1. FORECASTING (overview)

2. The history of forecasting
The development of business forecasting in the 17th century was a major innovation [Bernstein P. (1996)]
Along with the development of data-based methods, forecasting has grown significantly over the last 50 years
Without any data history, human judgement may be the only way to make predictions about the future
If data are available, forecasts can be produced by quantitative techniques
Lack of managerial oversight and improper use of forecasting techniques can lead costly decisions

3. Is forecasting neccessary?
How can an operations manager realistically set production schedule
without some estimates of future sales..
How can a company determine staffing for its call centers
without some guess of future demand for service
Everyone requires forecasts
The need for forecasts cuts across all functional lines as well as types of organizations

4. Types of forecasts- quantitative or qualitative
A purely qualitative technique is one requiring no manipulation of data
judgement of the forecaster is used
A purely quantitative technique need no judgement
mechanical procedures that produce quantitative results are used
Effective management of modern organizations need
judgement and common sense along with mechanical and data-manipulative procedures

5. Choosing a forecasting method
Rarely (practically never)does one method work for all cases
While choosing the forecasting method, organization’s manager must consider:
Different products
New versus established
Characteristics of data
Stationary or unstationary
Has trend / seasonality /or wavelike fluctuation
Goals
simple prediction versus need for future values
Constraints
cost, required expertise, immediacy
Several methods can be tried in a given situation
The methodology producing the most accurate forecasts in one case may not be the best methodology in another situation

6. Forecasting steps Problem formulation and data collection
The problem determines the appropriate data
Often accessing and assembling appropriate data is challenging and time-consuming task
If appropriae data are not available, the problem may have to be redefined
Data manipulation and cleaning
Some data may not be relevant to problem
Some data may have missing values that must be estimated
Model building and evaluation
Involves fitting the collected data into a forecasting model that minimizes forecasting error
Model implementation
Generation of the actual model once the appropriate data have collected
Forecast evaluation
Involves comparing forecast values with actual historical values

7. Exploring time series data pattern
Horizontal pattern
When data collected over time fluctuate around a constant level or mean, horizontal pattern exists.
This type of series is said to be stationary in mean
Ex. Monthly sales for a food product that do not increase or decrease consistently over an extended period
Trend pattern
When data grow or decline over several time periods, trend pattern exists
Ex. Population growth, price, inflation, technological change, consumer preferences, productivity increases..

8. Exploring time series data pattern
Cyclical pattern
Is the wavelike fluctuation around the trend
Are usually affected by economic conditions
Cyclical peak in figure shows economic expansion
Cyclical vallye shows economic contradiction
Seasonal pattern
When observations are influenced by seasonal factors a seasonal pattern exists
It refers to a pattern of change that repeats itself year after year
Water power residential customers is highest in the first quarter, winter months
Seasonal variation may reflect weather conditions, school schedules, holidays

9. Measuring Forecast Error
Basic Forecasting Notation
𝑌 𝑡 :𝑡ℎ𝑒 𝑣𝑎𝑙𝑢𝑒𝑠 𝑜𝑓 𝑎 𝑡𝑖𝑚𝑒 𝑠𝑒𝑟𝑖𝑒𝑠 𝑎𝑡 𝑝𝑒𝑟𝑖𝑜𝑑 𝑡
𝑌 𝑡 :𝑡ℎ𝑒 𝑓𝑜𝑟𝑒𝑐𝑎𝑠𝑡 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝑌 𝑡
A residual
Is the difference between on actual observed value and its forecast value

10. Measuring Forecast Error
Mean absolute deviation:
𝑀𝐴𝐷= 1 𝑛 𝑡=1 𝑛 𝑌 𝑡 − 𝑌 𝑡
Mean Squared error
𝑀𝑆𝐸= 1 𝑛 𝑡=1 𝑛 𝑌 𝑡 − 𝑌 𝑡 2
Root mean squared error
𝑅𝑀𝑆𝐸= 1 𝑛 𝑡=1 𝑛 𝑌 𝑡 − 𝑌 𝑡 2
Mean absolute percentage error
𝑀𝐴𝑃𝐸= 1 𝑛 𝑡=1 𝑛 𝑌 𝑡 − 𝑌 𝑡 𝑌 𝑡
Mean percentage error
𝑀𝑃𝐸= 1 𝑛 𝑡=1 𝑛 𝑌 𝑡 − 𝑌 𝑡 𝑌 𝑡

11. Naive models
Often young businesses face the dilemma of trying to forecast with very small data sets
This situation creates a real problem, since many forecasting techniques require large amounts of data
These methods assume that recent periods are the best predictors of future
Ex. Tomorrow’s weather will be much likely today’s weather
𝑌 𝑡+1 = 𝑌 𝑡
When data values increase over time, they are said to be non-stationary in level or to have a trend
If the above equation is used the projections-estimations will be consistently low.
Technique can be adjusted to take trend into the consideration by adding the differences between last two periods. Then the adjusted equation is:
𝑌 𝑡+1 = 𝑌 𝑡 + 𝑌 𝑡 − 𝑌 𝑡−1

12. Methods Based on Averaging
Some quick, inexpensive, very simple short-term forecasting tools are needed when management faces with hundreds or thousands of items
Simple Averages
Decision is made to use the first t data points as the initialization parta and remaining data point as the test part
𝑌 𝑡+1 = 1 𝑡 𝑖=1 𝑡 𝑌 𝑖

13. Moving Averages
What if the analyst is more concerned with recent observations
We use moving averages.
𝑌 𝑡+1 = 𝑌 𝑡 + 𝑌 𝑡−1 +…+ 𝑌 𝑡−𝑘+1 𝑘
where
𝑌 𝑡+1 : the forecast value for the next period
𝑌 𝑡 : the actual value at period t
k: the number of terms in the moving average

14. Weighted Moving Average
Takes only the most recent observation into account,
But the weights of observations are not equal.
Gives higher weights most recent data.

15. Exercise
month
yield
January
9.29
February
9.99
March
10.16
April
10.25
May
10.61
June
11.07
July
11.52
August
11.09
September
10.80
October
10.50
November
10.96
December
9.97
The yield on a general obligation bond for the city of Davenport fluctuates with the market. The monthly quotations for 2014 are given as:

16. Exercise
Find the forecast value of the yield for the obligation bonds for each month, starting with April, using a trend adjusted naive method
Find the forecast value of the yield for the obligation bonds for each month, starting with April, using a two-month moving average
Find the forecast value of the yield for the obligation bonds for each month, starting with June, using a five-month moving average
Evaluate the performance of the methods using MAD
Evaluate the performance of the methods using MSE
Forecast the yield for January 2007 using the better technique