A Demand Forecasting Method Based on Stochastic Frontier Analysis and Model Average: An Application in Air Travel Demand Forecasting
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摘要
Demand forecasting is often difficult due to the unobservability of the applicable historical demand series. In this study, the authors propose a demand forecasting method based on stochastic frontier analysis(SFA) models and a model average technique. First, considering model uncertainty,a set of alternative SFA models with various combinations of explanatory variables and distribution assumptions are constructed to estimate demands. Second, an average estimate from the estimated demand values is obtained using a model average technique. Finally, future demand forecasts are achieved, with the average estimates used as historical observations. An empirical application of air travel demand forecasting is implemented. The results of a forecasting performance comparison show that in addition to its ability to estimate demand, the proposed method outperforms other common methods in terms of forecasting passenger traffic.
Demand forecasting is often difficult due to the unobservability of the applicable historical demand series. In this study, the authors propose a demand forecasting method based on stochastic frontier analysis(SFA) models and a model average technique. First, considering model uncertainty,a set of alternative SFA models with various combinations of explanatory variables and distribution assumptions are constructed to estimate demands. Second, an average estimate from the estimated demand values is obtained using a model average technique. Finally, future demand forecasts are achieved, with the average estimates used as historical observations. An empirical application of air travel demand forecasting is implemented. The results of a forecasting performance comparison show that in addition to its ability to estimate demand, the proposed method outperforms other common methods in terms of forecasting passenger traffic.
Demand forecasting is often difficult due to the unobservability of the applicable historical demand series. In this study, the authors propose a demand forecasting method based on stochastic frontier analysis(SFA) models and a model average technique. First, considering model uncertainty,a set of alternative SFA models with various combinations of explanatory variables and distribution assumptions are constructed to estimate demands. Second, an average estimate from the estimated demand values is obtained using a model average technique. Finally, future demand forecasts are achieved, with the average estimates used as historical observations. An empirical application of air travel demand forecasting is implemented. The results of a forecasting performance comparison show that in addition to its ability to estimate demand, the proposed method outperforms other common methods in terms of forecasting passenger traffic.
引文
[1]Clements M P and Hendry D F,The Oxford Handbook of Economic Forecasting,Oxford University Press,Oxford,2011.
[2]Kulendran N and Wilson K,Is there a relationship between international trade and international travel?Applied Economics,2000,32(8):1001-1009.
[3]Lim C and Mc Aleer M,Cointegration analysis of quarterly tourism demand by Hong Kong and Singapore for Australia,Applied Economics,2001,33(12):1599-1619.
[4]Song H and Witt S F,Forecasting international tourist flows to Macau,Tourism Management,2006,27(2):214-224.
[5]Koen R and Holloway J,Application of multiple regression analysis to forecasting South Africa’s electricity demand,Journal of Energy in Southern Africa,2014,25(4):48-58.
[6]Mc Nown R,Aburizaizah O S,Howe C,et al.,Forecasting annual water demands dominated by seasonal variations:The case of water demands in Mecca,Applied Economics,2005,47(6):544-552.
[7]Cho V,Tourism forecasting and its relationship with leading economic indicators,Journal of Hospitality and Tourism Research,2001,25(4):399-420.
[8]Goh C and Law R,Modeling and forecasting tourism demand for arrivals with stochastic nonstationary seasonality and intervention,Tourism Management,2002,23(5):499-510.
[9]Gil-Alana L A,Modelling international monthly arrivals using seasonal univariate long-memory processes,Tourism Management,2005,26(6):867-878.
[10]Ediger V S?and Akar S,ARIMA forecasting of primary energy demand by fuel in Turkey,Energy Policy,2007,35(3):1701-1708.
[11]Cho V,A comparison of three different approaches to tourist arrival forecasting,Tourism Management,2003,24(3):323-330.
[12]Kon S C and Turner L W,Neural network forecasting of tourism demand,Tourism Economics,2005,11(3):301-328.
[13]Alekseev K P G and Seixas J M,A multivariate neural forecasting modeling for air transportPreprocessed by decomposition:A Brazilian application,Journal of Air Transport Management,2009,15(5):212-216.
[14]Tay F E and Cao L,Application of support vector machines in financial time series forecasting,Omega,2001,29(4):309-317.
[15]Pai P F and Hong W C,Forecasting regional electricity load based on recurrent support vector machines with genetic algorithms,Electric Power Systems Research,2005,74(3):417-425.
[16]Chen K Y and Wang C H,Support vector regression with genetic algorithms in forecasting tourism demand,Tourism Management,2007,28(1):215-226.
[17]Xie G,Wang S Y,and 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,2014,37:20-26.
[18]Armstrong J S,Principles of Forecasting:A Handbook for Researchers and Practitioners,Springer Science and Business Media,New York,2001.
[19]Oh C O and Morzuch B J,Evaluating time-series models to forecast the demand for tourism in Singapore:Comparing within-sample and post-sample results,Journal of Travel Research,2005,43(4):404-413.
[20]Karlaftis M G,Demand forecasting in regional airports:Dynamic Tobit models with GARCHerrors,Sitraer,2008,7:100-111.
[21]Yu L A,Wang S Y,and Lai K K,Forecasting China’s foreign trade volume with a kernel-based hybrid econometric-AI ensemble learning approach,Journal of Systems Science and Complexity,2008,21(1):1-19.
[22]Xiao Y,Xiao J,Liu J,et al.,A multiscale modeling approach incorporating ARIMA and anns for financial market volatility forecasting,Journal of Systems Science and Complexity,2014,27(1):225-236.
[23]Xiao Y,Liu J J,Hu Y,et al.,A neuro-fuzzy combination model based on singular spectrum analysis for air transport demand forecasting,Journal of Air Transport Management,2014,39:1-11.
[24]Huang A Q,Lai K K,Li Y H,et al.,Forecasting container throughput of Qingdao port with a hybrid model,Journal of Systems Science and Complexity,2015,28(1):105-121.
[25]Weatherford L R and Kimes S E,A comparison of forecasting methods for hotel revenue management,International Journal of Forecasting,2003,19(3):401-415.
[26]Orkin E B,Wishful thinking and rocket science:The essential matter of calculating unconstrained demand for revenue management,The Cornell Hotel and Restaurant Administration Quarterly,1998,39(4):15-19.
[27]Wickham R R,Evaluation of forecasting techniques for short-term demand of air transportation,Department of Aeronautics and Astronautics,Flight Transportation Laboratory,Massachusetts Institute of Technology,Cambridge,1995.
[28]Weatherford L R and P¨olt S,Better unconstraining of airline demand data in revenue management systems for improved forecast accuracy and greater revenues,Journal of Revenue and Pricing Management,2002,1(3):234-254.
[29]Battese G E and Coelli T J,A model for technical inefficiency effects in a stochastic frontier production function for panel data,Empirical Economics,1995,20(2):325-332.
[30]Jacobs R,Alternative methods to examine hospital efficiency:Data envelopment analysis and stochastic frontier analysis,Health Care Management Science,2001,4(2):103-115.
[31]Cullinane K,Wang T F,Song D W,et al.,The technical efficiency of container ports:Comparing data envelopment analysis and stochastic frontier analysis,Transportation Research Part A:Policy and Practice,2006,40(4):354-374.
[32]Longford N T,Editorial:Model selection and efficiency is‘Which model···?’the right question?Journal of the Royal Statistical Society A,2005,168:469-472.
[33]Leung G and Barron A R,Infromation theory and mixing least squares regressions,IEEE Transactions on Information Theory,2006,52:3396-3410.
[34]Hoeting J A,Madigan D,Raftery A E,et al.,Bayesian model averaging:A tutorial,Statistical Science,1999,14:382-417.
[35]Buckland S T,Burnham K P,and Augustin N H,Model selection:An integral part of inference,Biometrics,1997,53:603-618.
[36]Hansen B E,Least squares model averaging,Econometrica,2007,75:1175-1189.
[37]Zhang X and Liang H,Focused information criterion and model averaging for generalized additive partial linear models,Annals of Statistics,2011,39:174-200.
[38]Hansen B E and Racine J S,Jackknife model averaging,Journal of Econometrics,2012,167(1):38-46.
[39]Ba-Fail A O,Abed S Y,Jasimuddin S M,et al.,The determinants of domestic air travel demand in the Kingdom of Saudi Arabia,Journal of Air Transportation World Wide,2000,5(2):72-86.
[40]Carson R T,Cenesizoglu T,and Parker R,Forecasting(aggregate)demand for US commercial air travel,International Journal of Forecasting,2011,27(3):923-941.
[41]Teyssier N,How the consumer confidence index could increase air travel demand forecast accuracy?PhD’s degree thesis,Cranfield University,Bedfordshire,2012.
[42]Grubb H and Mason A,Long lead-time forecasting of UK air passengers by Holt-Winters methods with damped trend,International Journal of Forecasting,2001,17(1):71-82.
[43]Berm′udez J D,Segura J V,and Vercher E,Holt-Winters forecasting:An alternative formulation applied to UK air passenger data,Journal of Applied Statistics,2007,34(9):1075-1090.
[44]Wang S J,Sui D,and Hu B,Forecasting technology of national-wide civil aviation traffic,Journal of Transportation Systems Engineering and Information Technology,2010,10(6):95-102.
[45]Aigner D,Lovell C K,and Schmidt P,Formulation and estimation of stochastic frontier production function models,Journal of Econometrics,1977,6(1):21-37.
[46]Meeusen W and Van den Broeck J,Efficiency estimation from Cobb-Douglas production functions with composed error,International Economic Review,1977,18(2):435-444.
[47]Jorge-Calder′on J D,A demand model for scheduled airline services on international European routes,Journal of Air Transport Management,1997,3(1):23-35.
[48]Castelli L,Pesenti R,and Ukovich W,An airline-based multilevel analysis of airfare elasticity for passenger demand,Proceeding of the 7th Air Transport Research Society World Conference,France,2003.
[49]Demirsoy C,Analysis of stimulated domestic air transport demand in Turkey,Master’s degree thesis,Erasmus University,Rotterdam,2012.
[50]Lim C,Review of international tourism demand models,Annals of Tourism Rresearch,1997,24(4):835-849.
[51]Marazzo M,Scherre R,and Fernandes E,Air transport demand and economic growth in Brazil:A time series analysis,Transportation Research Part E:Logistics and Transportation Review,2010,46(2):261-269.
[52]Fernandes E and Pacheco R R,The causal relationship between GDP and domestic air passenger traffic in Brazil,Transportation Planning and Technology,2010,33(7):569-581.
[53]Dargay J and Hanly M,The determinants of the demand for international air travel to and from the UK,Proceeding of the 9th World Conference on Transport Research,Edinburgh,Scotland,2001.
[54]Abed S Y,Ba-Fail A O,and Jasimuddin S M,An econometric analysis of international air travel demand in Saudi Arabia,Journal of Air Transport Management,2001,7(3):143-148.
[55]Zhang X,Wan A T K,and Zou G,Model averaging by jackknife criterion in models with dependent data,Journal of Econometrics,2012,174(2):82-94.
[56]Zhang X,Zou G,and Liang H,Model averaging and weight choice in linear mixed effects models,Biometrika,2014,101(1):205-218.
[57]Ando T and Li K C,A model-averaging approach for high-dimensional regression,Journal of the American Statistical Association,2014,109(505):254-265.
[58]White H,Maximum likelihood estimation of misspecified models,Econometrica:Journal of the Econometric Society,1982,50(1):1-25.
[59]Zhang X,Model averaging and its applications,Ph.D.dissertation,Chinese Academy of Sciences.
[2]Kulendran N and Wilson K,Is there a relationship between international trade and international travel?Applied Economics,2000,32(8):1001-1009.
[3]Lim C and Mc Aleer M,Cointegration analysis of quarterly tourism demand by Hong Kong and Singapore for Australia,Applied Economics,2001,33(12):1599-1619.
[4]Song H and Witt S F,Forecasting international tourist flows to Macau,Tourism Management,2006,27(2):214-224.
[5]Koen R and Holloway J,Application of multiple regression analysis to forecasting South Africa’s electricity demand,Journal of Energy in Southern Africa,2014,25(4):48-58.
[6]Mc Nown R,Aburizaizah O S,Howe C,et al.,Forecasting annual water demands dominated by seasonal variations:The case of water demands in Mecca,Applied Economics,2005,47(6):544-552.
[7]Cho V,Tourism forecasting and its relationship with leading economic indicators,Journal of Hospitality and Tourism Research,2001,25(4):399-420.
[8]Goh C and Law R,Modeling and forecasting tourism demand for arrivals with stochastic nonstationary seasonality and intervention,Tourism Management,2002,23(5):499-510.
[9]Gil-Alana L A,Modelling international monthly arrivals using seasonal univariate long-memory processes,Tourism Management,2005,26(6):867-878.
[10]Ediger V S?and Akar S,ARIMA forecasting of primary energy demand by fuel in Turkey,Energy Policy,2007,35(3):1701-1708.
[11]Cho V,A comparison of three different approaches to tourist arrival forecasting,Tourism Management,2003,24(3):323-330.
[12]Kon S C and Turner L W,Neural network forecasting of tourism demand,Tourism Economics,2005,11(3):301-328.
[13]Alekseev K P G and Seixas J M,A multivariate neural forecasting modeling for air transportPreprocessed by decomposition:A Brazilian application,Journal of Air Transport Management,2009,15(5):212-216.
[14]Tay F E and Cao L,Application of support vector machines in financial time series forecasting,Omega,2001,29(4):309-317.
[15]Pai P F and Hong W C,Forecasting regional electricity load based on recurrent support vector machines with genetic algorithms,Electric Power Systems Research,2005,74(3):417-425.
[16]Chen K Y and Wang C H,Support vector regression with genetic algorithms in forecasting tourism demand,Tourism Management,2007,28(1):215-226.
[17]Xie G,Wang S Y,and 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,2014,37:20-26.
[18]Armstrong J S,Principles of Forecasting:A Handbook for Researchers and Practitioners,Springer Science and Business Media,New York,2001.
[19]Oh C O and Morzuch B J,Evaluating time-series models to forecast the demand for tourism in Singapore:Comparing within-sample and post-sample results,Journal of Travel Research,2005,43(4):404-413.
[20]Karlaftis M G,Demand forecasting in regional airports:Dynamic Tobit models with GARCHerrors,Sitraer,2008,7:100-111.
[21]Yu L A,Wang S Y,and Lai K K,Forecasting China’s foreign trade volume with a kernel-based hybrid econometric-AI ensemble learning approach,Journal of Systems Science and Complexity,2008,21(1):1-19.
[22]Xiao Y,Xiao J,Liu J,et al.,A multiscale modeling approach incorporating ARIMA and anns for financial market volatility forecasting,Journal of Systems Science and Complexity,2014,27(1):225-236.
[23]Xiao Y,Liu J J,Hu Y,et al.,A neuro-fuzzy combination model based on singular spectrum analysis for air transport demand forecasting,Journal of Air Transport Management,2014,39:1-11.
[24]Huang A Q,Lai K K,Li Y H,et al.,Forecasting container throughput of Qingdao port with a hybrid model,Journal of Systems Science and Complexity,2015,28(1):105-121.
[25]Weatherford L R and Kimes S E,A comparison of forecasting methods for hotel revenue management,International Journal of Forecasting,2003,19(3):401-415.
[26]Orkin E B,Wishful thinking and rocket science:The essential matter of calculating unconstrained demand for revenue management,The Cornell Hotel and Restaurant Administration Quarterly,1998,39(4):15-19.
[27]Wickham R R,Evaluation of forecasting techniques for short-term demand of air transportation,Department of Aeronautics and Astronautics,Flight Transportation Laboratory,Massachusetts Institute of Technology,Cambridge,1995.
[28]Weatherford L R and P¨olt S,Better unconstraining of airline demand data in revenue management systems for improved forecast accuracy and greater revenues,Journal of Revenue and Pricing Management,2002,1(3):234-254.
[29]Battese G E and Coelli T J,A model for technical inefficiency effects in a stochastic frontier production function for panel data,Empirical Economics,1995,20(2):325-332.
[30]Jacobs R,Alternative methods to examine hospital efficiency:Data envelopment analysis and stochastic frontier analysis,Health Care Management Science,2001,4(2):103-115.
[31]Cullinane K,Wang T F,Song D W,et al.,The technical efficiency of container ports:Comparing data envelopment analysis and stochastic frontier analysis,Transportation Research Part A:Policy and Practice,2006,40(4):354-374.
[32]Longford N T,Editorial:Model selection and efficiency is‘Which model···?’the right question?Journal of the Royal Statistical Society A,2005,168:469-472.
[33]Leung G and Barron A R,Infromation theory and mixing least squares regressions,IEEE Transactions on Information Theory,2006,52:3396-3410.
[34]Hoeting J A,Madigan D,Raftery A E,et al.,Bayesian model averaging:A tutorial,Statistical Science,1999,14:382-417.
[35]Buckland S T,Burnham K P,and Augustin N H,Model selection:An integral part of inference,Biometrics,1997,53:603-618.
[36]Hansen B E,Least squares model averaging,Econometrica,2007,75:1175-1189.
[37]Zhang X and Liang H,Focused information criterion and model averaging for generalized additive partial linear models,Annals of Statistics,2011,39:174-200.
[38]Hansen B E and Racine J S,Jackknife model averaging,Journal of Econometrics,2012,167(1):38-46.
[39]Ba-Fail A O,Abed S Y,Jasimuddin S M,et al.,The determinants of domestic air travel demand in the Kingdom of Saudi Arabia,Journal of Air Transportation World Wide,2000,5(2):72-86.
[40]Carson R T,Cenesizoglu T,and Parker R,Forecasting(aggregate)demand for US commercial air travel,International Journal of Forecasting,2011,27(3):923-941.
[41]Teyssier N,How the consumer confidence index could increase air travel demand forecast accuracy?PhD’s degree thesis,Cranfield University,Bedfordshire,2012.
[42]Grubb H and Mason A,Long lead-time forecasting of UK air passengers by Holt-Winters methods with damped trend,International Journal of Forecasting,2001,17(1):71-82.
[43]Berm′udez J D,Segura J V,and Vercher E,Holt-Winters forecasting:An alternative formulation applied to UK air passenger data,Journal of Applied Statistics,2007,34(9):1075-1090.
[44]Wang S J,Sui D,and Hu B,Forecasting technology of national-wide civil aviation traffic,Journal of Transportation Systems Engineering and Information Technology,2010,10(6):95-102.
[45]Aigner D,Lovell C K,and Schmidt P,Formulation and estimation of stochastic frontier production function models,Journal of Econometrics,1977,6(1):21-37.
[46]Meeusen W and Van den Broeck J,Efficiency estimation from Cobb-Douglas production functions with composed error,International Economic Review,1977,18(2):435-444.
[47]Jorge-Calder′on J D,A demand model for scheduled airline services on international European routes,Journal of Air Transport Management,1997,3(1):23-35.
[48]Castelli L,Pesenti R,and Ukovich W,An airline-based multilevel analysis of airfare elasticity for passenger demand,Proceeding of the 7th Air Transport Research Society World Conference,France,2003.
[49]Demirsoy C,Analysis of stimulated domestic air transport demand in Turkey,Master’s degree thesis,Erasmus University,Rotterdam,2012.
[50]Lim C,Review of international tourism demand models,Annals of Tourism Rresearch,1997,24(4):835-849.
[51]Marazzo M,Scherre R,and Fernandes E,Air transport demand and economic growth in Brazil:A time series analysis,Transportation Research Part E:Logistics and Transportation Review,2010,46(2):261-269.
[52]Fernandes E and Pacheco R R,The causal relationship between GDP and domestic air passenger traffic in Brazil,Transportation Planning and Technology,2010,33(7):569-581.
[53]Dargay J and Hanly M,The determinants of the demand for international air travel to and from the UK,Proceeding of the 9th World Conference on Transport Research,Edinburgh,Scotland,2001.
[54]Abed S Y,Ba-Fail A O,and Jasimuddin S M,An econometric analysis of international air travel demand in Saudi Arabia,Journal of Air Transport Management,2001,7(3):143-148.
[55]Zhang X,Wan A T K,and Zou G,Model averaging by jackknife criterion in models with dependent data,Journal of Econometrics,2012,174(2):82-94.
[56]Zhang X,Zou G,and Liang H,Model averaging and weight choice in linear mixed effects models,Biometrika,2014,101(1):205-218.
[57]Ando T and Li K C,A model-averaging approach for high-dimensional regression,Journal of the American Statistical Association,2014,109(505):254-265.
[58]White H,Maximum likelihood estimation of misspecified models,Econometrica:Journal of the Econometric Society,1982,50(1):1-25.
[59]Zhang X,Model averaging and its applications,Ph.D.dissertation,Chinese Academy of Sciences.
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