ACEEE Int. J. on Control System and Instrumentation, Vol. 03, No. 01, Feb 2012 Demand Modelling of Asymmetric Digital Subs...
ACEEE Int. J. on Control System and Instrumentation, Vol. 03, No. 01, Feb 2012                                           ...
ACEEE Int. J. on Control System and Instrumentation, Vol. 03, No. 01, Feb 20128. If the network error compared to the sele...
ACEEE Int. J. on Control System and Instrumentation, Vol. 03, No. 01, Feb 2012                                            ...
ACEEE Int. J. on Control System and Instrumentation, Vol. 03, No. 01, Feb 2012                                            ...
ACEEE Int. J. on Control System and Instrumentation, Vol. 03, No. 01, Feb 2012                       CONCLUSION           ...
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Demand Modelling of Asymmetric Digital Subscriber Line in the Czech Republic

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This article describes and analyses the existing
possibilities for using Standard Statistical Methods and
Artificial Intelligence Methods for a short-term forecast and
simulation of demand in the field of Asymmetric Digital
Subscriber Line Internet Connection in the Czech Republic.
The most widespread methods are based on Time Series
Analysis. Nowadays, approaches based on Artificial
Intelligence Methods, including Neural Networks, are
booming. Separate approaches will be used in the study of
Demand Modelling in the field of Asymmetric Digital
Subscriber Line, and the results of these models will be
compared with actual guaranteed values. Then we will examine
the quality of Neural Network models. The another part of
study will be focused on improving the quality of Neural
Network models with the use of indicator Gross Domestic
Product.

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Demand Modelling of Asymmetric Digital Subscriber Line in the Czech Republic

  1. 1. ACEEE Int. J. on Control System and Instrumentation, Vol. 03, No. 01, Feb 2012 Demand Modelling of Asymmetric Digital Subscriber Line in the Czech Republic Martin Chvalina Czech Technical University, Department of Economics, Management and Humanities, Zikova 4, 166 29 Praha, Czech Republic Email: martin.chvalina@email.czAbstract - This article describes and analyses the existing the Box-Jenkins Metodology, or by applying Artificialpossibilities for using Standard Statistical Methods and Intelligence methods, including for example Neural NetworksArtificial Intelligence Methods for a short-term forecast and [8].simulation of demand in the field of Asymmetric DigitalSubscriber Line Internet Connection in the Czech Republic. A. Decomposition Time SeriesThe most widespread methods are based on Time Series The series {yt, t = 1, ..., T} is gradually decomposed toAnalysis. Nowadays, approaches based on Artificial several components: trend, circular component, seasonalIntelligence M ethods, including Neural Networks, arebooming. Separate approaches will be used in the study of component and residual component (unsystematicDemand Modelling in the field of Asymmetric Digital component). This method is based on work with time seriesSubscriber Line, and the results of these models will be systematic components. Features of time series behaviourcompared with actual guaranteed values. Then we will examine can be better observed in separate components than in thethe quality of Neural Network models. The another part of undecomposed original time series [8]. In this research studystudy will be focused on improving the quality of Neural from the field of standard statistical methods, exponentialNetwork models with the use of indicator Gross Domestic smoothing will be used for demand modelling of theProduct. Asymmetric Digital Subscriber Line internet connection.Index Terms - Demand, Telecommunications, Standard I. Exponential SmoothingStatistical Methods, Neural Network, Asymmetric Digital The above defined time series will be written as {yt ,Subscriber Line, Gross Domestic Product t = 1, ..., T}. Simple Exponential Smoothing is described in the recurrent form I. INTRODUCTION ˆ ˆ y t  y t  (1   ) y t 1 , Demand can be defined as the relation between price andthe quantity of goods that buyers are willing to purchase.This correlation is displayed in relation to the global market ˆ ˆ y t is the Exponential Average in time t, y t 1 is theby the sold product quantity at one time-point. If we focus Exponential Average in time t-1, value  is the Smoothingon the telecommunication services sector, we can note the Constant from the interval   0;1  [8]. The Exponentialdevelopment of the sale of cell phones and internetconnection (Asymmetric Digital Subscriber Line, Wireless Average can be expressed on the basis of the recurrent formconnection, etc.). This article will be focused on Demand as [8]:Modelling of the Asymmetric Digital Subscriber Line internet yt  yt  (1   ) yt 1  yt  (1   )[yt 1  (1   ) yt 2 ]  ˆ ˆ ˆconnection (ADSL) in the Czech Republic. Considering the  yt   (1   ) yt 1  (1   ) 2 [yt  2 (1   ) yt 3 ]  ...  ˆfact that in the literature listed in the paper, an effectiveprocedure of demand modelling of the Asymmetric Digital  yt   (1   ) yt 1  (1   ) 2 yt 2  ...   (1   ) i yt i  .... t 1Subscriber Line Internet Connection was not described, this ..  (1   ) t y 0    (1   ) i yt i  (1   )t y0 ˆ ˆresearch project conceives the demand as time series under i 0which the demand model can be designed and trendspredicted. The demand model was formed on the basis of the II. Brown’s Simple Exponential Smoothingdata of statistical survey on the territory of the Czech Republic The time series yt is constructed with a stationary process(e.g. number of households in the Czech Republic who havethe technology of ADSL) which were published by the Czech in the form y t   0   t ,  0 is the mean value of theStatistical Office in the period of 2006 – 2011. The theoreticaldescription of the methods for construction of the demand process, and  t are random values with the features of whitemodel is listed below. noise. After applying Exponential Smoothing to the Time Series we obtain the relation [8]: II. CONSTRUCTION OF THE DEMAND MODEL    yt (1)i yti (1)i (0 ti )  0 (1)i ti ˆ The demand model can be constructed using standard i0 i0 i0statistical methods including Decomposition Time Series, and© 2012 ACEEE 53DOI: 01.IJCSI.03.01.518
  2. 2. ACEEE Int. J. on Control System and Instrumentation, Vol. 03, No. 01, Feb 2012  comparison of traditional non-linear models and a back-because   (1   )  1 applies to the mean value and propagation network). The neurone function scheme can be i 1dispersion: demonstrated graphically as follows [8]:Brown’s Linear (double) Exponential Smoothing, alternatively,we can make a double application of the Simple ExponentialSmoothing method on the time series yt expression in theform [8]: ˆ ( 2) ˆ ( 2) yt  yt  (1   ) yt 1B. Box-Jenkins Methodology Unlike classical decompositional methods, which dealwith systematic time series components (trend, circular andseasonal), the Box-Jenkins methodology deals with a Figure 1. Model of a neurone [8]residual (unsystematic) component. The method involvessearching for relations of individual observations. By this N  y  S  wi x i   method we are able to describe time series which are not  i 1 manageable by standard methods [8]. The time series is where y is the output (neurone activity), S demonstrates aperceived as a realization of the stochastic process which isdefined as a series of accidental quantities arranged in time transmission function (jump, linear, non-linear), xi is neuroneX (s, t ), s  S, t  T, where S is a selective space and T is an input (inputs are in total N), wi represents a level of synopticindex series. For each s S the realization of the stochasticprocess is defined on the index series T [8]. For the Box- weight,  describes a trigger level.Jenkins methodology, the following special accesses are I. The Principle of Back-Propagation Network Learningsignificant: autoregressive process AR, moving average Let us consider a neurone network with L – layers l = 1,process MA, and combined process ARMA. These ….,L and as the output i-th neurone in the 1-th layer we useprocesses result from the linear process by resetting allparameters till the final number. The parameters are chosen the indication Vi l . Vi 0 means xi , i.e. the i-th output. Thein such a way that the stationarity and invertibility of the lprocesses will be ensured. A special non-stationary ARIMA indication wij expresses a connection from Vi l 1 to . Vi l .model also exists in the Box-Jenkins metodology [8]. An algorithm can then be inscribed after separate stages asI. ARIMA Processes follows [8] : 1. Subranged random numbers based - Weight Some integrated processes may be arranged by means of Initializationdifferentiation to stationary and are expressed in the form of 2. Insertion of into the network input (layer l = 0), i.e.the stationary and invertible ARMA(p,q) model. The originalintegrated process in the form [8]: Vk0  x kp  p ( B)(1  B) d y t   q ( B) t 3. Network signal propagation: Vi l  g (hil )  g ( wijV jl 1 ) lis called the autoregressive integrated process of sliding kaverages of the order p, d, q. This is called ARIMA (p, d, 4. Calculation of delta for the output layer:q). Models with d = 1,2 are usually used [8].   i p  g (hiP )  y ip  Vi P C. Artificial Intelligence Methods - Neural Networks 5. Calculation of delta for previous layers by Error Back- The benefit of the Artificial Neural Network lies in its Propagationability to implement complex non-linear functions. Neuralsystems co-execute a large number of operations and work  il 1  g (hil 1 ) w lji  lj iwithout an algorithm [8]. Their activity is based upon thelearning process, when the neural network gradually 6. Weight change according to formula:conforms to calculation. In the course of a learning phase wij   il V jl 1 , wij  wij  wij l new oldwe do not have to be occupied by the problem of the rightselection function, because the neural network is able to 7. If all samples have been submitted to the networkmake do only with practise examples [8]. This is the main we continue in phase no. 8, otherwise we go back todifference in comparison with a traditional approach (e.g. phase no. 2.© 2012 ACEEE 54DOI: 01.IJCSI.03.01.518
  3. 3. ACEEE Int. J. on Control System and Instrumentation, Vol. 03, No. 01, Feb 20128. If the network error compared to the selected criterionvalue was minor or the maximum number of steps wasexhausted, then the learning process can be completed, elsephase no. 2.D. Choice of a Relevant Model An appropriate model can be determined on the basis ofa) the graph of the time series, or from its absolute or relativecharacteristics [8],b) interpolative criteria (a decisive deviation of residues,coefficient of determination, coefficient of autocorrelation of Figure 2. ARIMA Demand Modelling of ADSLresidues, average characteristics of residues ) [8],c) extrapolative criteria (average characteristics of “ex post” The figure 3 shows the course of residual values (i.e. theforecast mistakes, graph forecasts) [8]. difference between the number of Households which are using the Asymmetric Digital Subscriber Line InternetE. Average Characteristics of Residues Connection, and the value predicted by demand model based The average square mistake - dispersion [8]: on ARIMA(1,1,0)). 1 n 1 nMSE   ( y t  yt ) 2   a t2 ˆ ˆ n t 1 n t 1The root mean square mistake [8]: 1 n 1 nRMSE  ( yt  yt )2  at2 ˆ ˆ n t 1 n t 1The average absolute mistake [8]: 1 n 1 nMAE   n t 1 y t  yt   at ˆ n t 1 ˆ Figure 3. Residual values for ARIMA Demand Modelling of ADSLThe lower the values of the specified characteristics, the In the figure 4, we can observe the course of residualbetter the chosen model is [8]. autocorrelations for a demand model based on ARIMA(1,1,0). In this case, the residual autocorrelation was not recorded. III. DEMAND MODELLING OF ASYMMETRICDIGITAL SUBSCRIBER LINE INTERNET CONNECTION The above mentioned methods will be used for demandmodelling of the Asymmetric Digital Subscriber Line InternetConnection (ADSL) in the Czech Republic. The ADSL DemandModel (i.e. the number of households which are using aAsymmetric Digital Subscriber Line Internet Connection) isbased on the values from the Czech Statistical Office (between2006 and 2011) and estimate made by an expert. The resultsfor the ADSL demand model based upon Box-Jenkinsmethodology, Brown’s linear exponential smoothing andNeural Networks are graphically displayed below.A. ARIMA Processes Figure 4. Residual Autocorrelations for ADSL The figure 2 describes the comparison of the real values B. Brown’s linear exponential smoothing(i.e. the number of households which are using anAsymmetric Digital Subscriber Line Internet Connection), and The figure 5 shows the comparison of the real values (i.e.the values from a demand model based on ARIMA (1,1,0). the number of households which are using an Asymmetric Digital Subscriber Line Internet Connection), and the values from a demand model based on Brown’s linear exponential smoothing.© 2012 ACEEE 55DOI: 01.IJCSI.03.01. 518
  4. 4. ACEEE Int. J. on Control System and Instrumentation, Vol. 03, No. 01, Feb 2012 Figure 8. Residual values for ADSL Figure 5. Brown’s linear exponential smoothing of ADSL The figure 9 shows the course of residual autocorrelationsIn the figure 6, we can observe the course of residual for a demand model based on Neural Network. In this case,autocorrelations for a demand model based on Brown’s lin- the residual autocorrelation was recorded.ear exponential smoothing. In this case, the residualautocorrelation was not recorded. Figure 6. Residual Autocorrelation for ADSL Figure 9. Residual Autocorrelation for Neural NetworkC. Back-Propagation Neural Network Within the research project on demand modelling in the field of Asymmetric Digital Subscriber Line Internet Connection The figure 7 shows the comparison of the real values (i.e. in the Czech Republic we obtained the following values forthe number of households which are using the Asymmetric the average characteristics of residues, as shown in Table I.Digital Subscriber Line Internet Connection), and the valuesfrom a demand model based on Neural Network. TABLE I. AVERAGE CHARACTERISTICS OF RESIDUES On the basis of the results of RMSE and MAE average char- acteristics of residues, the demand model based upon Neural Networks can be considered as best, but a different result arises from an evaluation of prediction quality, because the best prediction value result was obtained from a demand model based on ARIMA (1,1,0). In the figure 10, we can observe an evaluation of prediction quality for the ADSL demand model based upon ARIMA(1,1,0), Brown’s linear Figure 7. Neural Network Demand Modelling exponential smoothing and Neural Network. With respect to the above mentioned facts, another part of the study wasThe course of residual values (i.e. the difference between the focused on improving the quality or accuracy of the ADSLnumber of Households which are using the Asymmetric Digi- demand model with the use of neuron networks.tal Subscriber Line Internet Connection), and the value pre-dicted by demand model based on Neural Network is shownin figure 8.© 2012 ACEEE 56DOI: 01.IJCSI.03.01. 518
  5. 5. ACEEE Int. J. on Control System and Instrumentation, Vol. 03, No. 01, Feb 2012 Figure 13. Residual values for ADSL The figure 14 describes the course of residual autocorrelations for a demand model based on Neural Network (including GDP). The residual autocorrelation wasFigu re 10. Comparison of the ADSL internet connection used byhouseholds in the 2nd quarter of 2010, values published on February not recorded.10th, 2011 by the Czech Statistical Office, and results predictedby demand models for ADSL.D. Back-Propagation Neural Network (including GDP) Within the framework of the progressive proposal forbringing more precision to the current approach, theAsymmetric Digital Subscriber Line Internet Connectiondemand model was extended by the effect of the indicatorGross Domestic Product (GDP) of the Czech Republic and aBack-Propagation neural network was subsequently appliedto the model formed in this way, as shown in figure 11. Figure 14. Residual Autocorrelation for Neural Network (GDP) In this case, we obtained the following values for the aver- age characteristics of residues, as shown in Table II.Figure 11. Inclusion of GDP into Neural Network Demand Model TABLE II. AVERAGE CHARACTERISTICS OF RESIDUESIn the figure 12, we can observe the comparison of the realvalues (i.e. the number of households which are using an On the basis of the results of RMSE and MAE average char-Asymmetric Digital Subscriber Line Internet Connection), and acteristics of residues, the demand model based upon Neuralthe values from a demand model based on Neural Network Networks (including GDP) can be considered as best andwhich was extended by the effect of the indicator GDP Czech same result arises from an evaluation of prediction qualityRepublic. because the best prediction value result was obtained from a demand model based on Neural Network (including GDP), as shown in figure 15. Figure 12. Neural Network (including GDP) Demand ModellingThe course of residual values (i.e. the difference between thenumber of Households which are using the Asymmetric Digi-tal Subscriber Line Internet Connection, and the value pre-dicted by demand model based on Neural Network which Figure 15. Comparison of the ADSL internet connection used bywas extended by the effect of the indicator GDP Czech Re- households in the 2nd quarter of 2010, values published on July 8th, 2011 by the Czech Statistical Office, and results predicted by demandpublic) is shown in figure 13. models for Asymmetric Digital Subscriber Line Internet Connection.© 2012 ACEEE 57DOI: 01.IJCSI.03.01.518
  6. 6. ACEEE Int. J. on Control System and Instrumentation, Vol. 03, No. 01, Feb 2012 CONCLUSION With respect to the above mentioned results, the figure 16 offers the percentage accuracy of the values predicted by This article deals with the demand modelling of the demand models for Asymmetric Digital Subscriber LineAsymmetric Digital Subscriber Line Internet Connection in Internet Connection which were drawn up on the basis ofthe Czech Republic. Considering the fact that in the literature the above described methods. Unlike the approaches whichlisted in the paper, an effective procedure of demand have been applied so far, the accuracy of the demand modelsmodelling of the Asymmetric Digital Subscriber Line Internet drawn up on the basis of neural networks was reached by the Connection was not described, this research project progressive method resting in implementation of the indicatorconceives the demand as time series under which the demand GDP, as shown in figure 15, 16. The progressive method ofmodel can be designed and trends predicted. The modelling the demand in the course of which the results ofintroductory chapters summarize in theory individual the research project were obtained may potentially contributeapproaches of formation of demand modelling based on to economic parameters of telecommunication companies,statistical analysis of time series and further current because quality demand models which provide precise resultsprocedures based on Artificial Intelligence Methods including in a short-term forecast, contribute to telecommunicationNeural Networks. Furthermore, the objective of article was to companies from the point of view of planning and evaluationevaluate contemporary possibilities concerning application of investment strategy, and furthermore, they positively affectof standard statistical methods and approaches of artificial the whole financial results and economic indicators of aintelligence with focusing on neural networks in forecasting company.and modelling demand in the segment of the AsymmetricDigital Subscriber Line Internet Connection in the CzechRepublic. Individual demand models which were drawn up REFERENCESon the basis of the above described methods were evaluatedand the results of forecast following from these models were [1] M. Šnorek, “Neural Network and Neural Computers”, Praguecompared with real development. On the basis of the results, CVUT, 2002it is possible to make a conclusion that the demand models [2] J. Artl, M. Artlová, “Financial Time Series”, Grada Publishingformed with the aid of standard statistical methods prove a.s., Prague, 2003higher quality or accuracy of the short-term forecast than the [3] J. Artl, M. Artlová, E. Rulíková, “Analysis of Economicalmodels drawn up by the aid of a neural network, as shown in Time Series with examples”, Prague VŠE, 2002 [4] P. McBurney, S. Parsons, J. Green, “Forecasting marketfigure 10. With respect to the above mentioned facts, another demand for new telecommunications services: an introduction”,part of the study was focused on improving the quality or Telematics and Informatics, 2002accuracy of the demand models with the use of neuron [5] C. Garbacz, H. G. Thompson, “Demand for telecommunicationnetworks. Within the framework of the progressive proposal services in developing countries”, Telecommunications Policy, 2007for bringing more precision to the current approach, the [6] T. Evens, D. Schuurman, L. Marez, G. Verleye, “Forecastingdemand models in the segment of Asymmetric Digital broadband Internet adoption on trains in Belgium”, TelematicsSubscriber Line Internet Connection were extended by the and Informatics, vol. 27, pp. 10-20, 2010effect of the indicator GDP Czech Republic and a neural [7] S. Crone, “Business Forecasting with Neural Networks”,network was subsequently applied to the model formed in Institute of Business Forecasting, Boston, 2004 [8] M. Chvalina, “Demand Modelling in Telecommunications,this way, as shown in figure 11. The values resulting from Comparison of Standard Statistical Methods and Approaches Basedsuch demand models proved positive effect of the indicator upon Artificial Intelligence Methods Including Neural Networks”,GDP on the quality or accuracy of the short-term forecast, as Acta Polytechnica, vol. 49, Prague, 2009shown in figure 15. [9] R. Nau, “Introduction to ARIMA”, Duke University Durham, 2007 [10] M. Kuba, “Neural Networks”, Masaryk University Brno, 1995 [11] J. G. De Gooijer, R. J. Hyndman, “25 years of time series forecasting”, International Journal of Forecasting, 2006 [12] C. Chakraborty, B. Nandi, “Mainline telecommunications infrastructure, levels of developmentand economic growth: Evidence from a panel of developing countries”, Telecommunications Policy, 2011 [13] P. N. Baecker, G. Grass and U. Hommel, “Business value and risk in the presence of price controls: an option-based analysis of margin squeeze rules in the telecommunications industry”, Annals of operations research, 2010 [14] R. Fildes, V. Kumar, “Telecommunications demand forecasting”, International Journal of Forecasting, 2002 [15] Ch. Agiakloglou, S. Karkalakos, “A spatial and economic analysis for telecommunication: evidence from the European Figure 16. Quality of prediction Union”, Journal of Applied Economics, vol. 12, pp. 11-33, 2009© 2012 ACEEE 58DOI: 01.IJCSI.03.01. 518

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