1. A Practical Application
of Monte Carlo Simulation
in Forecasting
James D. Whiteside
2008 AACE INTERNATIONAL TRANSACTIONS
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2. Contents
• Research Issue
• Extrapolation/Forecasting Models
• Monte-Carlo simulation
• Brownian walk
• Requirements: Uniform Probability Distribution
• Experiment1: Forecasting Raw Mode
• Experiment2: Forecasting Regression Mode
• Interpretation of Results
• Real Life Application of Brownian-walk approach
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3. Research Issue
• Practical application of the Brownian-walk Monte Carlo simulation in
forecasting is focused in this paper.
• Simple spreadsheet and time-dependent historical data
• Monte Carlo routine is used to forecasting productivity,
installation rates and labor trends.
• Outlines a more robust methodology to create a composite
forecast by combining several single commodities.
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4. Research Goal:
Extrapolation/Forecasting Models
• Extrapolating or forecasting beyond or outside the known data
• Predicting a point that is well beyond the last data point requires a
good extrapolation routine
• This numerically-based routine should be combined with other
parameters.
• Result is a range of probable outcomes that can be individually
evaluated to assist with the decision-making process.
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5. Published forecast challenges
• Based purely on the data, science, and available mathematical
models.
• Published forecasts generally can not capture changing policies,
unintended consequences in market dynamics.
• This paper is focused on the science of data forecasting
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6. Methodology: THREE FORECASTING
MODELS
• Causal Model: forecast is associated with the changes in other
variables
• Judgmental Model: experience and intuition outweighs the lack of
hard data.
• Time Series Model: Time series is based a direct correlation of data to
time, with a forecast that is able to mimic the pattern of past
behavior.
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7. Monte-Carlo Simulation
The Monte Carlo method provides
approximate solutions to a variety of
mathematical problems by performing
statistical sampling experiments on a
computer.
Use: Error estimation
Increased number of random variables as
inputs will ensure better output of
Monte-Carlo simulation
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8. MONTE CARLO SIMULATION
• Iteratively evaluating a deterministic model using sets of random
numbers as inputs.
• Monte Carlo simulation is a specialized probability application that is
no more than an equation where the variables have been replaced
with a random number generator.
• Power of Monte Carlo simulation
• simple
• fast.
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9. Brownian-walk
• Time series equation
• Geometric Brownian – walk
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10. Formula: Monte Carlo simulation of
Brownian Walk
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11. Uniform probability distribution function
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12. Important issues about the Brownian-
walk
• Historical data is used to calculate the annualized growth and annual
volatility values.
• Based on these values, a set of possible outcomes are generated until
they represent a data regression with an acceptable “goodness of fit”
(observed value and expected value obtained from a model) value.
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13. Experiment: Forecasting Raw Mode
• Raw mode: there is no attempt to correct the forecasts
• The raw mode is a pure Brownian-walk output.
• The outputs are totally random
• No re-adjustment of values are executed
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14. Experiment: Forecasting Regression
mode
• Monte-Carlo is used to obtain a regression data set
• Error is the difference between the actual value and the predicted value.
• RMSE is the average of the forecast errors.
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15. Analysis of Results
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16. Interpretation 1: Simple Probability
• Line “F1” suggests that the units will continue to rise.
• Line “F2” suggests that the units will continue to rise until time 145
and then drop off.
• Given that “time now” is at 125, in order for the forecast Line “F3” to
be correct, the units will start dropping precipitously in the next few
time periods.
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17. Interpretation 2: Weighted Data
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18. Interpretation 3: Simple Statistics
• Looking at time 150 there is a 2/3 chance that the units will remain
between 40 and 50.
• There is only a 1/3 chance that the Units will remain above 60.
• Line “F2” and Line “F3” suggest that the units will flatten out or
decline between time 125 and time 150.
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19. Application of Brownian Walk-Monte
Carlo approach
• Asset distribution
• Material Forecast
• Resource allocation forecast
• Growth of a product over a period of time
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20. Thank you
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