19.297 4.18%

Year 6 142 6 119.929 22.071 22.071 487.148 15.54%

Year 7 122 7 130.464 -8.464 8.464 71.644 6.94%Average 8.582 110.403 8.22%

Intercept 56.714 MAD MSE MAPE

Slope 10.536

Next period 141.000 8


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Least Squares Graph

Trend Analysis

y = 10.536x + 56.714

0

20

40

60

80

100

120

140

160

1 2 3 4 5 6 7

Time

Value

Actual values Linear (Actual values)


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Seasonality Analysis

Eichler Supplies

Year Month DemandAverageDemand Ratio

SeasonalIndex

1 January 80 94 0.851 0.957February 75 94 0.798 0.851

March 80 94 0.851 0.904April 90 94 0.957 1.064May 115 94 1.223 1.309

June 110 94 1.170 1.223July 100 94 1.064 1.117

August 90 94 0.957 1.064

September 85 94 0.904 0.957October 75 94 0.798 0.851

November 75 94 0.798 0.851December 80 94 0.851 0.851

2 January 100 94 1.064

February 85 94 0.904March 90 94 0.957April 110 94 1.170May 131 94 1.394

June 120 94 1.277July 110 94 1.170

August 110 94 1.170

September 95 94 1.011October 85 94 0.904

November 85 94 0.904December 80 94 0.851

Seasonal Index ratio of the average

value of the item in a season to the

overall average annual value.

Example: average of year 1 January

ratio to year 2 January ratio.

(0.851 + 1.064)/2 = 0.957

Ratio = demand / average demand

If Year 3 average monthly demand isexpected to be 100 units.Forecast demand Year 3 January:

100 X 0.957 = 96 units

Forecast demand Year 3 May:

100 X 1.309 = 131 units


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Deseasonalized Data

Going back to the conceptual model, solve fortrend:

Trend = Y / Season (96

units/ 0.957 = 100.31) This eliminates seasonal variation and isolates

the trend

Now use the Least Squares method tocompute the Trend


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Forecast

Now that we have the Seasonal Indices and

Trend, we can reseasonalize the data and

generate the forecast

Y = Trend x Seasonal Index

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Forecasting for statistics for management