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# Forecasting using signal tracking approach

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this study address the relations between signal tracking and coef. of determination to form Poor-Fair Accuracy Matrix, it is also address all values of the signal tracking along the span 36 data selected to point out the fairness of the model

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### Forecasting using signal tracking approach

1. 1. Forecasting of Major US AIRPORTSUsing Signal Tracking ApproachBy: M. S. Awad ©If you can look into the seeds oftime, and say which grain will growand which will not, speak thenunto me.William Shakespeare
2. 2. Forecasting of Major US AIRPORTSUsing Signal Tracking ApproachBy: M. S. Awad ©Still the issue of Forecasting Accuracy is our major concerned, normally most of researcher usedARIMA model to forecast and define seasonality patterned, while in practice we can developedalmost the same model but in different approach using the state of art forecasting program tofit data. Getting back to issue of accuracy of forecasting which is one of the our majorchallenges in the forecasting, so how far we can accept the results, is it reliable and practical orit might mislead us in undesirable direction, how we can set a reasonable targets, that can beachieved , is it good to forecast with a negative trends or not, andwhen we can to do that and how to adjust it. How we caninterpret the trend analysis with seasonality model. All theseissues have their own impact on the accuracy formula. So what isthe best method to define and measure the accuracy offorecasting modelFurther to my previous article, there are many questions left tothe reader, as why we are need to adjust the signal tracking tocertain value that satisfy the boundary instead of setting thesignal to Zero, and why Zero value is not fair enough to hold adecision, and is possible to set Signal Tracking to Zero value forany forecasting model, if so, how to do that. Here our issue how we set these values of signaltracking? As in the following table.How we setThese Values
3. 3. Fair – Poor Forecasting Matrix.:One of the new creative methodology. It basically developed based on two main estimatedmathematical parameters, Displacement and Directional factors which has a consequenceimpacts on R2and Signal Tracking, so by settingboundary accuracy:For Fair forecasting, the model should fulfill thesecriteriaR2≥ 80 andSignal Tracking should be - 4 ≤ S. T. ≤ + 4Then by developed Fair – Poor Forecasting Matrix thefollowing outcomes will be concluded1- Fair Forecast – when R2and Signal Tracking arein boundary .2- Mislead – Displacement Issue. This case whenR2is in boundary and Signal Tracking is outboundary. we can adjusted signal tracking to bein boundary when there is a room for R2in thesame analysis so that it can be consider as a fairforecast.3- Unrelated – Directional Issue. This case whenR2is out of the boundary and Signal Tracking inthe boundary. i.e the balance of accumulatederror without any correlation4- Poor Forecast – when both R2and SignalTracking are out of the boundary ( Total Mess).This matrix manipulate the four decision regions todevelop the right and best picture of the accuracy offorecasting. And to enhance the process of decisionmaking for airline data analysis especially trafficforecasting, that maps the overall forecastingaccuracy of major US airports.
4. 4. Case Study: Traffic Forecasting of Major US AirportsData Collections:Based on the data published in RITA website, concerningtraffic passengers of US major airports, for the period ofthree years data base on a monthly bases, started fromJan 2009 to July 2011Forecasting Model :The classical method to forecast is to drop and drag atrend line by using ADD TREND LINE by Microsoft Excel,as shown by the next box, but unfortunately that boxmeasure only one measuring critical element i.ecoefficient of Determination R2and that may lead us tomislead region in Fair – Poor Forecasting Matrix.The basic data span is 36 months ( Input ) with 12months forecasting, the fair boundary restricted by thepreset design values of R2and Signal Tracking. 12 USairports are addressed.Actually the forecasting process has two stages,Evaluation, and Forecasting. In the evaluation stage wetry to analysis the input data, and align the practical datawith a mathematical model, we use state of artforecasting program to fit data. Two control factors havea great impact on the model, First displacement factor (Displacement Issue ), this factor acts to shift the wholedata from it running bath to a new one but keeping thetrend and direction of the analysis. While the secondfactor is Directional factor, definitely if we manipulatethis factor and try to use many trail values (positive andnegative value), the model will position itself accordinglyas a clock about the origin.As in the following forecasting graphs.
5. 5. Signal Tracking ApproachTuning of the Signal Tracking : Case Study Atlanta AirportThe process of Tuning Signal Tracking may achieved by three trails calculationFirst Trail:In practice when we forecast, we evaluate it by R2which indicate a highest value, but that toofar from the right result as it is not reflect and address the signal tracking calculation, whichactually if we calculate it, it may lay out of the preset boundary. ( red dot line ). That is clearlyshow in the first trail Atlanta Airport for signal tracking (36 ) = S.T.(36) = -21.62 while R = 96.6 %Second Trail:This is the best solution that we are looking for, i.e setting the Signal Tracking to Zero Valueprovide that there is a room to modify R2in the pre-set boundary, but some time it does notreflect the best scenario as some time, along the span of 36 reading points, some of them maylay out of the preset boundary.signal tracking (36 ) = S.T.(36) = 0 , S.T.(max) = 2.00 , S.T.(min) = -4.26 while R = 96.5 %
6. 6. Third Trail ( Final ):Based on Max and Min values of the signal tracking in the analysis, we calculate and modify thelast signal tracking (S.T.(36) ) to wave in these values out of the preset boundary.signal tracking (36 ) = S.T.(36) = 3 , S.T.(max) = 3.80 , S.T.(min) = -3.59 while R = 96.4 %Analysis of Major US Airports:About (16) major US airports are analysis-ed, based on a RITA input data, the analysis are variedfrom Mislead to Fair Category.The blue line represent the actual Input Data, for 36 input points ( Months ) while the red linerepresents the tracked and forecast points, tracked are 36 points for the purpose of monitoringand evaluation, while the forecast points for purpose of planning and setting goals and targetsof these airports for 2013 and 2014 respectively.All US airports shows a seasonality patterns. Summer, Winter, Back to school, and charismasvisitsNow the picture of the major US airports is completely different, and it is easy to set goals andtargets for each month ( 2013 and 2014 ) and consequently developed a KPI system to enhancethe airport activity program.These graphs shows clearly how airports to react, when they should response and what levelthey have to do that, off course the error will be there, but it will an acceptable one.Its also define its trends either it is positive or negative one, and how to align a minor negativetrend to be a positive one in an acceptable preset boundary.
7. 7. Analysis of Major US Airports:The following table explore 3 stages analysis for signal tracking, in a trails scenariosThe results is fair enough to hold forecasting which con consequently use for planning purpose.
8. 8. Forecasting of US Major Airports – Graphs
9. 9. Results of the three trails :The results of the three trails can be explored indetails below:1- First Trail:Based on the first analysis, which indicates theimpacts of R2, while signal tracking is evaluate asadditional parameter (just to know the value).without any interference in the calculation. Really it isa normal practice to relay on R2which clearly mayMISLEAD us if we accept it. So the results can beimprove if we hold a R2– Signal Tracking analysisthen the errors will reduced. In this trail all the valuesof R2are greater than 80 %.2- Second Trail ( Signal Tracking = Zero )This is the best solution we are looking for, it is theoptimum case, when Signal Tracking = ZERO and R2greater than 80 % but unfortunately some casesdoesn’t follow and reflect this rule, as the value of thesignal tracking is value is based on 36 reading samplei.e the 36threading in the sequence, if we repeat thisprocess for other data location we will find somevalue of Signal Tracking is out of the boundary ( as inthe case of Atlanta Airport). So if there a room tomodify and improve the Signal Tracking then we haveto hold the last trail.3- THIRD TrailThis is the final trail, we try to define the extremevalues of signal tracking on both sides ( +ve or –ve )along the 36 data points, and re-adjusted it wheneverthere is a room for that. i.e in the second trail wereached ZERO value for signal tracking, but somevalues along the data span of 36 reading points areout of the boundary so, it is good for us to re-calculate the values and adjust these S. T. in thepre-define boundaries. ( -4 and + 4 ) keeping in mind that R2should be greater than 80%. Forthe purpose of construction the last matrix, we assume that 3.95 = 4 and zero = 0.01.In terms of Forecasting of 2013, There is a significant improve in figures when we adjusted S. T.unless it will MISLEAD us if we rely on a First Trail.
10. 10. Summary:This study address the relation between R2and S. T. , we target US Major airport traffic datafrom RITA for 3 year data base. Really we will Mislead if we rely on the classical monitoringapproach to assign R2as the only factor for Goodness of Fit to the data, and it is clear with thevalue of R2in the analysis and undesirables level of S. T. but if we add and reflect S. T. to beadjusted in the required boundary. Then the picture will be different as shown in the lastcolumns (Final Adjusted), which will have a significant impact on 2013 forecasting figures(please compare the results).Finally Fair – Poor Forecasting Matrix it is a unique method that reflects the impacts of R2andSignal Tracking by manipulating the mathematical factor (Displacement and Directional) to alignfor best scenario of actual data (US major airports data).While the forecasting model can be further improve, whenever there is a room to adjustedalong the entire input data.So any data can be set to Zero Signal Tracking but it doesn’t mean a fair forecasting unless itsaccompany with R that greater than 80%.And to relay on R2alone to reflect the goodness of fit in practice is a Mislead Approach.