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Quantitative Analysis for Management Decisions Lecture 5
Forecasting
What
is
Forecasting?
- Forecasting is the art and science of predicting future events
- Underlying basis of all business decision - production, inventory, personnel, facilities
"It is far better to foresee even without certainty than not to foresee at all. "
--Henri Poincare in The Foundations of Science , page 129.
Department
Uses
of
Forecasts
Accounting – Cost/profit estimates
Finance – Cash flow and funding
Human Resources – Hiring/ recruiting/ training
Marketing – Pricing, promotion, strategy
MIS – IT/IS systems, services
Operations – Schedules, MRP, workloads
Product/ service design – new products and services
Time
Series
Data
• Numerical data obtained at regular time intervals
• The time intervals can be annually, quarterly, daily, hourly, etc.
• Example:
Year: 1999 2000 2001 2002 2003
Sales: 75.3 74.2 78.5 79.7 80.2
A time series plot is a two-dimensional plot of time series data
• The vertical axis measures the variable of interest
• The horizontal axis corresponds to the time periods
Page 1 of 37 Quantitative Analysis for Management Decisions Lecture 5
Introduction
to
Time
Series
Analysis
• A time-series is a set of observations on a quantitative variable collected over time.
• Examples
− Dow Jones Industrial Averages
− Historical data on sales, inventory, customer counts, interest rates, cos ts, etc
• Businesses are often very interested in forecasting time series variables.
• Often, independent variables are not available to build a regression model of a time series variable.
• In time series analysis, we analyze the past behavior of a variable in order to predict its future behavior.
Forecast based only on past values, no other variables are important
Assumes that factors influencing past and present will continue influence in future
Time
Series
Components
• Trend can be upward or downward
• Trend can be linear or non-linear
Page 2 of 37 Quantitative Analysis for Management Decisions Lecture 5
Page 3 of 37 Quantitative Analysis for Management Decisions Lecture 5
Some
Time
Series
Terms
• Stationary Data - a time series variable exhibiting no significant upward or downward trend over time.
• Nonstationary Data - a time series variable exhibiting a significant upward or downward t rend over time.
• Seasonal Data - a time series variable exhibiting a repeating patterns at regular intervals over time.
Example
-‐
Consumers'
Expenditure
Page 4 of 37 Quantitative Analysis for Management Decisions Lecture 5
Approaching
Time
Series
Analysis
• There are many, many different time series techniques.
• It is usually impossible to know which technique will be best for a particular data set.
• It is customary to try out several different techniques and select the one that seems to work best.
• To be an effective time series modeler, you need to keep several time series tec hniques in your “tool box.”
Time
Series
Models
A. Stationary Models
1. Moving Average
2. Weighted Moving Average
3. Exponential Smoothing
4. Seasonality
a. Additive
b. Multiplicative
B. Trend Models
1. Double Moving Average
2. Double Exponential Smoothing (Holt’s)
3. Seasonality (Holt-Winter’s)
a. Additive
b. Multiplicative
C. Regression Models (Trend and/or Seasonality)
How do you know if it’s a good forecast? How will you use these results to evaluate the quality of forecast?
Measuring
Accuracy
Page 5 of 37 Quantitative Analysis for Management Decisions Lecture 5
Common
Measures
of
Error
(Evaluating
the
Forecast)
Computing
MAD,
MSE
1) Use the desired forecasting method to forecast BACK IN TIME for time period for which you have actual data.
2) Compare the model’s forecast to the actual historical values -> calculate the MAD and MSE based on the differences
between forecast and actual values.
3) Repeat for each method you would like to evaluate.
4) Compare resulting MAD’s and MSE’s.
Page 6 of 37 Quantitative Analysis for Management Decisions Lecture 5
Have student come up to compute MAD from the data. Tell them about ABS function in Excel for computing absolute values.
Suggest use of a full period of seasonality (e.g. 4 quarters) to eliminate seasonal effects and focus on any trends that may be
present. Note the results on the graph (plot also historical predictions for MA).
Large errors have more impact in the MSE calculation
Ask students what they’d do to compute MSE. Tell them about SUMXMY2 function to compute numerator for MSE. Show the
computation.
Page 7 of 37 Quantitative Analysis for Management Decisions Lecture 5
A
Comment
on
Comparing
MSE
Values
• Care should be taken when comparing MSE values of two different forecasting techniques.
• The lowest MSE may result from a technique that fits older values very well but fits recent values poorly.
• It is sometimes wise to compute the MSE using only the most recent values.
The
Simplest
Forecast:
A
Naive
Approach
• Assumes demand in next
period is the same as
demand in most recent period
• e.g., If January sales were 68, then February sales will be 68
• Sometimes cost effective and efficient
• Can be good starting point
Extrapolation
Models
• Extrapolation models try to account for the past behavior of a time seri es variable in an effort to predict the future
behavior of the variable.
We’ll first talk about several extrapolation techniques that are appropriate for stationary data.
Smoothing
Techniques…
If we can determine which components actually exist in a ti me series, we can develop better forecasts.
We can reduce random variation by smoothing the time series.
Two methods to smooth the data are:
Moving averages and
Exponential smoothing.
Time
Series
Models
A. Stationary Models
1. Moving Average
2. Weighted Moving Average
3. Exponential Smoothing
4. Seasonality
a. Additive
b. Multiplicative
B. Trend Models
1. Regression Models
Moving
Average
Method
• A forecasting technique that uses an average of the most recent periods of the data to forecast the next period
• Looks back at history for a fixed period of time
Page 8 of 37 Quantitative Analysis for Management Decisions Lecture 5
Moving
Averages
(Textbook
Notation)
No general method exists for determining k.
We must try out several k values to see what works best.
• Example: Four-quarter moving average
– First average:
– Second average:
– etc…
• The Carbondale Hospital is considering the purchase of a new ambulance. The decision will rest partly on the
anticipated mileage to be driven next year. The miles driven during the past 5 years are asfollows:
Forecast the mileage for the next year usin g 2-year moving average.
Page 9 of 37 Quantitative Analysis for Management Decisions Lecture 5
Moving
Average
Example
In Excel: Tools > Data Analysis… > Moving Average
Page 10 of 37 Quantitative Analysis for Management Decisions Lecture 5
Graph
of
Moving
Average
Moving
Average
• What is the effect of choosing a larger value for n? What happens when n matches the period of the data?
Try n=2, n=4 and n=6 for “Clothing and Footwear”.
Page 11 of 37 Quantitative Analysis for Management Decisions Lecture 5
• How does the forecast compare to actual values?
• What happens to the forecast as you forecast further into the future?
Evaluating
the
Forecast
• How do you know if it’s a good forecast?
• MAD
• MSE
Page 12 of 37 Quantitative Analysis for Management Decisions Lecture 5
Time
Series
Models
A. Stationary Models
1. Moving Average
2. Weighted Moving Average
3. Exponential Smoothing
4. Seasonality
a. Additive
b. Multiplicative
B. Trend Models
1. Regression Models
Weighted
Moving
Average
• Used when trend is present
• Older data usually less important
• Weights based on experience and intuition
Weighted
Moving
Average
(Textbook
Notation)
• The moving average technique assigns equal weight to all previous observations
Page 13 of 37 Quantitative Analysis for Management Decisions Lecture 5
The weighted moving average technique allows for different weights to be assigned to previous observa tions.
We must determine values for k and the w i
Weighted
Moving
Average
Carbondale
Hospital
Example
Revisited
Page 14 of 37 Quantitative Analysis for Management Decisions Lecture 5
Graph
of
Weighted
Moving
Average
MA
and
Seasonality?
Is it possible to assign weights to capture effects due to seasonality?
How might you do this?
Potential
Problems
With
Moving
Average
• Increasing the size of n (the number of periods averaged) does smooth out the forecast but makes it less sensitive to
real changes in the data
Page 15 of 37 Quantitative Analysis for Management Decisions Lecture 5
• Does not forecast trends well -> used for short term forec asting
Time
Series
Models

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