Evaluación de modelos de series de tiempo para pronosticar la demanda de transporte aéreo a corto y mediano plazo en Colombia
ilustraciones, gráficas, tablas
- Autores:
-
Amezquita Bravo, Cristian Camilo
- Tipo de recurso:
- Fecha de publicación:
- 2021
- Institución:
- Universidad Nacional de Colombia
- Repositorio:
- Universidad Nacional de Colombia
- Idioma:
- spa
- OAI Identifier:
- oai:repositorio.unal.edu.co:unal/81124
- Palabra clave:
- 330 - Economía
Time-series analysis
Aeronautics, commercial
Forecasting techniques
Análisis de series de tiempo
Aviación comercial
Técnicas de predicción
Pronóstico de demanda
Transporte aéreo
Series de tiempo
ARIMA
SARIMA
ARIMAX
Forecasting demand
Air transport
Air passengers demand
ARIMA
SARIMA
ARIMAX
Time series
- Rights
- openAccess
- License
- Atribución-NoComercial-SinDerivadas 4.0 Internacional
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Universidad Nacional de Colombia |
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|
dc.title.spa.fl_str_mv |
Evaluación de modelos de series de tiempo para pronosticar la demanda de transporte aéreo a corto y mediano plazo en Colombia |
dc.title.translated.eng.fl_str_mv |
Evaluation of time series models to forecast air transportation demand in the short and medium term in Colombia |
title |
Evaluación de modelos de series de tiempo para pronosticar la demanda de transporte aéreo a corto y mediano plazo en Colombia |
spellingShingle |
Evaluación de modelos de series de tiempo para pronosticar la demanda de transporte aéreo a corto y mediano plazo en Colombia 330 - Economía Time-series analysis Aeronautics, commercial Forecasting techniques Análisis de series de tiempo Aviación comercial Técnicas de predicción Pronóstico de demanda Transporte aéreo Series de tiempo ARIMA SARIMA ARIMAX Forecasting demand Air transport Air passengers demand ARIMA SARIMA ARIMAX Time series |
title_short |
Evaluación de modelos de series de tiempo para pronosticar la demanda de transporte aéreo a corto y mediano plazo en Colombia |
title_full |
Evaluación de modelos de series de tiempo para pronosticar la demanda de transporte aéreo a corto y mediano plazo en Colombia |
title_fullStr |
Evaluación de modelos de series de tiempo para pronosticar la demanda de transporte aéreo a corto y mediano plazo en Colombia |
title_full_unstemmed |
Evaluación de modelos de series de tiempo para pronosticar la demanda de transporte aéreo a corto y mediano plazo en Colombia |
title_sort |
Evaluación de modelos de series de tiempo para pronosticar la demanda de transporte aéreo a corto y mediano plazo en Colombia |
dc.creator.fl_str_mv |
Amezquita Bravo, Cristian Camilo |
dc.contributor.advisor.spa.fl_str_mv |
Moreno Rivas, Álvaro Martin |
dc.contributor.author.spa.fl_str_mv |
Amezquita Bravo, Cristian Camilo |
dc.subject.ddc.spa.fl_str_mv |
330 - Economía |
topic |
330 - Economía Time-series analysis Aeronautics, commercial Forecasting techniques Análisis de series de tiempo Aviación comercial Técnicas de predicción Pronóstico de demanda Transporte aéreo Series de tiempo ARIMA SARIMA ARIMAX Forecasting demand Air transport Air passengers demand ARIMA SARIMA ARIMAX Time series |
dc.subject.lemb.eng.fl_str_mv |
Time-series analysis Aeronautics, commercial Forecasting techniques |
dc.subject.lemb.spa.fl_str_mv |
Análisis de series de tiempo Aviación comercial Técnicas de predicción |
dc.subject.proposal.spa.fl_str_mv |
Pronóstico de demanda Transporte aéreo Series de tiempo ARIMA SARIMA ARIMAX |
dc.subject.proposal.eng.fl_str_mv |
Forecasting demand Air transport Air passengers demand ARIMA SARIMA ARIMAX Time series |
description |
ilustraciones, gráficas, tablas |
publishDate |
2021 |
dc.date.issued.none.fl_str_mv |
2021 |
dc.date.accessioned.none.fl_str_mv |
2022-03-03T16:58:34Z |
dc.date.available.none.fl_str_mv |
2022-03-03T16:58:34Z |
dc.type.spa.fl_str_mv |
Trabajo de grado - Maestría |
dc.type.driver.spa.fl_str_mv |
info:eu-repo/semantics/masterThesis |
dc.type.version.spa.fl_str_mv |
info:eu-repo/semantics/acceptedVersion |
dc.type.content.spa.fl_str_mv |
Text |
dc.type.redcol.spa.fl_str_mv |
http://purl.org/redcol/resource_type/TM |
status_str |
acceptedVersion |
dc.identifier.uri.none.fl_str_mv |
https://repositorio.unal.edu.co/handle/unal/81124 |
dc.identifier.instname.spa.fl_str_mv |
Universidad Nacional de Colombia |
dc.identifier.reponame.spa.fl_str_mv |
Repositorio Institucional Universidad Nacional de Colombia |
dc.identifier.repourl.spa.fl_str_mv |
https://repositorio.unal.edu.co/ |
url |
https://repositorio.unal.edu.co/handle/unal/81124 https://repositorio.unal.edu.co/ |
identifier_str_mv |
Universidad Nacional de Colombia Repositorio Institucional Universidad Nacional de Colombia |
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spa |
language |
spa |
dc.relation.references.spa.fl_str_mv |
Aeronáutica Civil, (2014a). Guía para la elaboración de Planes Maestros Aeroportuarios – PMA, Circular Reglamentaria N° 053, https://www.aerocivil.gov.co/normatividad/CIRCULARES%20AGA/CI%20053%20-%20V2.pdf Aeronáutica Civil, (2014b). Actualización del plan maestro del Aeropuerto Internacional ElDorado reporte final, Tylin international, https://www.aerocivil.gov.co/aeropuertos/_layouts/15/WopiFrame,aspx?sourcedoc=/aeropuertos/Consecionados/El%20Dorado%20-%20Bogot%C3%A1,pdf&action=default Aeronáutica Civil, (2019). Aeropuertos – Planes Maestro, https://www.aerocivil.gov.co/aeropuertos/planes%20maestros/forms/allitems.aspx Alhassan, R., Abdulaal, R., & Alsulami, H. (2017). A Forecasting Model for Satisfying the Demand of International Flight Passengers Having Domestic Flight Connection. Journal of King Abdulaziz University Engineering Sciences, 28(1), 49–63. https://doi.org/10.4197/eng.28-1.4 Andreoni, A., & Postorino, M. N. (2006). a Multivariate Arima Model To Forecast. Artis, M. J., Clavel, J. G., Hoffmann, M., & Nachane, D. M. (2007). Harmonic Regression Models: A Comparative Review with Applications. SSRN Electronic Journal, 333. https://doi.org/10.2139/ssrn.1017519 Bloomfield, P. (2000). Fourier Analysis of Time Series: An Introduction. In Journal of the American Statistical Association (Vol. 95, Issue 452, p. 1373). https://doi.org/10.2307/2669794 Chatfield, C. (2000). Time-Series Forecasting. In Urologiia (Moscow, Russia : 1999) (Issue 1). Chapman & Hall/CRC. http://www.ncbi.nlm.nih.gov/pubmed/16856455 Chen, C. F., Chang, Y. H., & Chang, Y. W. (2009). Seasonal ARIMA forecasting of inbound air travel arrivals to Taiwan. Transportmetrica, 5(2), 125–140. https://doi.org/10.1080/18128600802591210 Chow, G. C., & Lin, A. (1971). Best Linear Unbiased Interpolation, Distribution, and Extrapolation of Time Series by Related Series. The Review of Economics and Statistics, 53(4), 372. https://doi.org/10.2307/1928739 Coshall, J. (2006). Time series analyses of UK outbound travel by air. Journal of Travel Research, 44(3), 335–347. https://doi.org/10.1177/0047287505279003 Cowpertwait, P., & Metcalfe, A. (2009). Introductory Time Series with R. Springer. http://www.springer.com/la/book/9780387886978%0Ahttp://www.springer.com/la/book/9780387886978?wt_mc=ThirdParty.SpringerLink.3.EPR653.About_eBook Dantas, T. M., Cyrino Oliveira, F. L., & Varela Repolho, H. M. (2017). Air transportation demand forecast through Bagging Holt Winters methods. Journal of Air Transport Management, 59, 116–123. https://doi.org/10.1016/j.jairtraman.2016.12.006 Denton, F. T. (1971). Adjustment of monthly or quarterly series to annual totals: An approach based on quadratic minimization. Journal of the American Statistical Association, 66(333), 99–102. https://doi.org/10.1080/01621459.1971.10482227 Díaz Olariaga, O., Girón Amaya, E., & Mora-Camino, F. (2017, October). Pronóstico de la demanda de pasajeros en aeropuertos privatizados. In VI Congreso Internacional de la Red Iberoamericana de Investigación en Transporte Aéreo (pp. 10-12). https://www.researchgate.net/publication/320434160_PRONOSTICO_DE_LA_DEMANDA_DE_PASAJEROS_EN_AEROPUERTOS_PRIVATIZADOS Díaz Olariaga, Ó. (2016). Análisis del desarrollo reciente del transporte aéreo en Colombia. Revista Transporte y Territorio, 0(14), 122–143. https://doi.org/10.34096/rtt.i14.2432 du Preez, J., & Witt, S. F. (2003). Univariate versus multivariate time series forecasting: An application to international tourism demand. International Journal of Forecasting, 19(3), 435–451. https://doi.org/10.1016/S0169-2070(02)00057-2 Emiray, E.; Rodríguez, G. (2003). Evaluating time series models in short and long-term forecasting of Canadian air passenger data. No. 0306E, January 2003. Franses, P. H. (1990). TESTING FOR SEASONAL UNIT ROOTS IN MONTHLY DATA. Erasmus University Rotterdam. Goh, C., & Law, R. (2002). Modeling and forecasting tourism demand for arrivals with stochastic nonstationary seasonality and intervention. Tourism Management, 23(5), 499–510. https://doi.org/10.1016/S0261-5177(02)00009-2 Granger, C. W. J., & Newbold, P. (1974). Spurious Regressions in Econometrics. Journal of Econometrics, 2, 111–120. https://doi.org/10.1002/9780470996249.ch27 Greene, W. H. (1999). Análisis Econométrico (3rd ed.). Prentice Hall. Gujarati, D., & Porter, D. (2010). Econometría (Quinta edi). McGraw Hill. Hamilton, J. (1994). Time Series Analysis. Princeton University Press. Harvey, A. C. (1993). Time Series Models. In Angewandte Chemie International Edition (2nd Editio, Vol. 6, Issue 11). MIT Press. Hylleberg, S., Engle, R. F., Granger, C. W. J., & Yoo, B. S. (1990). Seasonal integration and cointegration. Journal of Econometrics, 44(1–2), 215–238. https://doi.org/10.1016/0304-4076(90)90080-D IATA. (2007). Aviation Economic Benefits. IATA Economics Briefing, N° 8. IATA. (2020). Air connectivity: Measuring the connections that drive economic growth. 57(2), Contents2–Contents2. https://doi.org/10.3143/geriatrics.57.contents2 Kim, J. H., & Moosa, I. (2001). Seasonal behaviour of monthly international tourist flows: Specification and implications for forecasting models. Tourism Economics, 7(4), 381–396. https://doi.org/10.5367/000000001101297937 Lim, C., & Mcaleer, M. (2010). A seasonal analysis of Asian tourist arrivals to Australia. Applied Economics, 32(4), 499–509. https://doi.org/10.1080/000368400322660 Lim, C., & McAleer, M. (2001). Forecasting tourist arrivals. Annals of Tourism Research, 28(4), 965–977. https://doi.org/10.1016/S0160-7383(01)00006-8 Lin, C. J., Chen, H. F., & Lee, T. S. (2011). Forecasting Tourism Demand Using Time Series, Artificial Neural Networks and Multivariate Adaptive Regression Splines:Evidence from Taiwan. International Journal of Business Administration, 2(2). https://doi.org/10.5430/ijba.v2n2p14 Lutkepohl, H., & Kratzig, M. (2013). Applied Time Series Econometrics Time. In Journal of Chemical Information and Modeling (Vol. 53, Issue 9). Cambridge University Press. Marazzo, M., Scherre, R., & Fernandes, E. (2010). Air transport demand and economic growth in Brazil: A time series analysis. Transportation Research Part E: Logistics and Transportation Review, 46(2), 261–269. https://doi.org/10.1016/j.tre.2009.08.008 Martínez-Ortíz, A., & García-Romero, H. (2016). Competitividad en el transporte aéreo en Colombia. 218. https://www.repository.fedesarrollo.org.co/bitstream/handle/11445/3280/Repor_Junio_2016_Martinez_y_Garcia.pdf?sequence=2&isAllowed=y&fbclid=IwAR2zdrF15WDXB7QHagHNepZLhhwPxF5nAE-06gXbchtCeFt6oq1I8ChgYGo%0Ahttp://www.repository.fedesarrollo.org.co/handle/11 Mogollón, J. D. (2020). Pronóstico de la demanda del transporte aéreo en aeropuerto distribuidor. Aplicación al caso de Aeropuerto Internacional el Dorado. 15, 1–137. Nieto, M. R., & Carmona-Benítez, R. B. (2018). ARIMA + GARCH + Bootstrap forecasting method applied to the airline industry. Journal of Air Transport Management, 71(June), 1–8. https://doi.org/10.1016/j.jairtraman.2018.05.007 Oh, C. O., & Morzuch, B. J. (2005). Evaluating time-series models to forecast the demand for tourism in Singapore: Comparing within-sample and postsample results. Journal of Travel Research, 43(4), 404–413. https://doi.org/10.1177/0047287505274653 Olivera, M., Cabrera, P., Bermúdez, W., & Hernandez, A. (2011). El impacto del transporte aéreo en la economía colombiana y las políticas públicas. In Cuaderno de fedesarrollo N.34. www.atac.aero/imagenesindex/cuaderno_fedesarrollo_34.pdf Ramos, I., & Cardenas, L. (2016). Prognosis de tráfico en el Aeropuerto de Bogotá-El Dorado y análisis de la relación demanda-capacidad. Sharif Azadeh, S., Labib, R., & Savard, G. (2013). Railway demand forecasting in revenue management using neural networks. International Journal of Revenue Management, 7(1), 18–36. https://doi.org/10.1504/IJRM.2013.053358 Straszheim, M. (1978). Airline demand functions in the North Atlantic and their pricing implications. Journal of Transport Economics and Policy, 12(2), 179–195. The R Development Core Team. (2008). R: A Language and Environment for Statistical Computing: Vol. Version 2. https://www.r-project.org/ Tsui, W. H. K., Ozer Balli, H., Gilbey, A., & Gow, H. (2014). Forecasting of Hong Kong airport’s passenger throughput. Tourism Management, 42(2014), 62–76. https://doi.org/10.1016/j.tourman.2013.10.008 United States Bureau Census. (2021). X-13ARIMA-SEATS Reference Manual Accessible HTML Output Version. Wei, W. (2006). Time Series Analysis: Univariate and Multivariate Methods. In Technometrics (Vol. 33, Issue 1). Pearson. https://doi.org/10.1080/00401706.1991.10484777 Williams, B. M. (2001). Multivariate Vehicular Traffic Flow Prediction: Evaluation of ARIMAX Modeling. Transportation Research Record, 01, 194–200. Yule, G. U. (1926). Why do we Sometimes get Nonsense-Correlations between Time-Series?: A Study in Sampling and the Nature of Time-Series. Journal of the Royal Statistical Society, 89(1), 1–63. |
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x, 46 páginas |
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dc.coverage.country.spa.fl_str_mv |
Colombia |
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Universidad Nacional de Colombia |
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Bogotá - Ciencias Económicas - Maestría en Ciencias Económicas |
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Escuela de Economía |
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Facultad de Ciencias Económicas |
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Bogotá, Colombia |
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Universidad Nacional de Colombia - Sede Bogotá |
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Universidad Nacional de Colombia |
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Atribución-NoComercial-SinDerivadas 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Moreno Rivas, Álvaro Martin75e8c605f438ea79d3e97f0d61ed2d5fAmezquita Bravo, Cristian Camilo38d502586f0357ae4c3076c51706333f2022-03-03T16:58:34Z2022-03-03T16:58:34Z2021https://repositorio.unal.edu.co/handle/unal/81124Universidad Nacional de ColombiaRepositorio Institucional Universidad Nacional de Colombiahttps://repositorio.unal.edu.co/ilustraciones, gráficas, tablasEl presente trabajo suministra una evaluación de la capacidad predictiva de diferentes modelos de serie de tiempo en datos mensuales del transporte aéreo de pasajeros de tráfico nacional, internacional y total entre 1994 y el 2019. Los modelos estimados son: modelo de regresión armónica, modelo de suavizado exponencial de Holt-Winters, modelo autorregresivo integrado de media móvil (ARIMA), ARIMA estacional (SARIMA) y ARIMA con variable exógena (ARIMAX). Los resultados muestran que los modelos SARIMA y SARIMAX proveen los mejores resultados en cuanto a bondad de ajuste y precisión con pronósticos en términos de MAPE y RMSE por debajo del umbral del 3% de la realización puntual media. El modelo multivariado SARIMAX supera los resultados de pronóstico de los modelos univariantes. El PIB logra potenciar los resultados del modelo y se confirma la relación positiva que posee con el sector aéreo. Se evaluaron otras variables como los precios del petróleo y choques exógenos locales e internacionales pero su efecto resultó ser no significativo. El modelo de regresión armónica solo puede predecir con alta precisión los pasajeros de tráfico internacional mientras que el modelo de Holt Winters logra obtener previsiones altamente precisas para la serie de tráfico internacional y total. (Texto tomado de la fuente).This thesis provides an evaluation of the predictive capacity of different time series models in monthly data of the air transport of passengers of national, international, and total traffic between 1994 and 2019. The estimated models are harmonic regression model, Holt-Winters exponential smoothing model, integrated moving average autoregressive model (ARIMA), seasonal ARIMA (SARIMA) and ARIMA with exogenous variable (ARIMAX). The results show that the SARIMA and SARIMAX models provide the best results in terms of goodness of fit and precision with forecasts in terms of MAPE and RMSE below the threshold of 3% of the average punctual realization. The SARIMAX multivariate model exceeds the forecast results of the univariate models. The GDP manages to enhance the results of the model and the positive relationship it has with the airline sector is confirmed. Other variables such as oil prices and local and international exogenous shocks were evaluated, but their effect was not significant. The harmonic regression model can only predict international traffic passengers with high precision while the Holt Winters model manages to obtain highly accurate forecasts for the international and total traffic series.MaestríaMagíster en Ciencias Económicasx, 46 páginasapplication/pdfspaUniversidad Nacional de ColombiaBogotá - Ciencias Económicas - Maestría en Ciencias EconómicasEscuela de EconomíaFacultad de Ciencias EconómicasBogotá, ColombiaUniversidad Nacional de Colombia - Sede Bogotá330 - EconomíaTime-series analysisAeronautics, commercialForecasting techniquesAnálisis de series de tiempoAviación comercialTécnicas de predicciónPronóstico de demandaTransporte aéreoSeries de tiempoARIMASARIMAARIMAXForecasting demandAir transportAir passengers demandARIMASARIMAARIMAXTime seriesEvaluación de modelos de series de tiempo para pronosticar la demanda de transporte aéreo a corto y mediano plazo en ColombiaEvaluation of time series models to forecast air transportation demand in the short and medium term in ColombiaTrabajo de grado - Maestríainfo:eu-repo/semantics/masterThesisinfo:eu-repo/semantics/acceptedVersionTexthttp://purl.org/redcol/resource_type/TMColombiaAeronáutica Civil, (2014a). Guía para la elaboración de Planes Maestros Aeroportuarios – PMA, Circular Reglamentaria N° 053, https://www.aerocivil.gov.co/normatividad/CIRCULARES%20AGA/CI%20053%20-%20V2.pdfAeronáutica Civil, (2014b). Actualización del plan maestro del Aeropuerto Internacional ElDorado reporte final, Tylin international, https://www.aerocivil.gov.co/aeropuertos/_layouts/15/WopiFrame,aspx?sourcedoc=/aeropuertos/Consecionados/El%20Dorado%20-%20Bogot%C3%A1,pdf&action=defaultAeronáutica Civil, (2019). Aeropuertos – Planes Maestro, https://www.aerocivil.gov.co/aeropuertos/planes%20maestros/forms/allitems.aspxAlhassan, R., Abdulaal, R., & Alsulami, H. (2017). A Forecasting Model for Satisfying the Demand of International Flight Passengers Having Domestic Flight Connection. Journal of King Abdulaziz University Engineering Sciences, 28(1), 49–63. https://doi.org/10.4197/eng.28-1.4Andreoni, A., & Postorino, M. N. (2006). a Multivariate Arima Model To Forecast.Artis, M. J., Clavel, J. G., Hoffmann, M., & Nachane, D. M. (2007). Harmonic Regression Models: A Comparative Review with Applications. SSRN Electronic Journal, 333. https://doi.org/10.2139/ssrn.1017519Bloomfield, P. (2000). Fourier Analysis of Time Series: An Introduction. In Journal of the American Statistical Association (Vol. 95, Issue 452, p. 1373). https://doi.org/10.2307/2669794Chatfield, C. (2000). Time-Series Forecasting. In Urologiia (Moscow, Russia : 1999) (Issue 1). Chapman & Hall/CRC. http://www.ncbi.nlm.nih.gov/pubmed/16856455Chen, C. F., Chang, Y. H., & Chang, Y. W. (2009). Seasonal ARIMA forecasting of inbound air travel arrivals to Taiwan. Transportmetrica, 5(2), 125–140. https://doi.org/10.1080/18128600802591210Chow, G. C., & Lin, A. (1971). Best Linear Unbiased Interpolation, Distribution, and Extrapolation of Time Series by Related Series. The Review of Economics and Statistics, 53(4), 372. https://doi.org/10.2307/1928739Coshall, J. (2006). Time series analyses of UK outbound travel by air. Journal of Travel Research, 44(3), 335–347. https://doi.org/10.1177/0047287505279003Cowpertwait, P., & Metcalfe, A. (2009). Introductory Time Series with R. Springer. http://www.springer.com/la/book/9780387886978%0Ahttp://www.springer.com/la/book/9780387886978?wt_mc=ThirdParty.SpringerLink.3.EPR653.About_eBookDantas, T. M., Cyrino Oliveira, F. L., & Varela Repolho, H. M. (2017). Air transportation demand forecast through Bagging Holt Winters methods. Journal of Air Transport Management, 59, 116–123. https://doi.org/10.1016/j.jairtraman.2016.12.006Denton, F. T. (1971). Adjustment of monthly or quarterly series to annual totals: An approach based on quadratic minimization. Journal of the American Statistical Association, 66(333), 99–102. https://doi.org/10.1080/01621459.1971.10482227Díaz Olariaga, O., Girón Amaya, E., & Mora-Camino, F. (2017, October). Pronóstico de la demanda de pasajeros en aeropuertos privatizados. In VI Congreso Internacional de la Red Iberoamericana de Investigación en Transporte Aéreo (pp. 10-12). https://www.researchgate.net/publication/320434160_PRONOSTICO_DE_LA_DEMANDA_DE_PASAJEROS_EN_AEROPUERTOS_PRIVATIZADOSDíaz Olariaga, Ó. (2016). Análisis del desarrollo reciente del transporte aéreo en Colombia. Revista Transporte y Territorio, 0(14), 122–143. https://doi.org/10.34096/rtt.i14.2432du Preez, J., & Witt, S. F. (2003). Univariate versus multivariate time series forecasting: An application to international tourism demand. International Journal of Forecasting, 19(3), 435–451. https://doi.org/10.1016/S0169-2070(02)00057-2Emiray, E.; Rodríguez, G. (2003). Evaluating time series models in short and long-term forecasting of Canadian air passenger data. No. 0306E, January 2003.Franses, P. H. (1990). TESTING FOR SEASONAL UNIT ROOTS IN MONTHLY DATA. Erasmus University Rotterdam.Goh, C., & Law, R. (2002). 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Journal of the Royal Statistical Society, 89(1), 1–63.Público generalORIGINAL1018467917.2021.pdf1018467917.2021.pdfTesis de Maestría en Ciencias Económicasapplication/pdf1391521https://repositorio.unal.edu.co/bitstream/unal/81124/3/1018467917.2021.pdf97a1d3ff7678d42fdf7b80b3d181ed51MD53LICENSElicense.txtlicense.txttext/plain; charset=utf-84074https://repositorio.unal.edu.co/bitstream/unal/81124/4/license.txt8153f7789df02f0a4c9e079953658ab2MD54THUMBNAIL1018467917.2021.pdf.jpg1018467917.2021.pdf.jpgGenerated Thumbnailimage/jpeg5134https://repositorio.unal.edu.co/bitstream/unal/81124/5/1018467917.2021.pdf.jpgdb943816ca04a69934eb2c2327a8ca99MD55unal/81124oai:repositorio.unal.edu.co:unal/811242023-08-02 23:03:47.241Repositorio Institucional Universidad Nacional de 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