SEASONAL FORECASTING FOR AIR PASSENGER TRAFIC

Transcription

1 Section Name SEASONAL FORECASTING FOR AIR PASSENGER TRAFIC Dr. Katarzyna Chudy-Laskowska 1 Dr. Tomasz Pisula 2 1 Rzeszow University of Technology, Poland 2 Rzeszow University of Technology, Poland ABSTRACT Air transport is currently one of the fastest-growing service sectors. People constantly travel for various reasons (tourism, business) to distant locations worldwide. Consequently, analyses of data concerning both passenger and cargo air traffic is of great importance in designing development strategies for regions with airports in their resources. The main purpose of this study is to prepare a forecast of air passenger transport in the one of the airport which is located in south-western of Poland. There are very few publications regarding passengers traffic forecast in Podkarpacie Region. This is a very important topic for the region development, and therefore it has been taken in this study. The research period covers the period from January 2007 to October Data were presented in monthly cycles. Four research methods were used for forecast calculations: seasonal exponential smoothing, seasonal ARIMA, artificial neural networks and support vector machines (SVM). The Kruskal - Wallis analysis of variance (ANOVA) was used to ascertain if there were any statistically significant differences in mean passenger volumes in individual months. A confidence level of α=0.05 was assumed for the test. The final value of forecast volumes was determined by employing the results of all methods discussed in the article. The forecast retains the characteristics of historical data, i.e. seasonal fluctuations, though its values do not rise substantially. Rather, it seems that the dynamic growth is slowing down. The passenger traffic is linked to many factors, and the inclusion of the time factor alone is a considerable simplification. It is a well-known fact that air passenger transport may be affected by many diverse variables (the future amount of the GDP, the population of the country, the volume and value of foreign exchange, consumption levels). To a certain extent such forecasts enable the right decisions on future activities in the analysed area to be taken. Thanks to the use of suitable forecasting methods, key decisions become more justified and substantiated with an appropriate analysis. Keywords: air passenger forecast, seasonal ARIMA, seasonal exponential smoothing, neural networks, support vector machines INTRODUCTION Air transport is currently one of the fastest-growing service sectors. People constantly travel for various reasons (tourism, business) to distant locations worldwide. Consequently, analyses and forecasts of data concerning both passenger and cargo air traffic is of great importance in designing development strategies for regions with airports in their resources. An advantage of Poland's location in Central Europe is that it lies at the junction of key trade routes leading north/south and east/west. Air transport stimulates

2 4 th International Multidisciplinary Scientific Conferences on Social Sciences & Arts SGEM 2017 the growth of local economy, contributing to the development of companies, and therefore increasing the competitiveness of businesses. It generates jobs, which also translates into the society's wealth. This creates possibilities of boosting the flow of goods and people as well as enhancing their mobility. All of this favours higher living standards, increasingly greater travel comfort and a wider choice of services offered by the aviation market. Poland's accession to the European Union in May 2004 was a breakthrough point in the development of the country's air transport market. Joining the EU involved the implementation of the European air transport law on the basis of the so-called Third Package, which sets forth the principles of airborne transport in EU countries, e.g.: the principle of free access to the market within EU member states; the principle of a free price system and the principle of uniform certification criteria. The solutions referred to above opened the Polish market to budget carriers, who introduced much cheaper flights and quickly adapted to the Polish aviation market. Before 2004, the Polish aviation market was protected from competition; flights to other countries were operated only by Polish carriers, often on a limited number of routes. Ticket prices imposed a limit on services, and international flights took off and landed practically only at the Warsaw airport. The changes discussed above reinforced the importance of regional airports, with local residents being able to use an affordable means of transport previously beyond their reach. A wide array of services of available airlines allows passengers to make use of all conveniences related to flying to their destinations of choice. The rising importance of regional airlines may be confirmed by growing numbers of passengers carried in the years , with nearly a six-fold increase (from 2 million to 11 million). Being part of the European Community market, the Polish aviation is faced with a challenge of effectively satisfying the society's demand for air transport. Such demand is not limited to the throughput of air infrastructure, but also involves fitting it effectively in the Polish, but primarily European, transport system. The biggest changes affecting the size and structure of demand for transport are taking place in the technological and innovative aspect of transport, in the structure and technologies of manufacturing, and in the society's lifestyle. Opening the market to new carriers, greater competition and decreasing ticket prices increasingly attract people to air travel. The trend is expected to continue in the next few years, provided that new airports appear and old ones become modernized. Accordingly, there is a need to make predictions in the form of passenger flow forecasts at existing and new civil airports that would give, even to a limited extent, an overview of the future situation. Therefore, we must stress the importance of traffic forecasts as the basis not only for financial, but also investment and infrastructure planning. For example, designing an airport's throughput requires longterm aircraft traffic forecasts. Estimated number of aircraft operations determines the number of runways, taxiways or gangways (jet bridges). Also, the number of passengers of various categories (e.g. arrivals, departures, in transit) determines requirements concerning the terminal's throughput. The traditional approach to generating long-term forecasts consists in the use of statistical methods involving time series and econometric models in order to extrapolate observable growth patterns (gravity models, analyses and variants). Forecasting traffic intensity using (regional) air traffic models involves determining the demand for air transport in the region. Another important aspect is the seasonality of air transport. Seasonal variations make it necessary to monitor traffic intensity in each month of the year, and on each day of the month. Key output data of a traffic intensity forecast include: number of passengers (current traffic, traffic incoming from other airports, generated traffic), air fare (if applicable), classification of travel

3 Section Name according to origin/destination (for origin-destination and connecting flights), number of aircraft operations, mean number of passengers or cargo units for a given type of aircraft operation; mean seat occupancy ratio or mean payload use ratio, aircraft's mean maximum take-off weight (MTOW) for a given type of aircraft operation or total forecast if only one type of aircraft operations is being considered. The main purpose of this study is to prepare a forecast of air passenger transport. The subject of the analysis is Rzeszow International Airport, with passenger flights being the focus. The research period covers the years from 2007 to Data were presented in monthly cycles. Four research methods were used for forecast calculations: seasonal exponential smoothing, seasonal ARIMA, artificial neural networks and support vector machines (SVM). There are very few publications regarding passengers traffic forecast in Podkarpacie Region. This is a very important topic for the region development, and therefore it has been taken in this study. LITERATURE REVIEW Issues forecasts of passenger traffic are widely discussed in the literature. The analysis includes a general overview of applied forecasting techniques categories as econometric models, spatial models or time series models. Latest research methods used for forecasting tourist and passenger traffic in air transport may be found in a dissertation [6]. Conventional approach to tourism traffic and passenger traffic forecasting involves the use of various econometric models and time series models. Traditional forecast methods applied in air traffic at airports include: naive method and moving average method; linear and non-linear models, e.g. multivariate linear regression models; seasonal decomposition models and exponential smoothing models; autoregressive and moving average (ARIMA), and seasonal (SARIMA) univariate time series methods; volatility models, e.g. GARCH class models and their modifications; multivariate models, e.g. ARIMAX; combined approach (forecast model combinations) this approach makes use of forecasting by several methods, and the final output forecast is determined as a combination (weighted mean) of component forecasts. There are many publications concerning tourist and passenger traffic forecasts at airports using conventional econometric models, e.g. [1]. Many authors apply ARMA and ARIMA class models to forecast tourist and passenger traffic at airports (for example [12]). Exponential comparison models were utilized and applied in such studies as [10], which employed the exponential smoothing method with a damped trend for long leadtime forecasting of passenger traffic at UK airports. Multi-dimensional ARIMA models were used in such works as: [2] and [3]. They used a multi-dimensional ARIMAX model to forecast the number of passengers at an airport in Calabria in south Italy. In the recent years non-conventional forecasting methods are increasingly used, including time series methods based on artificial intelligence. Such non-standard methods involving machine learning systems include: forecasting methods based on Artificial Neural Networks; regressive methods based on Support Vector Regression (SVMR); fuzzy regression models; fuzzy time series methods and the so-called Grey Theory methods. The use of artificial neural networks for forecasting tourist and passenger traffic at

4 4 th International Multidisciplinary Scientific Conferences on Social Sciences & Arts SGEM 2017 airports may be found in [8]. In this paper a neural network model was used with Back- Propagation Neural Network algorithm in order to increase forecast accuracy in relation to the classic neural model with an FFNN (Feed-Forward NN) trainer. Authors in [13] compared the effectiveness of the application of neural networks with other classic models. In [7] was presented a very exhaustive analysis of various approaches to tourist traffic forecasts. The main forecasting method used in the study was the regressive method with SVR (Support Vector Regression). However, the proper selection of parameters was of utmost significance in the approach. The researchers used the appropriate genetic algorithm to select optimization algorithms in the SVR method. The model applied in the study was based on a seasonal approach to tourist traffic forecasting using the SVR method (AGA-SVR, Adaptive Genetic Algorithm Support Vector Regression). The forecast accuracy of both AI (Artificial Intelligence) models was tested in comparison to classic models of exponential smoothing and moving average, while in [14] was applied a hybrid (decomposition and forecasting) method, the so-called neurofuzzy combination model. Researchers in [4] used a time series decomposition method called EEMD (Ensemble Empirical Mode Decomposition) to forecast air passenger traffic on 6 lines from USA and UK. For the output time series, a decomposition of n- component series for which an SVMR-based forecast was conducted. The final forecast was a combination of which results were compared with forecasting errors for the Holt- Winters and ARIMA methods. It was reported that the decomposition-based forecasting method yielded better results than the classic (individual) approach. Many studies concern the hybrid and combined approach with the use of many component methods. This kind of approach was used, among other works, in a study [15]. AIRPORT AND DATA PRESENTATION Rzeszow International Airport is the south-eastern Polish airport and one of the twelve airports belonging to the Trans-European Transport Networks (TEN-T). It has the second longest runway in Poland (among civil airports) and features modern, world-class navigation equipment, allowing large planes to land in difficult conditions. The airport's area is over 650 hectares, its nearest vicinity is flat and free of natural obstacles, and the number of flight days is the highest in the country. Extremely low density of other civilian airports near Rzeszow makes the location interesting for airlines. Access to air transport services is in the interest of the region's economy and private businesses. By generating return on investment, airports ensure the necessary infrastructure, which may support social and economic growth of regions. Of key importance here are good connections offered by budget airlines, which open new markets for tourism and thus accelerate its growth. For this reason, the development of aviation infrastructure in Poland is vital to the country's active participation both in Europe and globally. Data on the flow of passengers at Rzeszow International Airport in Jasionka were collected in the period from January 2007 to October 2016; they were gathered at monthly intervals. An analysis of data shown in Figure 1 allows to formulate a thesis that in the time series there will be isolate: the trend (which is damped), the seasonal factor and the irregular component. Passenger flows are characterised by a damped growth tendency and additive fluctuations.

5 Section Name Figure 1. The number of passengers at Rzeszow International Airport. Due to the airport's expansion (a new terminal was opened in April 2012) it was decided to use models which would enable the inclusion of an increasing growth tendency in the designed forecast. Passenger traffic intensity becomes apparent in the summer months. An increased flow of passengers starts in April, to reach its maximum in July (x and August (x The holiday period is characterised by the appearance of various promotions, of which passengers readily take advantage; note that booking a flight well in advance allows them to save money and shorten the travel time. Airlines are becoming a competitive means of transport, with flight prices frequently as low as railway or coach tickets. The winter months, particularly November (x 29927, January (x and February (x 30018, are characterised by the lowest intensity of passenger traffic. A limited increase in passenger flows is observable during the holiday period in late December. The economic crisis which started in 2007 affected the operations of the airport in Jasionka, which is noticeable primarily in the second half of In early November 2008 budget Irish carrier RYANAIR suspended its flights from Rzeszow to England and Ireland. The airport was left with only three passenger flights per day. It was a considerable loss for the airport. At that time the lowest passenger count over the entire analysed time period was reported, namely 7808 persons. The Irish airline justified its withdrawal from Jasionka by stating that the airport has the highest charges in Poland. Several months later the number of passengers at the airport returned to its previous growth track. The Kruskal - Wallis analysis of variance (ANOVA) was used to ascertain if there were any statistically significant differences in mean passenger volumes in individual months. A confidence level of α=0.05 was assumed for the test. It was found that a statistically significant difference in mean passenger volumes occurred across months p<α (p=0.0000). Seasonality of data is normally identified by studying the autocorrelation function of time series for consecutive delays. Air passenger traffic from Rzeszow International Airport was tested for the presence of seasonality. The autocorrelation function very clearly indicates the seasonality of analysed data, descends along a sine curve and reaches maximum and minimum values every twelve periods (months). FORECAST METHODOLOGY AND RESULTS For the purpose of the estimation of forecasting quality of the models applied, input data were divided into two samples: a learning-validation sample comprising data for the period from January 2007 to December 2015 (108 cases), which also comprising

6 4 th International Multidisciplinary Scientific Conferences on Social Sciences & Arts SGEM 2017 validation sample for neural networks - the period from January 2015 to December 2015 (12 cases) and a test sample - to be used for all forecasting models in order to evaluate their forecasting quality - comprising the final period from January 2016 to October 2016 (10 cases) unused for estimating model parameters. Exponential smoothing. There was used damped trend model with additive seasonality where smoothed time series components were calculated from the formulas [9]: 2 where: 1 (1) 1 2 0,1 smoothing parameter for the level of the time series; 0,1 smoothing parameter for seasonal factors; 0,1 smoothing parameter for damped trend modification; number of the periods in the seasonal cycle; - observed value of the time series; - smoothed level of the series; - smoothed trend; - smoothed seasonal index; - one-period-ahead forecast error. Best values of smoothing parameters were estimated using network search methods, assuming their range of variability from 0.1 to 0.9 with an increment of 0.1 and Mean Absolute Percentage Error (MAPE) as the decisive criterion. Optimum model parameter values were as follows: 0.7, 0.1, 0.3, and the MAPE error equal to 9,07%. After the evaluation of the model the residuals were tested for normal distribution and the absence of high correlations for consecutive delay periods. The residual distribution with matched normal distribution were compared and determined values of the statistic for the chi-squared normality test and Kolmogorov-Smirnov goodness of fit test. The value of chi-squared test statistic is 4.68, and the test probability p=0.197 is greater than the significance level (α=0.05). Accordingly, there are no premises to reject the hypothesis that the residuals of the exponential smoothing model have normal distribution. The above is also confirmed by a low value of the test statistic for the Kolmogorov-Smirnov goodness of fit test: d=0.06. Autocorrelation function of the residuals of the model also suggests lack of autocorrelations for consecutive delays. Absolute values of residuals autocorrelations are less then 0.18 and p-values of Q-Ljung Box test are greater then Thus, it should be assumed that the evaluated model is correct: it meets all assumptions and will offer good forecasting properties. ARIMA seasonal model. The ARIMA model was introduced by Box & Jenkins in 1976 (see: [5]). It may be used for modelling stationary time series, i.e. series in which only random fluctuations around mean occur, or non-stationary time series, reduced to stationary ones. The model's structure is based on autocorrelation. The ARIMA model contains two basic processes (auto-regression and a moving average): (2) where: model constant,, delay parameters,,, auto-regression parameters,,, moving average parameters,,,, model residuals in the periods: t, t-1,,t-q, - value of the time series explained for the time period t.

7 Section Name Such process is referred to as the auto-regression process with a moving average of the order (p, q), abbreviated as ARMA (p, q). The model assumes that the value of the forecast variable at a moment or over a time period depends on its past values, and the difference between past real values of the forecast variable and its values obtained from the model. The ARIMA model contains autoregressive parameters, moving average parameters and introduces a differencing operator. Three parameters may be identified within the model: ARIMA (p, d, q): autoregressive parameters p, differencing order d, and moving average parameters q. The input time series for the ARIMA method must be stationary, i.e. it should have a time-constant average, variance and no autocorrelation. In studies on more seasonal time series, seasonal models are also employed, where three additional seasonality parameters for the ARIMA model (Ps, Ds, Qs) are specified: autoregressive seasonal parameters Ps, seasonal differencing parameters Ds and seasonal moving average parameters Qs. In passenger flow data a damped growing tendency, periodic additive seasonal fluctuations and random fluctuations (seasonal decomposition) were identified. Therefore, the data needed to be prepared for analysis in order to be able to use the ARIMA model. The series was not stationary, it featured autocorrelations, and its mean and variance differed over time. For this reason, prior to the data being input for analysis, they had to be adjusted to achieve stationarity, which required logarithmisation and differencing (D(1), Ds(12)). Following the two operations, the mean and variance were constant in time (see: [11]). Having prepared the data, the most adequate model containing seasonal parameters (Ps, Ds, Qs) was used. Several models were constructed. After an analysis of parameter significance and testing distributions of residuals, as well as checking autocorrelations, the best model was selected, in which the residuals were characterised by normal distribution and did not feature autocorrelation. This is the ARIMA model (1,1,1) (0,1,1). All parameters are statistically significant (Table 1) Table 1. ARIMA model parameter estimations. Coefficient Coefficient value p-value constant p(1) *** q(1) *** Qs(1) *** The residuals of the ARIMA model were checked for autocorrelations and normal distribution. The Q-Ljung Box test showed lack of autocorrelations. Absolute values of residuals autocorrelations are less then 0.15 and p-values of Q-Ljung Box test are greater then A further test was meant to verify if the distribution of residuals conforms to normal distribution. The chi-squared Pearson test demonstrated that the distribution of the residuals is normal p>α (p=0.13), so there were no premises for rejecting the hypothesis on normal distribution of residuals. The above is also confirmed by the value of the statistic d= in the Kolmogorov-Smirnov goodness of fit test. Artificial Neural Networks. In the present study, MLP (Multi Layer Perceptron) neural networks with a single layer of hidden neurons were used for predicting passenger traffic. Variables at the neural network input in the input layer included variables for 12 consecutive seasonal delays,,. At the network output, variable (current passenger count at the airport in a given month) was considered. At the input there are m=12 delayed values of the forecast time series. After the inclusion of weights, for every hidden neuron (k=1,,n) information from the input variables is summated and

8 4 th International Multidisciplinary Scientific Conferences on Social Sciences & Arts SGEM 2017 each hidden neuron transmits total net value of the information (the so-called net stimulus of the neuron):,,, where, is a bias term. Subsequently, the net stimulus of the neuron is transformed by the neuron's activation function for hidden neurons, creating their output signal, which is then transmitted to the output layer. Various forms of hidden neuron's activation functions were used in the calculations: linear, logistic (sigmoid), hyperbolic tangent, exponential. Next, the output signals from hidden neurons are transmitted to the output layer, and their weights are determined. The weights are used to determine the output neuron's net stimulus:, where: is the bias of the output neuron. The ultimate value of the output signal that emerges at the network output is calculated by transforming the net stimulus of the output neuron y by its activation function. The activation functions of the output neuron are identical to the activations function of hidden neurons. Optimum weight values for the networks being trained were established through the following learning error function:, which was the sum of squares of the differences of values at the output of the neural network being trained and the real value of the output variable. As the learning algorithm a quasi-newton method, the socalled BFGS (Broyden-Fletcher-Goldfarb-Shanno) algorithm, was applied with a learning error function. Statistica 12.0 Neural Networks module and the capability of selecting best forecast networks were used in calculations for predicting the number of passengers. This approach automatically selects networks of best forecast properties on the basis of set learning, validation and test samples, neuron activation functions and various numbers of neurons in the hidden layer. It was assumed that the number of neurons in the hidden layer would vary from 2 to 12. In order to determine the optimum value of weights for best neural networks, the data from lerning and validation samples were used. The validation sample is used for determining the extent to which the model of the network matches the input data, while preventing the network weights from overadjusting only for learning data. On the basis of the validation sample, 5 networks with the best forecasting properties (greatest percentage ratio of matching the validation data) were selected. Statistical data from the period starting January 2016 and ending October 2016 were selected as the final test sample. The best values obtained for the learning sample and the validation sample were presented in the Table 1. The network with the best forecasting properties both for the validation and the learning sample will be used in the final forecast of passenger traffic at Rzeszow International Airport. It is the network of an MLP architecture with 2 hidden neurons and an tanh activation function for the hidden layer and exponential activation function the output layer. The network achieved the greatest forecasting quality coefficient for the validation and the learning sample, respectively 98% and 92%. Table 2. Five best MLP neural networks offering superior forecasting quality for the validation sample and their quality coefficients for data from learning, validation and test samples. Neural network Activation function (hidden layer) Activation function (output layer) Quality % forecasting quality of matching data (Learning) Quality (Validation) Quality (Test) MLP Tanh Tanh (93%) (98%) (96%) MLP Tanh Exponential (92%) (98%) (97%) MLP Exponential Linear (91%) (96%) (98%) MLP Tanh Exponential (91%) (97%) (97%) MLP Tanh Exponential (91%) (97%) (97%)

9 Section Name Support Vector Machines. SVM is a non-parametric method based on machine learning and artificial intelligence solutions. Like neural networks, the approach is increasingly used for classification and forecasting. The main concept behind the application of SVM for regression and function value approximation consists in appropriately mapping data from time series onto a multi-dimensional feature space. Such space is associated with support vectors, i.e. feature vectors that represent numerical properties of mapped objects. Mapping takes place by a non-linear transformation into a support vector space, which is subsequently subjected to linear regression. A forecast was prepared with the use of the SVM method using the SVM module of Statistica 12.0 software. Owing to the fact that in the SVM approach parameters, and kernel parameter may significantly affect the method's accuracy, it is crucial to determine values which would give the best results. A v-fold cross-validation tool (v=10) integrated in Statistica SVM module was used for learning data within the parameters' range of variability: C from 1 to 10 with an increment of 1, and ε from 0.1 to 0.5 with an increment of 0.1. Parameter γ was established on a constant level depending on the number of input variables used. Possible variants of input variables included 6 input variable configuration variants. For each input variable variant, optimum values of SVM parameters were obtained by solving problem (8), and a forecast was prepared using equation (7). Estimations were made on the basis of a learning sample identical to the one used in the neural network method, while the final effectiveness of the forecast was tested for the test sample containing cases not covered when training the SVM machine. Table 3 shows estimated parameters and forecasting errors for the SVM approach with different variants of input variables. Table 3. Forecast parameters and errors for the SVM approach. Input variable variant Optimum parameters (SVM approach) Forecast quality measures (learning sample) Forecast quality measures (test sample) RMSE MAPE [%] RMSE MAPE [%] Xt=f(Xt-1,Xt-2) C=10, ε=0.1, γ= Xt=f(Xt-1,,Xt-4) C=7, ε=0.2, γ= Xt=f(Xt-1,,Xt-6) C=10, ε=0.1, γ= Xt=f(Xt-1,,Xt-8) C=10, ε=0.1, γ= Xt=f(Xt-1,,Xt-10) C=10, ε=0.1, γ= Xt=f(Xt-1,,Xt-12) C=8, ε=0.1, γ= The SVM model was selected as the final forecasting method, in which input variables included 12 variables with all seasonal delays (variant 6), as it was characterised by the smallest forecast errors, both for the learning and the test sample. Comparison of the forecast effectiveness. A comparison of the effectiveness of the proposed forecasting methods concerning the number of passengers for the learning and test samples is presented in Table 4. Error measures included RMSE and MAPE. The SVMR model offers the lowest error values for the learning sample but for the test sample MLP is the best. Among AI-based and machine learning forecasting methods, the neural network approach is characterized by low percentage forecasting errors. Table 4. Forecast errors for the learning sample and the test sample for different forecast models. Forecasting Forecast errors

10 4 th International Multidisciplinary Scientific Conferences on Social Sciences & Arts SGEM 2017 method RMSE (learning sample) MAPE [%] (learning sample) RMSE (test sample) MAPE [%] (test sample) Exponential smoothing ARIMA MLP Neural Net (12-2-1) SVMR (X t - 1,,X t-12 ) The final forecast was computed as a mean weighted forecast from the forecasts obtained by all four methods. Weights for each method in the mean weighted forecasts were calculated as: / where: - mean percentage forecast error for the learning sample using the j-th forecasting method. The final mean forecast was determined using the weighting system in the following manner: (3) (4) where: the forecast for the moment t obtained with the j-th method. The figure (fig. 2) presents mean forecast for the analysed time series for the previous years as well as the forthcoming year Figure 2. Passengers traffic mean forecast at Rzeszow International Airport. CONCLUSION Four time series-based forecasting methods were used to construct a passenger traffic forecast. They included two analytical methods: exponential smoothing and ARIMA, and the neural network method and Support Vector Machines (SVMR) approach involving machine learning and artificial intelligence. All methods used to compute a forecast of

11 Section Name passenger flows at Rzeszow International Airport gave similar results. Nevertheless, on the basis of Table 4 it could be indicate the method besed by lowest errors (MAPE and RMSE) both for the learning and the test sample. The SVMR model offers the lowest error values for the learning sample but for the test sample MLP is the best. The final value of forecast volumes was determined by employing the results of all methods discussed here. The forecast retains the characteristics of historical data, i.e. seasonal fluctuations, though its values do not rise substantially. Rather, it seems that the dynamic growth is slowing down. The hypothesis could be formulated that the air services market in the region is stabilising while preserving its seasonal character. The forecasts obtained here are plausible and reliable, but one must note that the passenger traffic is linked to many factors, and the inclusion of the time factor alone is a considerable simplification. It is a well-known fact that air passenger transport may be affected by many diverse variables. The main factors determining the demand for transport include: the future amount of the GDP, the population of the country, the volume and value of foreign exchange, consumption levels, household spending structure, the rationalisation of a set of indicators concerning the use of specific means of transport, tendencies to alter travel and transport distances as a result of European integration processes and the changes in the geography of manufacturing and settlement in the country. Consequently, although the forecasts clearly indicate growth tendencies of the phenomenon (in this case, passenger traffic at Rzeszow Airport), they should be approached with caution. To a certain extent such forecasts enable the right decisions on future activities in the analysed area to be taken. Thanks to the use of suitable forecasting methods, key decisions become more justified and substantiated with an appropriate analysis. REFERENCES [1] Abed S. Y., Ba-Fail A. O., Jasimuddin S. M., An Econometric Analysis of International Air Travel Demand in Saudi Arabia. Journal of Air Transport Management, pp , [2] Abdelghany A., Guzhava V. S., A time series modelling approach for airport short term demand forecasting. Airport Management, 5, pp 72-87, [3] Andreoni A., Postorino M. N., A multivariate ARIMA model to forecast air transport demand. Paper presented at the association for European transport and contributors [online] Available at: < download/id/2535> [Accessed 17 November 2016]. [4] Bao Y., Xiong T., Hu Z., Forecasting Air Passenger Traffic by Support Vector Machines with Ensemble Empirical Mode Decomposition and Slope-Based Method. Discrete Dynamics in Nature and Society, pp 1-12, [5] Box G. E. P., Jenkins G. M., Reinsel G. C., Ljung G. M., Time Series Analysis. Forecasting and Control. John Wiley & Sons, Hoboken, [6] Bougas C., Forecasting Air Passenger Traffic Flows in Canada: An Evaluation of Time Series Models and Combination Methods. Ph.D. Thesis, Universite LAVAL, Quebec Canada, 2013.

12 4 th International Multidisciplinary Scientific Conferences on Social Sciences & Arts SGEM 2017 [7] Chen S. C., Kuo S. Y., Chang K. W., Wang Y. T., Improving the Forecasting Accuracy of air Passenger and Air Cargo Demand: The Application of Back Propagation Neural Networks. Transplantation Planning and Technology, 35(3), pp , [8] Fernandes P., Teixeira J., Ferreira M., Azevedo S. G., Modelling Tourism Demand: A Comparative Study between Artificial Neural Networks and The Box Jenkins Methodology. Romanian Journal of Economic Forecasting, 3, pp 30-50, [9] Gardner E. S., Exponential Smoothing: The State of the Art. Journal of Forecasting, pp 1-28, [10] Grubb H., Mason A., Long lead-time forecasting of UK air passengers by Holt- Winters methods with damped trend. International Journal of Forecasting, 17, pp 71-82, [11] Makridakis S., Wheelwright S. C., Hyndman R. J., Forecasting. Methods and Applications. John Wiley & Sons, New York, [12] Tsui W. H. K., Balli H. O., Gilbey A., Gow H., Forecasting of Hong Kong airport s passenger throughput. Tourism Management, 42, pp 62-76, [13] Weatherford L. R., Gentry T. W., Wilamowski B., Neural network forecasting for airlines: a comparative analysis. Journal of Revenue and Pricing Management, 1, pp , [14] Xiao Y., Liu J. J., Hu Y., Wang Y., Lai K. K., Wang S., A neuro-fuzzy combination model based on singular spectrum analysis for air transport demand forecasting. Journal of Air Transport Management, 39, pp 1-11, [15] Xie G., Wang S., Lai K. K., Short-term forecasting of air passenger by using hybrid seasonal decomposition and least squares support vector regression approaches. Journal of Air Transport Management, 37, pp 20-26, 2014.