1. Module 4. Forecasting
MGS3100

2. Forecasting

3. 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

4. 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

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:
Regression formula is an optional learning objective

6. 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

7. 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)
R-Squared
Data shows both a trend and a seasonal pattern
Classical decomposition
Find Seasonal Index
Use regression analyses to find the trend component

8. 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

9. 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

10. 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 (yesterday’s forecast) by adding adjusted error (α * error). This will compensate over (under) forecast of yesterday.

11. 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

12. 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

13. Smoothing Effect of MA Model
Longer-period moving averages (larger n) react to actual changes more slowly

14. 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

15. 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

16. 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

17. 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:
weight
Decreasing weights given
to older observations
Today

18. 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

19. 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

20. 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

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

22. 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,…

23. 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

24. 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.

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

26. Pattern-based forecasting – Seasonal
Deseasonalization
Deseasonalized data = Actual / SI
Reseasonalization
Reseasonalized forecast
= deseasonalized forecast * SI

27. Seasonal Index What’s an index? Suppose 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?!

28. 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

29. 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

30. Causal or Time series?
What are the difference?
Which one to use?

31. 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?