Monte carlo presentation for analysis of business growth

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Monte carlo presentation for analysis of business growth

  1. 1. A Practical Application of Monte Carlo Simulation in Forecasting James D. Whiteside 2008 AACE INTERNATIONAL TRANSACTIONS A Practical Application of Monte-Carlo in Forecasting 1
  2. 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 A Practical Application of Monte-Carlo in Forecasting 2
  3. 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. A Practical Application of Monte-Carlo in Forecasting 3
  4. 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. A Practical Application of Monte-Carlo in Forecasting 4
  5. 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 A Practical Application of Monte-Carlo in Forecasting 5
  6. 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. A Practical Application of Monte-Carlo in Forecasting 6
  7. 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 A Practical Application of Monte-Carlo in Forecasting 7
  8. 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. A Practical Application of Monte-Carlo in Forecasting 8
  9. 9. Brownian-walk • Time series equation • Geometric Brownian – walk A Practical Application of Monte-Carlo in Forecasting 9
  10. 10. Formula: Monte Carlo simulation of Brownian Walk A Practical Application of Monte-Carlo in Forecasting 10
  11. 11. Uniform probability distribution function A Practical Application of Monte-Carlo in Forecasting 11
  12. 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. A Practical Application of Monte-Carlo in Forecasting 12
  13. 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 A Practical Application of Monte-Carlo in Forecasting 13
  14. 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. A Practical Application of Monte-Carlo in Forecasting 14
  15. 15. Analysis of Results A Practical Application of Monte-Carlo in Forecasting 15
  16. 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. A Practical Application of Monte-Carlo in Forecasting 16
  17. 17. Interpretation 2: Weighted Data A Practical Application of Monte-Carlo in Forecasting 17
  18. 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. A Practical Application of Monte-Carlo in Forecasting 18
  19. 19. Application of Brownian Walk-Monte Carlo approach • Asset distribution • Material Forecast • Resource allocation forecast • Growth of a product over a period of time A Practical Application of Monte-Carlo in Forecasting 19
  20. 20. Thank you A Practical Application of Monte-Carlo in Forecasting 20

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