MGS3100_03.ppt/Feb 11, 2016/Page 1 Georgia State University - Confidential MGS 3100 Business Analysis Time Series Forecasting Feb 11, 2016

MGS3100_03.ppt/Feb 11, 2016/Page 1Georgia State University - Confidential

MGS 3100

Business Analysis

Time Series Forecasting

Feb 11, 2016


Agenda

Qualitative Forecasting

Models

Quantitative Forecasting

ModelsForecasting


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


Model Differences

• Qualitative (ex: Delphi) – incorporates judgmental & subjective factors into forecast.

• Quantitative (ex: Time-Series) – attempts to predict the future by using historical data.

• Causal – incorporates factors that may influence the quantity being forecasted into the model


Agenda


Models


ModelsForecasting


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


Qualitative Forecasting Models

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 compositeEach 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 regarding future

purchases.

• Used for forecasts and product design & planning


Agenda


Models


ModelsForecasting


Time Series Forecasting Process

Look at the data (Scatter Plot)

Forecast using one or more techniques

Evaluate the technique and pick the best one.

Look Forecast Evaluate

• Look at data – Graph it!

• Forecast using appropriate method, based on best possible fit

• Evaluate using indicators (Bias, MAD, MAPE, MSE, Std Error, R2)

• Use indicators to evaluate model


Time Series Forecasting Process

Observations from the scatter Plot

Techniques to try Ways to evaluate

1. Data is reasonably stationary (no trend or seasonality)

Heuristics - Averaging methods

Naive Moving Averages Simple Exponential

Smoothing

MAD MAPE Standard Error BIAS

1. Data shows a consistent trend

Simple Regression Quadratic Regression Log Y Regression Other non-linear

Regressions (not covered in this course)

MAD MAPE Standard Error BIAS R-Squared

1. Data shows both a trend and a seasonal pattern

Classical decomposition Find Seasonal Index Use one of the

above regression analyses to find the trend component

MAD MAPE Standard Error BIAS R-Squared


Forecast Error

TFA

MSE

tt

T

t

/)(

/T|errorforecast |

2

1

T

1t

2

TFAMAD tt

T

t

/|| /T|errorforecast |1

T

1t

• Error - Difference between the actual value and the forecasted value. Also called the deviation

• Bias - The average of the errors• MAD - Mean Absolute Deviation - Take the average of the absolute errors

• MAPE - Mean Absolute Percentage Error - Calculate the % of the error using the absolute error, then average the results

• MSE - Mean Square Error

• Standard Error - Take the square root of the MSE

TAFAMAPE ttt

T

t

/]/|[|1001


Quantitative Forecasting Models - 1) Naïve Forecast

Naïve

• Whatever happened recently will happen again this time (same time period)

• The model is simple and flexible

• Provides a baseline to measure other models

• Attempts to capture seasonal factors at the expense of ignoring trend

• The easiest possible method - use last periods number as your forecast

dataMonthly:dataQuarterly:

12

4

tt

tt

YFYF

1 tt YF


Qualitative Forecasting Models- 1) Naïve Forecast

Wallace Garden SupplyForecasting

PeriodActual Value

Naïve Forecast Error

Absolute Error

Percent Error

Squared Error

January 10 N/AFebruary 12 10 2 2 16.67% 4.0March 16 12 4 4 25.00% 16.0April 13 16 -3 3 23.08% 9.0May 17 13 4 4 23.53% 16.0June 19 17 2 2 10.53% 4.0July 15 19 -4 4 26.67% 16.0August 20 15 5 5 25.00% 25.0September 22 20 2 2 9.09% 4.0October 19 22 -3 3 15.79% 9.0November 21 19 2 2 9.52% 4.0December 19 21 -2 2 10.53% 4.0

0.818 3 17.76% 10.091BIAS MAD MAPE MSE

Standard Error (Square Root of MSE) = 3.176619

Storage Shed Sales


Qualitative Forecasting Models- 1) Naïve Forecast

Wallace Garden - Naive Forecast

0

5

10

15

20

25

February March April May June July August September October November December

Period

Shed

s Actual Value

Naïve Forecast


Qualitative Forecasting Models- 2) Moving Averages

Moving Averages

• Assumes item forecasted will stay steady over time.

• Technique will smooth out short-term irregularities in the time series.

• Sliding scale for n time periods

/k periods)k previousin value(Actual average moving period-kk

1

k

Σ Yii=T-1

nYT=^

T-n




PeriodActual Value Three-Month Moving Averages

January 10February 12March 16April 13 10 + 12 + 16 / 3 = 12.67May 17 12 + 16 + 13 / 3 = 13.67June 19 16 + 13 + 17 / 3 = 15.33July 15 13 + 17 + 19 / 3 = 16.33August 20 17 + 19 + 15 / 3 = 17.00September 22 19 + 15 + 20 / 3 = 18.00October 19 15 + 20 + 22 / 3 = 19.00November 21 20 + 22 + 19 / 3 = 20.33December 19 22 + 19 + 21 / 3 = 20.67

Storage Shed Sales



Wallace Garden SupplyForecasting 3 period moving average

Input Data Forecast Error Analysis

Period Actual Value Forecast ErrorAbsolute

errorSquared

errorAbsolute % error

Month 1 10Month 2 12Month 3 16Month 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



Three Period Moving Average

0

5

10

15

20

25

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

Time

Valu

e Actual Value

Forecast


Qualitative Forecasting Models- 3) Weighted Moving Averages

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)k previousin valuei)(Actual periodeach for (Weight

average moving weightedperiod-kk

1i

k

1

i




PeriodActual Value Weights Three-Month Weighted Moving Averages

January 10 0.222February 12 0.593March 16 0.185April 13 2.2 + 7.1 + 3 / 1 = 12.298May 17 2.7 + 9.5 + 2.4 / 1 = 14.556June 19 3.5 + 7.7 + 3.2 / 1 = 14.407July 15 2.9 + 10 + 3.5 / 1 = 16.484August 20 3.8 + 11 + 2.8 / 1 = 17.814September 22 4.2 + 8.9 + 3.7 / 1 = 16.815October 19 3.3 + 12 + 4.1 / 1 = 19.262November 21 4.4 + 13 + 3.5 / 1 = 21.000December 19 4.9 + 11 + 3.9 / 1 = 20.036

Next period 20.185

Sum of weights = 1.000

Storage Shed Sales



Wallace Garden Supply Forecasting 3 period weighted moving average


Period Actual value Weights Forecast ErrorAbsolute

errorSquared


Month 1 10 0.222Month 2 12 0.593Month 3 16 0.185Month 4 13 12.298 0.702 0.702 0.492 5.40%Month 5 17 14.556 2.444 2.444 5.971 14.37%Month 6 19 14.407 4.593 4.593 21.093 24.17%Month 7 15 16.484 -1.484 1.484 2.202 9.89%Month 8 20 17.814 2.186 2.186 4.776 10.93%Month 9 22 16.815 5.185 5.185 26.889 23.57%Month 10 19 19.262 -0.262 0.262 0.069 1.38%Month 11 21 21.000 0.000 0.000 0.000 0.00%Month 12 19 20.036 -1.036 1.036 1.074 5.45%

Average 1.988 6.952 6.952 10.57%Next period 20.185 BIAS MAD MSE MAPE

Sum of weights = 1.000


Qualitative Forecasting Models- 4) Exponential Smoothing

• Moving average technique that requires little record keeping of past data.

• Uses a smoothing constant α with a value between 0 and 1. (Usual range 0.1 to 0.3)

• Applies alpha to most recent period, and applies one minus alpha distributed to previous values

• α = The weight assigned to the latest period

)- tperiodfor forecast - - tperiodin value(actual - tperiodfor forecast t periodfor Forecast

111

YT=α(YT-1) + (1- α)(YT-1)^ ^




Exponential Smoothing

PeriodActual Value Ft α At Ft Ft+1

January 10 10 0.1February 12 10 + 0.1 *( 10 - 10 ) = 10.000March 16 10 + 0.1 *( 12 - 10 ) = 10.200April 13 10 + 0.1 *( 16 - 10 ) = 10.780May 17 11 + 0.1 *( 13 - 11 ) = 11.002June 19 11 + 0.1 *( 17 - 11 ) = 11.602July 15 12 + 0.1 *( 19 - 12 ) = 12.342August 20 12 + 0.1 *( 15 - 12 ) = 12.607September 22 13 + 0.1 *( 20 - 13 ) = 13.347October 19 13 + 0.1 *( 22 - 13 ) = 14.212November 21 14 + 0.1 *( 19 - 14 ) = 14.691December 19 15 + 0.1 *( 21 - 15 ) = 15.322

Storage Shed Sales



Wallace Garden SupplyForecasting Exponential smoothing


Period Actual value Forecast ErrorAbsolute

errorSquared


Month 1 10 10.000Month 2 12 10.000 2.000 2.000 4.000 16.67%Month 3 16 10.838 5.162 5.162 26.649 32.26%Month 4 13 13.000 0.000 0.000 0.000 0.00%Month 5 17 13.000 4.000 4.000 16.000 23.53%Month 6 19 14.675 4.325 4.325 18.702 22.76%Month 7 15 16.487 -1.487 1.487 2.211 9.91%Month 8 20 15.864 4.136 4.136 17.106 20.68%Month 9 22 17.596 4.404 4.404 19.391 20.02%Month 10 19 19.441 -0.441 0.441 0.194 2.32%Month 11 21 19.256 1.744 1.744 3.041 8.30%Month 12 19 19.987 -0.987 0.987 0.973 5.19%

Average 2.608 9.842 14.70%Alpha 0.419 MAD MSE MAPE

Next period 19.573



Exponential Smoothing

0

5

10

15

20

25

Shed

s Actual value

Forecast


Qualitative Forecasting Models- 5) Trend Forecasting

Trend analysis • technique that fits a trend equation (or curve) to a series of historical data

points.• projects the curve into the future for medium and long term forecasts.

Simple Regression

• Regression can be used to forecast trends

• Averages do not consider a trend

Y=b0+b1*X^

Intercept Slope = ΔY ΔX



Evaluation Method for Regression

R2=SSR SSTR2 is the proportion of variability in Y that is explained by the regression model. Remaining is random.

MAD = Sum Absolute Errors n-2 (Residual degrees of freedom)

MAPE = Sum % Errors n-2

MSE = Sum Errors Squaredn-2



Non-Linear Regression Examplesi) Quadratic Regression

Y = b0+b1+b2X2^

050

100150200250300350400450



Non-Linear Regression Examplesii) Exponential Logarithmic Regression

110100100010000

=====

100

101

102

103

104

Therefore Log 10100=2

(To what power do we raise the base?)

0

200

400

600

800

1000

1200



Non-Linear Regression Examplesiii) Classical Decomposition

Y = (Trend x Cyclicality x Seasonality) + ErrorX

Business / Economic Cycles too long

0

20

40

60

80

100

120

140

160

Yd=YSI

To Deseasonalize: To Reseasonalize:

Y=Yd(SI)^


Qualitative Forecasting Models- 5) Linear Trend Analysis

Scatter Diagram

Actual value (or)

Y

Period number (or) X

74 199579 199680 199790 1998

105 1999142 2000122 2001

Sales(in units) vs. Time

0

20

40

60

80

100

120

140

160

1994 1996 1998 2000 2002

Period number (or) X

Midwestern Manufacturing Sales


Qualitative Forecasting Models- 5) Least Squares for Linear Regression

Midwestern Manufacturing

Least Squares Method

Time

Valu

es o

f Dep

ende

nt V

aria

bles


Qualitative Forecasting Models- 5) Least Squares Method

bX a Y^

where

= predicted value of the dependent variable (demand)

X = value of the independent variable (time)

a = Y-axis intercept

b = slope of the regression line

Y^

]Xn - XY[ __

Y

_

22 Xn -Xb =


Qualitative Forecasting Models- 5) Linear Trend Data & Error Analysis

Midwestern Manufacturing CompanyForecasting Linear trend analysis


PeriodActual value

(or) YPeriod number

(or) X Forecast ErrorAbsolute

errorSquared


Year 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 MAPESlope 10.536

Next period 141.000 8


Qualitative Forecasting Models- 5) 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

Valu

e

Actual values Linear (Actual values)


Qualitative Forecasting Models- 6) Seasonality

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 a season to the overall annual average value.

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


Qualitative Forecasting Models- 6) Seasonality Analysis

Eichler Supplies

Year Month DemandAverage Demand Ratio

Seasonal Index

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 1.309June 110 94 1.170 1.223July 100 94 1.064 1.117

August 90 94 0.957 1.064September 85 94 0.904 0.957

October 75 94 0.798 0.851November 75 94 0.798 0.851December 80 94 0.851 0.851

2 January 100 94 1.064February 85 94 0.904

March 90 94 0.957April 110 94 1.170May 131 94 1.394June 120 94 1.277July 110 94 1.170

August 110 94 1.170September 95 94 1.011

October 85 94 0.904November 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 is expected to be 100 units.Forecast demand Year 3 January: 100 X 0.957 = 96 unitsForecast demand Year 3 May: 100 X 1.309 = 131 units


Qualitative Forecasting Models- 6) Deseasonalized Data

• Going back to the conceptual model, solve for trend:

Trend = Y / Season (96 units/ 0.957 = 100.31)

• This eliminates seasonal variation and isolates the trend

• Now use the Least Squares method to compute the Trend

• Now that we have the Seasonal Indices and Trend, we can reseasonalize the data and generate the forecast

Y = Trend x Seasonal Index

Documents

MGS3100_03.ppt/Feb 11, 2016/Page 1 Georgia State University - Confidential MGS 3100 Business Analysis Time Series Forecasting Feb 11, 2016