A Practical Application of Monte-Carlo in Forecasting 1

A Practical Applicationof Monte Carlo Simulation

in ForecastingJames D. Whiteside

2008 AACE INTERNATIONAL TRANSACTIONS

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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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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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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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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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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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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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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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Brownian-walk

• Time series equation

• Geometric Brownian – walk

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Formula: Monte Carlo simulation of Brownian Walk

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Uniform probability distribution function

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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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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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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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Analysis of Results

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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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Interpretation 2: Weighted Data

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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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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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Thank you