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1 Module 4. Forecasting MGS3100

1 Module 4. Forecasting MGS3100. 2 Forecasting Quantitative Causal Model Trend Time series Stationary Trend Trend + Seasonality Qualitative Expert Judgment

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Page 1: 1 Module 4. Forecasting MGS3100. 2 Forecasting Quantitative Causal Model Trend Time series Stationary Trend Trend + Seasonality Qualitative Expert Judgment

1

Module 4. Forecasting

MGS3100

Page 2: 1 Module 4. Forecasting MGS3100. 2 Forecasting Quantitative Causal Model Trend Time series Stationary Trend Trend + Seasonality Qualitative Expert Judgment

2

Forecasting

Forecasting

Quantitative Qualitative

Causal Model

Time series

Expert Judgment

Trend

Stationary

Trend

Trend + Seasonality

Delphi Method

Grassroots

Page 3: 1 Module 4. Forecasting MGS3100. 2 Forecasting Quantitative Causal Model Trend Time series Stationary Trend Trend + Seasonality Qualitative Expert Judgment

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• Casual Models:

Causal Model

Year 2000 Sales

Price PopulationAdvertising

……

• Time Series Models:

Time Series Model

Year 2000 Sales

Sales1999 Sales1998

Sales1997……

--Forecasting based on data and models

Quantitative Forecasting

Page 4: 1 Module 4. Forecasting MGS3100. 2 Forecasting Quantitative Causal Model Trend Time series Stationary Trend Trend + Seasonality Qualitative Expert Judgment

4

Causal forecasting

• RegressionFind a straight line that fits the data best.

y = Intercept + slope * x (= b0 + b1x)

Slope = change in y / change in x

0

2

4

6

8

10

12

10 11 12 13 14 15 16 17 18 19 20

Best line!

Intercept

Page 5: 1 Module 4. Forecasting MGS3100. 2 Forecasting Quantitative Causal Model Trend Time series Stationary Trend Trend + Seasonality Qualitative Expert Judgment

5

Causal Forecasting Models

• Curve Fitting: Simple Linear Regression– One Independent Variable (X) is used to predict one

Dependent Variable (Y): Y = a + b X

– Given n observations (Xi, Yi), we can fit a line to the overall pattern of these data points. The Least Squares Method in statistics can give us the best a and b in the sense of minimizing (Yi - a - bXi)2:

n

Xb

n

Ya

n

XX

n

YXYXb

ii

ii

iiii

22 )(

/

Regression formula is an optional learning objective

Page 6: 1 Module 4. Forecasting MGS3100. 2 Forecasting Quantitative Causal Model Trend Time series Stationary Trend Trend + Seasonality Qualitative Expert Judgment

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• Curve Fitting: Simple Linear Regression – Find the regression line with Excel

• Use Function:

a = INTERCEPT(Y range; X range)

b = SLOPE(Y range; X range) • Use Solver

• Use Excel’s Tools | Data Analysis | Regression

• Curve Fitting: Multiple Regression– Two or more independent variables are used to

predict the dependent variable:

Y = b0 + b1X1 + b2X2 + … + bpXp

– Use Excel’s Tools | Data Analysis | Regression

Page 7: 1 Module 4. Forecasting MGS3100. 2 Forecasting Quantitative Causal Model Trend Time series Stationary Trend Trend + Seasonality Qualitative Expert Judgment

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Time Series Forecasting Process

Look at the data (Scatter Plot)

Forecast using one or more techniques

Evaluate the technique and pick the best one.

Observations from the scatter Plot

Techniques to try Ways to evaluate

Data is reasonably stationary (no trend or seasonality)

Heuristics - Averaging methods Naive Moving Averages Simple Exponential Smoothing

MAD MAPE Standard Error BIAS

Data shows a consistent trend

Regression Linear Non-linear Regressions (not covered in this course)

MAD MAPE Standard Error BIAS R-Squared

Data shows both a trend and a seasonal pattern

Classical decomposition Find Seasonal Index Use regression analyses to find the trend component

MAD MAPE Standard Error BIAS R-Squared

Page 8: 1 Module 4. Forecasting MGS3100. 2 Forecasting Quantitative Causal Model Trend Time series Stationary Trend Trend + Seasonality Qualitative Expert Judgment

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• BIAS - The arithmetic mean of the errors

– n is the number of forecast errors– Excel: =AVERAGE(error range)

• Mean Absolute Deviation - MAD

– No direct Excel function to calculate MAD

Evaluation of Forecasting Model

n

Error

n

Forecast) - (Actual BIAS

n

|Error|

n

Forecast - Actual| MAD

|

Page 9: 1 Module 4. Forecasting MGS3100. 2 Forecasting Quantitative Causal Model Trend Time series Stationary Trend Trend + Seasonality Qualitative Expert Judgment

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• Mean Square Error - MSE

– Excel: =SUMSQ(error range)/COUNT(error range)

– Standard error is square root of MSE

• Mean Absolute Percentage Error - MAPE

• R2 - only for curve fitting model such as regression• In general, the lower the error measure (BIAS, MAD,

MSE) or the higher the R2, the better the forecasting model

n

(Error)

n

Forecast) - (Actual MSE

22

nActual

|Forecast - Actual|

MAPE

%100*

Evaluation of Forecasting Model

Page 10: 1 Module 4. Forecasting MGS3100. 2 Forecasting Quantitative Causal Model Trend Time series Stationary Trend Trend + Seasonality Qualitative Expert Judgment

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Stationary data forecasting

• Naïve I sold 10 units yesterday, so I think I will sell 10 units

today.

• n-period moving averageFor the past n days, I sold 12 units on average.

Therefore, I think I will sell 12 units today.

• Exponential smoothing I predicted to sell 10 units at the beginning of yesterday;

At the end of yesterday, I found out I sold in fact 8 units. So, I will adjust the forecast of 10 (yesterday’s forecast) by adding adjusted error (α * error). This will compensate over (under) forecast of yesterday.

Page 11: 1 Module 4. Forecasting MGS3100. 2 Forecasting Quantitative Causal Model Trend Time series Stationary Trend Trend + Seasonality Qualitative Expert Judgment

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Naïve Model

• The simplest time series forecasting model

• Idea: “what happened last time (last year,

last month, yesterday) will happen again this

time”

• Naïve Model:– Algebraic: Ft = Yt-1

• Yt-1 : actual value in period t-1

• Ft : forecast for period t

– Spreadsheet: B3: = A2; Copy down

Page 12: 1 Module 4. Forecasting MGS3100. 2 Forecasting Quantitative Causal Model Trend Time series Stationary Trend Trend + Seasonality Qualitative Expert Judgment

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Moving Average Model• Simple n-Period Moving Average

• Issues of MA Model – Naïve model is a special case of MA with n = 1 – Idea is to reduce random variation or smooth data– All previous n observations are treated equally (equal

weights)– Suitable for relatively stable time series with no trend or

seasonal pattern

nnt

Y2t

Y1t

Y=

n

periodsn previousin valuesactual of Sumt

F

Page 13: 1 Module 4. Forecasting MGS3100. 2 Forecasting Quantitative Causal Model Trend Time series Stationary Trend Trend + Seasonality Qualitative Expert Judgment

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Smoothing Effect of MA Model

Longer-period moving averages (larger n) react to actual changes more slowly

Page 14: 1 Module 4. Forecasting MGS3100. 2 Forecasting Quantitative Causal Model Trend Time series Stationary Trend Trend + Seasonality Qualitative Expert Judgment

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Moving Average Model

• Weighted n-Period Moving Average

– Typically weights are decreasing:

w1>w2>…>wn

– Sum of the weights = wi = 1

– Flexible weights reflect relative importance of each previous observation in forecasting

– Optimal weights can be found via Solver

ntY

nw

2tY

2w

1tY

1 w=

tF

Page 15: 1 Module 4. Forecasting MGS3100. 2 Forecasting Quantitative Causal Model Trend Time series Stationary Trend Trend + Seasonality Qualitative Expert Judgment

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Weighted MA: An Illustration

Month Weight Data

August 17% 130

September 33% 110

October 50% 90

November forecast:

FNov = (0.50)(90)+(0.33)(110)+(0.17)(130)

= 103.4

Page 16: 1 Module 4. Forecasting MGS3100. 2 Forecasting Quantitative Causal Model Trend Time series Stationary Trend Trend + Seasonality Qualitative Expert Judgment

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Exponential Smoothing

• Concept is simple!– Make a forecast, any forecast– Compare it to the actual– Next forecast is

• Previous forecast plus an adjustment• Adjustment is fraction of previous forecast error

– Essentially• Not really forecast as a function of time• Instead, forecast as a function of previous actual and

forecasted value

Page 17: 1 Module 4. Forecasting MGS3100. 2 Forecasting Quantitative Causal Model Trend Time series Stationary Trend Trend + Seasonality Qualitative Expert Judgment

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Simple Exponential Smoothing

• A special type of weighted moving average – Include all past observations– Use a unique set of weights that weight recent observations

much more heavily than very old observations:

( )

( )

( )

1

1

1

2

3

weight

Decreasing weights given to older observations

0 1

Today

Page 18: 1 Module 4. Forecasting MGS3100. 2 Forecasting Quantitative Causal Model Trend Time series Stationary Trend Trend + Seasonality Qualitative Expert Judgment

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Simple ES: The Model

New forecast = weighted sum of last period actual value and last

period forecast – : Smoothing constant

– Ft : Forecast for period t

– Ft-1: Last period forecast

– Yt-1: Last period actual value

321

32

21

)1()1(

)1()1(

tttt

tttt

YaYYF

YYYF

11 )1( ttt FYF

Page 19: 1 Module 4. Forecasting MGS3100. 2 Forecasting Quantitative Causal Model Trend Time series Stationary Trend Trend + Seasonality Qualitative Expert Judgment

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Simple Exponential Smoothing

• Properties of Simple Exponential Smoothing

– Widely used and successful model

– Requires very little data

– Larger , more responsive forecast; Smaller

, smoother forecast (See Table 13.2)

– “best” can be found by Solver

– Suitable for relatively stable time series

Page 20: 1 Module 4. Forecasting MGS3100. 2 Forecasting Quantitative Causal Model Trend Time series Stationary Trend Trend + Seasonality Qualitative Expert Judgment

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Time Series Components

• Trend– persistent upward or downward pattern in a time series

• Seasonal – Variation dependent on the time of year – Each year shows same pattern

• Cyclical – up & down movement repeating over long time frame– Each year does not show same pattern

• Noise or random fluctuations – follow no specific pattern – short duration and non-repeating

Page 21: 1 Module 4. Forecasting MGS3100. 2 Forecasting Quantitative Causal Model Trend Time series Stationary Trend Trend + Seasonality Qualitative Expert Judgment

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Time Series Components

Time

Trend

Randommovement

Time

Cycle

Time

Seasonalpattern

Dem

and

Time

Trend with seasonal pattern

Page 22: 1 Module 4. Forecasting MGS3100. 2 Forecasting Quantitative Causal Model Trend Time series Stationary Trend Trend + Seasonality Qualitative Expert Judgment

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Trend Model• Curve fitting method used for time series

data (also called time series regression model)

• Useful when the time series has a clear trend• Can not capture seasonal patterns

• Linear Trend Model: Yt = a + bt – t is time index for each period, t = 1, 2, 3,…

0

1

2

3

4

5

6

7

1 2 3 4 5 6 7 8 9 10

Page 23: 1 Module 4. Forecasting MGS3100. 2 Forecasting Quantitative Causal Model Trend Time series Stationary Trend Trend + Seasonality Qualitative Expert Judgment

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Pattern-based forecasting - Trend

• Regression – Recall Independent Variable X, which is now time variable – e.g., days, months, quarters, years etc. Find a straight line that fits the data best.

y = Intercept + slope * x (= b0 + b1x)

Slope = change in y / change in x

0

2

4

6

8

10

12

10 11 12 13 14 15 16 17 18 19 20

Best line!

Intercept

Page 24: 1 Module 4. Forecasting MGS3100. 2 Forecasting Quantitative Causal Model Trend Time series Stationary Trend Trend + Seasonality Qualitative Expert Judgment

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Pattern-based forecasting – Seasonal

• Once data turn out to be seasonal, deseasonalize the data.– The methods we have learned (Heuristic methods and

Regression) is not suitable for data that has pronounced fluctuations.

• Make forecast based on the deseasonalized data

• Reseasonalize the forecast– Good forecast should mimic reality. Therefore, it is

needed to give seasonality back.

Page 25: 1 Module 4. Forecasting MGS3100. 2 Forecasting Quantitative Causal Model Trend Time series Stationary Trend Trend + Seasonality Qualitative Expert Judgment

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Pattern-based forecasting – Seasonal

Deseasonalize

Forecast

Reseasonalize

Actual data Deseasonalized data

Example (SI + Regression)

Page 26: 1 Module 4. Forecasting MGS3100. 2 Forecasting Quantitative Causal Model Trend Time series Stationary Trend Trend + Seasonality Qualitative Expert Judgment

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Pattern-based forecasting – Seasonal

• DeseasonalizationDeseasonalized data = Actual / SI

• ReseasonalizationReseasonalized forecast

= deseasonalized forecast * SI

Page 27: 1 Module 4. Forecasting MGS3100. 2 Forecasting Quantitative Causal Model Trend Time series Stationary Trend Trend + Seasonality Qualitative Expert Judgment

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Seasonal Index

• What’s an index?– Ratio– SI = ratio between actual and average demand

• Suppose– SI for quarter demand is 1.20

• What’s that mean?• Use it to forecast demand for next fall

– So, where did the 1.20 come from?!

Page 28: 1 Module 4. Forecasting MGS3100. 2 Forecasting Quantitative Causal Model Trend Time series Stationary Trend Trend + Seasonality Qualitative Expert Judgment

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Calculating Seasonal Indices

• Quick and dirty method of calculating SI– For each year, calculate average demand– Divide each demand by its yearly average

• This creates a ratio and hence a raw index• For each quarter, there will be as many raw indices

as there are years– Average the raw indices for each of the quarters– The result will be four values, one SI per quarter

Page 29: 1 Module 4. Forecasting MGS3100. 2 Forecasting Quantitative Causal Model Trend Time series Stationary Trend Trend + Seasonality Qualitative Expert Judgment

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Classical decomposition

• Start by calculating seasonal indices• Then, deseasonalize the demand

– Divide actual demand values by their SI valuesy ’ = y / SI

– Results in transformed data (new time series)– Seasonal effect removed

• Forecast– Regression if deseasonalized data is trendy– Heuristics methods if deseasonalized data is stationary

• Reseasonalize with SI

Page 30: 1 Module 4. Forecasting MGS3100. 2 Forecasting Quantitative Causal Model Trend Time series Stationary Trend Trend + Seasonality Qualitative Expert Judgment

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Causal or Time series?

• What are the difference?

• Which one to use?

Page 31: 1 Module 4. Forecasting MGS3100. 2 Forecasting Quantitative Causal Model Trend Time series Stationary Trend Trend + Seasonality Qualitative Expert Judgment

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Can you…

• describe general forecasting process?

• compare and contrast trend, seasonality and cyclicality?

• describe the forecasting method when data is stationary?

• describe the forecasting method when data shows trend?

• describe the forecasting method when data shows seasonality?