Module 4. Forecasting

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Module 4. Forecasting

• MGS3100

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Forecasting
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Quantitative Forecasting
--Forecasting based on data and models

• Casual Models

Price Population Advertising
Causal Model
Year 2000 Sales

• Time Series Models

Sales1999 Sales1998 Sales1997
Time Series Model
Year 2000 Sales
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Causal forecasting

• Regression
• Find a straight line that fits the data best.
• y Intercept slope x ( b0 b1x)
• Slope change in y / change in x

Best line!
Intercept
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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

Regression formula is an optional learning
objective
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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 Excels 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 Excels Tools Data Analysis Regression

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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
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Evaluation of Forecasting Model

• 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

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Evaluation of Forecasting Model

• 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

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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 average
• For 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 (yesterdays forecast) by adding
  adjusted error (a error). This will compensate
  over (under) forecast of yesterday.

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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

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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

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Smoothing Effect of MA Model

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

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Moving Average Model

• Weighted n-Period Moving Average
• Typically weights are decreasing w1gtw2gtgtwn
• Sum of the weights ?wi 1
• Flexible weights reflect relative importance of
  each previous observation in forecasting
• Optimal weights can be found via Solver

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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
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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

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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

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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

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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

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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

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Time Series Components
Cycle
Trend
Random movement
Time
Time
Seasonal pattern
Trend with seasonal pattern
Demand
Time
Time
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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,

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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

Best line!
Intercept
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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.

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Pattern-based forecasting Seasonal
Example (SI Regression)
Actual data
Deseasonalized data
Deseasonalize
Forecast
Reseasonalize
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Pattern-based forecasting Seasonal

• Deseasonalization
• Deseasonalized data Actual / SI
• Reseasonalization
• Reseasonalized forecast
• deseasonalized forecast
  SI

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Seasonal Index

• Whats an index?
• Ratio
• SI ratio between actual and average demand
• Suppose
• SI for quarter demand is 1.20
• Whats that mean?
• Use it to forecast demand for next fall
• So, where did the 1.20 come from?!

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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

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Classical decomposition

• Start by calculating seasonal indices
• Then, deseasonalize the demand
• Divide actual demand values by their SI values
• y 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

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Causal or Time series?

• What are the difference?
• Which one to use?

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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?