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MGS3100_03.ppt/Feb 11, 2016/Page 3 Georgia State University - Confidential 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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MGS3100_03.ppt/Feb 11, 2016/Page 1Georgia State University - Confidential
MGS 3100
Business Analysis
Time Series Forecasting
Feb 11, 2016
MGS3100_03.ppt/Feb 11, 2016/Page 2Georgia State University - Confidential
Agenda
Qualitative Forecasting
Models
Quantitative Forecasting
ModelsForecasting
MGS3100_03.ppt/Feb 11, 2016/Page 3Georgia State University - Confidential
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
MGS3100_03.ppt/Feb 11, 2016/Page 4Georgia State University - Confidential
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
MGS3100_03.ppt/Feb 11, 2016/Page 5Georgia State University - Confidential
Agenda
Qualitative Forecasting
Models
Quantitative Forecasting
ModelsForecasting
MGS3100_03.ppt/Feb 11, 2016/Page 6Georgia State University - Confidential
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
MGS3100_03.ppt/Feb 11, 2016/Page 7Georgia State University - Confidential
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
MGS3100_03.ppt/Feb 11, 2016/Page 8Georgia State University - Confidential
Agenda
Qualitative Forecasting
Models
Quantitative Forecasting
ModelsForecasting
MGS3100_03.ppt/Feb 11, 2016/Page 9Georgia State University - Confidential
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
MGS3100_03.ppt/Feb 11, 2016/Page 10Georgia State University - Confidential
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
MGS3100_03.ppt/Feb 11, 2016/Page 11Georgia State University - Confidential
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
MGS3100_03.ppt/Feb 11, 2016/Page 12Georgia State University - Confidential
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
MGS3100_03.ppt/Feb 11, 2016/Page 13Georgia State University - Confidential
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
MGS3100_03.ppt/Feb 11, 2016/Page 14Georgia State University - Confidential
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
MGS3100_03.ppt/Feb 11, 2016/Page 15Georgia State University - Confidential
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
MGS3100_03.ppt/Feb 11, 2016/Page 16Georgia State University - Confidential
Qualitative Forecasting Models- 2) Moving Averages
Wallace Garden SupplyForecasting
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
MGS3100_03.ppt/Feb 11, 2016/Page 17Georgia State University - Confidential
Qualitative Forecasting Models- 2) Moving Averages
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
MGS3100_03.ppt/Feb 11, 2016/Page 18Georgia State University - Confidential
Qualitative Forecasting Models- 2) Moving Averages
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
MGS3100_03.ppt/Feb 11, 2016/Page 19Georgia State University - Confidential
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
MGS3100_03.ppt/Feb 11, 2016/Page 20Georgia State University - Confidential
Qualitative Forecasting Models- 3) Weighted Moving Averages
Wallace Garden SupplyForecasting
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
MGS3100_03.ppt/Feb 11, 2016/Page 21Georgia State University - Confidential
Qualitative Forecasting Models- 3) Weighted Moving Averages
Wallace Garden Supply Forecasting 3 period weighted moving average
Input Data Forecast Error Analysis
Period Actual value Weights Forecast ErrorAbsolute
errorSquared
errorAbsolute % error
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
MGS3100_03.ppt/Feb 11, 2016/Page 22Georgia State University - Confidential
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)^ ^
MGS3100_03.ppt/Feb 11, 2016/Page 23Georgia State University - Confidential
Qualitative Forecasting Models- 4) Exponential Smoothing
Wallace Garden SupplyForecasting
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
MGS3100_03.ppt/Feb 11, 2016/Page 24Georgia State University - Confidential
Qualitative Forecasting Models- 4) Exponential Smoothing
Wallace Garden SupplyForecasting Exponential smoothing
Input Data Forecast Error Analysis
Period Actual value Forecast ErrorAbsolute
errorSquared
errorAbsolute % error
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
MGS3100_03.ppt/Feb 11, 2016/Page 25Georgia State University - Confidential
Qualitative Forecasting Models- 4) Exponential Smoothing
Exponential Smoothing
0
5
10
15
20
25
Shed
s Actual value
Forecast
MGS3100_03.ppt/Feb 11, 2016/Page 26Georgia State University - Confidential
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
MGS3100_03.ppt/Feb 11, 2016/Page 27Georgia State University - Confidential
Qualitative Forecasting Models- 5) Trend Forecasting
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
MGS3100_03.ppt/Feb 11, 2016/Page 28Georgia State University - Confidential
Qualitative Forecasting Models- 5) Trend Forecasting
Non-Linear Regression Examplesi) Quadratic Regression
Y = b0+b1+b2X2^
050
100150200250300350400450
MGS3100_03.ppt/Feb 11, 2016/Page 29Georgia State University - Confidential
Qualitative Forecasting Models- 5) Trend Forecasting
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
MGS3100_03.ppt/Feb 11, 2016/Page 30Georgia State University - Confidential
Qualitative Forecasting Models- 5) Trend Forecasting
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)^
MGS3100_03.ppt/Feb 11, 2016/Page 31Georgia State University - Confidential
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
MGS3100_03.ppt/Feb 11, 2016/Page 32Georgia State University - Confidential
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
MGS3100_03.ppt/Feb 11, 2016/Page 33Georgia State University - Confidential
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 =
MGS3100_03.ppt/Feb 11, 2016/Page 34Georgia State University - Confidential
Qualitative Forecasting Models- 5) Linear Trend Data & Error Analysis
Midwestern Manufacturing CompanyForecasting Linear trend analysis
Input Data Forecast Error Analysis
PeriodActual value
(or) YPeriod number
(or) X Forecast ErrorAbsolute
errorSquared
errorAbsolute % error
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
MGS3100_03.ppt/Feb 11, 2016/Page 35Georgia State University - Confidential
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)
MGS3100_03.ppt/Feb 11, 2016/Page 36Georgia State University - Confidential
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.
MGS3100_03.ppt/Feb 11, 2016/Page 37Georgia State University - Confidential
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
MGS3100_03.ppt/Feb 11, 2016/Page 38Georgia State University - Confidential
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
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