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2011 02-04 - d sallier - prévision probabiliste
2011 02-04 - d sallier - prévision probabiliste
2011 02-04 - d sallier - prévision probabiliste
2011 02-04 - d sallier - prévision probabiliste
2011 02-04 - d sallier - prévision probabiliste
2011 02-04 - d sallier - prévision probabiliste
2011 02-04 - d sallier - prévision probabiliste
2011 02-04 - d sallier - prévision probabiliste
2011 02-04 - d sallier - prévision probabiliste
2011 02-04 - d sallier - prévision probabiliste
2011 02-04 - d sallier - prévision probabiliste
2011 02-04 - d sallier - prévision probabiliste
2011 02-04 - d sallier - prévision probabiliste
2011 02-04 - d sallier - prévision probabiliste
2011 02-04 - d sallier - prévision probabiliste
2011 02-04 - d sallier - prévision probabiliste
2011 02-04 - d sallier - prévision probabiliste
2011 02-04 - d sallier - prévision probabiliste
2011 02-04 - d sallier - prévision probabiliste
2011 02-04 - d sallier - prévision probabiliste
2011 02-04 - d sallier - prévision probabiliste
2011 02-04 - d sallier - prévision probabiliste
2011 02-04 - d sallier - prévision probabiliste
2011 02-04 - d sallier - prévision probabiliste
2011 02-04 - d sallier - prévision probabiliste
2011 02-04 - d sallier - prévision probabiliste
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2011 02-04 - d sallier - prévision probabiliste

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  • 1. Probabilistic demand forecasting Prepared & presented by Daniel SALLIER Traffic Data & Forecasting Director Aéroports de Paris [email_address] 01 70 03 45 68
  • 2. Content <ul><li>Foreground </li></ul><ul><ul><li>The &quot;classical&quot; forecasting approach </li></ul></ul><ul><ul><li>Drawbacks of the &quot;classical&quot; forecasting approach </li></ul></ul><ul><ul><li>2 generic sources of uncertainty in any forecast </li></ul></ul><ul><li>How to cope with the intrinsic technical uncertainty </li></ul><ul><ul><li>What we are looking for … </li></ul></ul><ul><ul><li>Let's go back to the very basics </li></ul></ul><ul><ul><li>Step #1: model determination </li></ul></ul><ul><ul><li>Step #2: determination of the law of probability of the models parameters </li></ul></ul><ul><ul><li>Step #3: determination of the law of probability of the models output: Y </li></ul></ul><ul><ul><li>Step #4: determination of the law of probability of the future values </li></ul></ul>
  • 3. Content (continued) <ul><ul><li>The data agregation / break-up issue </li></ul></ul><ul><ul><li>The data agregation issue </li></ul></ul><ul><ul><li>The data break-up issue </li></ul></ul><ul><li>Part of the prospective uncertainty: the residual issue </li></ul><ul><ul><li>What are residuals? </li></ul></ul><ul><ul><li>Taking into account part of the prospective risk </li></ul></ul><ul><li>Further developments and applications </li></ul><ul><ul><li>Vertical cuts for most of the short term utilisation </li></ul></ul><ul><ul><li>Horizontal cuts for most of the mid & long term utilisation </li></ul></ul><ul><li>Conclusions </li></ul><ul><ul><li>So many advantages, so few drawbacks </li></ul></ul>
  • 4. Foreground
  • 5. The &quot;classical&quot; forecasting approach <ul><li>Econometrical or chronological models most of the time; </li></ul><ul><li>Assumptions on the future value of the inputs leading to: </li></ul><ul><ul><li>Single forecasted value (base case?); </li></ul></ul><ul><ul><li>Scenario based forecast. </li></ul></ul><ul><li>&quot;Post-processing&quot; of the model outputs by the experts and/or the management; </li></ul>1950 1960 1970 1980 1990 2000 2010 2020 Year Passengers (M) Base case High case Low case Historical traffic
  • 6. Drawbacks of the &quot;classical&quot; forecasting approach <ul><li>The &quot;cheating/forgery&quot; risk: </li></ul><ul><ul><li>&quot;political&quot; figures decided by the management to be &quot;scientifically&quot; justified by the forecasting team; </li></ul></ul><ul><ul><li>experts eager to be as much consensual as possible with the rest of the community: better to be wrong together than right alone! </li></ul></ul><ul><li>It ends up with self deception in the company </li></ul><ul><li>The no ending &quot; what if … &quot; questions asked by a management afraid of having to make up a decision; </li></ul><ul><li>The forecasting team implicitly deciding what is the level of risk the company should incur ; </li></ul><ul><li>A single figure or even scenario related figures does not make any sense from a mathematical and statistical point of view. </li></ul>
  • 7. 2 generic sources of uncertainty in any forecast <ul><li>The intrinsic technical uncertainty : </li></ul><ul><ul><li>Assumptions on the future value of the inputs </li></ul></ul><ul><ul><li>(GDP, population, fares, …); </li></ul></ul><ul><ul><li>The very nature of the forecasting model </li></ul></ul><ul><ul><li>(linear law, exponentiation law, log law, …); </li></ul></ul><ul><ul><li>The uncertainty on the value of the parameters of the forecasting models; </li></ul></ul><ul><ul><li>The residuals: the difference between actual values and estimates. </li></ul></ul><ul><li>The prospective uncertainty ; any &quot;abnormal&quot; event which may happen in the future. </li></ul>The techniques developed by ADP's R&D team address mostly the 1st type of generic uncertainty: The intrinsic technical uncertainty
  • 8. How to cope with the intrinsic technical uncertainty
  • 9. What is the output we are looking for … <ul><li>The theory of probabilities provides the tools to answer most of the issues raised by the measurement of the present and the future uncertainty: </li></ul>… how to proceed? Dummy data
  • 10. Let's go back to the very basics <ul><li>The full story always starts with a cloud of dots out of which one should find one or several laws/models to be further used as forecasting model(s): </li></ul>Actual data
  • 11. Step #1: model determination <ul><li>1 or several models can fit the data. The way the models are determined is not important (econometrical models, behavioural models, etc.) </li></ul>Unless one has precise reason to select a specific model, there is no reasons to keep just one of them and to discard all the others. Each model is given an equal chance. R&D works under process to address this issue: the ADN engine for Alexander’s Drift Net. Actual data Actual data 1 st model Actual data 1 st model 2 nd model Actual data 1 st model 2 nd model 3 rd model
  • 12. Step #2: determination of the law of probability of the models parameters <ul><li>Let's take the 1 st model for instance. </li></ul><ul><li>It's equation is: </li></ul><ul><li>where  X is the residual </li></ul><ul><li>Bootstrap techniques allow to determine the laws of probability of the different parameters (  ,  ,  ,  ) of the model which are strongly correlated to each others. </li></ul>0% 1% 2% 3% 4% 5% 6% 7% 8% 9% 17.5 18.0 18.5 19.0 19.5 20.0 20.5  Probability 0% 1% 2% 3% 4% 5% 6% 7% 8% 9% 0.08 0.09 0.10 0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18  Probability Example of drawings of random samples of the model parameters
  • 13. Step #3: determination of the law of probability of the models output: Y <ul><li>At this stage we have all the probabilistic components of the forecasting model. That's where the Monté-Carlo techniques proves to be useful: </li></ul><ul><ul><li>Take a future deterministic or sampled value of X; </li></ul></ul><ul><ul><li>Draw a random sample of the model parameters; </li></ul></ul><ul><ul><li>Compute the corresponding value of Y; </li></ul></ul><ul><ul><li>Save the value of Y; </li></ul></ul><ul><ul><li>Start the process again until a sufficient number of Ys has been collected; </li></ul></ul><ul><ul><li>Compute the frequency/probability law of Y; </li></ul></ul>X Axis Y axis 98% probability for Y to be within the band Actual data 50% probability for Y to be greater or equal Forecasting model #2
  • 14. Step #4: determination of the law of probability of the future values <ul><li>At this stage of the process we have all the probabilistic future values of each forecasting model. </li></ul><ul><li>That where the Monté-Carlo techniques is used once again to combine all these values and get the final probabilistic forecast. </li></ul><ul><li>Each model is given an equal probability to occur. </li></ul>X axis Y axis 98% probability for Y to be within the band Actual data 50% probability for Y to be greater or equal
  • 15. The data aggregation / break-up issue
  • 16. The data aggregation issue <ul><li>Let's suppose that we are interested in the forecasted demand of the French residents which depends on the French GDP. </li></ul><ul><li>For a given value of the French GDP, we can calculate a forecasted demand to/from UK, to/from the USA, to/from Japan, etc… It means that, from a statistical point of view, the different flows of traffic from/to France cannot be regarded as being independent variables. </li></ul><ul><li>Straightforward application of the Monté-Carlo technique would mix around all the random samples along the computation process as if they were fully independent which they are not. </li></ul>
  • 17. The data agregation issue (continued) <ul><li>This problem can be overcome by &quot;flagging&quot; each value of the explanatory variables (i.e. French GDP, British GDP, etc.) and to &quot;stick&quot; the flag(s) value to the intermediate or final random samples which are sharing the same value of the explanatory variable(s). </li></ul><ul><li>Instead of &quot;mixing around&quot; all the data set, the Monté-Carlo engine just &quot;mixes around&quot; the random samples which are sharing the same flag. </li></ul>
  • 18. The data break-up issue (continued) <ul><li>Let's suppose that the overall business level of risk as been set to 80% of probability for the overall demand to be greater or equal for instance. How does it cascade down? What is the corresponding level of risk of each traffic flow? </li></ul><ul><li>One should bare in mind that, unfortunately, 1+1  2 when dealing with probabilities; 1 + 1 could make 1.9! </li></ul><ul><li>Flagging the random samples of each traffic flow is one of the solutions to trace back which ones have been used in the final computation. </li></ul>Cumulated distribution of probabilities Overall demand 100% 80% 0% Set of samples to be discarded Demand of the traffic flow # i 100% 74% 0% Set of samples to be elected Cumulated distribution of probabilities Frequency law of the elected samples
  • 19. Part of the prospective uncertainty: the residual issue
  • 20. Taking into account part of the prospective risk <ul><li>A very simple and straightforward idea: </li></ul><ul><ul><li>Determination of the law of probability of the residuals. </li></ul></ul><ul><ul><li>Addition of the residual effects to the &quot;regular&quot; probabilistic forecast which can be achieved with a new round of Monté-Carlo simulations. </li></ul></ul><ul><li>By doing so we can take into account part of the prospective risks: i.e. the risks linked to &quot;unusual&quot; events which already happened in the past and may happen again . </li></ul><ul><li>Of course there is no statistical or probabilistic methods to estimate the effects of future events which never happened yet; that where scenario based approaches can be brought back to the front stage. </li></ul><ul><li>This approach answers the amplitude and the likelihood question of the 'unusual&quot; events. It does not answer the when and how long questions: it just measures a &quot;latent risk&quot;. </li></ul>
  • 21. Taking into account part of the prospective risk (continued) There is ground here for the development of specific financial / management / industrial tools and policies to cover part of this latent risk 0% 5% 10% 15% 20% 25% -25% -20% -15% -10% -5% 0% 5% 10% 15% Residuals (% of total pax) Probability Probability distribution of the residuals 0 2 4 6 8 10 12 14 16 18 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 2014 2016 2018 2020 2022 2024 Traffic/demand (M pax) Actual traffic data 50% probability for the demand to be greater or equal No residuals 98% probability range No residuals 0 2 4 6 8 10 12 14 16 18 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 2014 2016 2018 2020 2022 2024 Traffic/demand (M pax) Actual traffic data 50% probability for the demand to be greater or equal Residuals included 98% probability range Residuals included 0 2 4 6 8 10 12 14 16 18 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 2014 2016 2018 2020 2022 2024 Traffic/demand (M pax) Actual traffic data 50% probability for the demand to be greater or equal No residuals 98% probability range No residuals 0 2 4 6 8 10 12 14 16 18 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 2014 2016 2018 2020 2022 2024 Traffic/demand (M pax) Actual traffic data 50% probability for the demand to be greater or equal Residuals included 98% probability range Residuals included 0 2 4 6 8 10 12 14 16 18 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 2014 2016 2018 2020 2022 2024 Traffic/demand (M pax) Actual traffic data 50% probability for the demand to be greater or equal No residuals 98% probability range No residuals 50% probability for the demand to be greater or equal Residuals included 98% probability range Residuals included
  • 22. Further developments and applications
  • 23. Vertical cuts for most of the short term utilisation Turnover (million €) Probability for the turnover to be greater or equal Capacity threshold Operational Profit (million €) Probability for the operating profit to be greater or equal Capacity threshold € O million etc. <ul><li>To be used for: </li></ul><ul><li>(human) Resources dimensioning </li></ul><ul><li>Budget, cash flow </li></ul><ul><li>Future financial ratios analysis </li></ul><ul><li>Short term risk assessment </li></ul><ul><li>etc. </li></ul>1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 2014 2016 2018 2020 2022 2024 Traffic/demand Actual capacity Demand/traffic (million pax) Probability for the demand to be greater or equal Capacity threshold
  • 24. Horizontal cuts for most of the mid & long term utilisation 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 2014 2016 2018 2020 2022 2024 Traffic/demand Actual capacity etc. To be mostly used for optimal dimensioning and planning of mid and long term capacity growth: heavy investments Planned capacity Annual 50% probability - actual capacity 50% probability - planned capacity 98% centred probability - actual capacity 98% centred probability - planned capacity Year 0 Operating profit
  • 25. Conclusions
  • 26. So many advantages, so few drawbacks <ul><li>A quite simple idea, but a rather complex and computer time consuming approach; </li></ul><ul><li>Put an end to the times when the forecasters were regarded as being fortune-tellers, gurus, devious crooks or scientific alibis for their boss misbehaviour (theirs of their boss' boss too); </li></ul><ul><li>Bring back the risk taking decision where it should have always been: the top management. In addition it offers the exhaustive set of data required by risk assessment tools; </li></ul><ul><li>Likely to offer a better legal protection to the forecasters in case of litigation with the share-holders or the financial markets; </li></ul><ul><li>Our own experience is that bankers are found of this way of making forecast. Aren't they mostly risk traders! </li></ul><ul><li>We (the ADP's forecasting team) are found of it too, since it saves us a lot of forecasting post-processing time while having no more pressures put on us for finding &quot;convenient figures&quot;. </li></ul>

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