Análisis comparativo de metodologías de pronóstico para múltiples series de tiempo de conteos

Ilustraciones

Autores:: Betancur Rodríguez, Daniel

Tipo de recurso:

Fecha de publicación:: 2024

Institución:: Universidad Nacional de Colombia

Repositorio:: Universidad Nacional de Colombia

Idioma:: spa

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dc.title.spa.fl_str_mv	Análisis comparativo de metodologías de pronóstico para múltiples series de tiempo de conteos
dc.title.translated.eng.fl_str_mv	Comparative analysis of forecasting methodologies for multiple time series of counts
title	Análisis comparativo de metodologías de pronóstico para múltiples series de tiempo de conteos
spellingShingle	Análisis comparativo de metodologías de pronóstico para múltiples series de tiempo de conteos 510 - Matemáticas::519 - Probabilidades y matemáticas aplicadas Análisis de series de tiempo Procesos de Poisson Redes neuronales (computadores) Aprendizaje automático (inteligencia artificial) Modelos lineales generalizados predicción datos de conteos regresión Poisson series de tiempo redes neuronales recurrentes transformers Generalized lineal models Prediction Count data Poisson regression Statespace models Time series Reuronal networks Recurrent neuronal networks Transformers
title_short	Análisis comparativo de metodologías de pronóstico para múltiples series de tiempo de conteos
title_full	Análisis comparativo de metodologías de pronóstico para múltiples series de tiempo de conteos
title_fullStr	Análisis comparativo de metodologías de pronóstico para múltiples series de tiempo de conteos
title_full_unstemmed	Análisis comparativo de metodologías de pronóstico para múltiples series de tiempo de conteos
title_sort	Análisis comparativo de metodologías de pronóstico para múltiples series de tiempo de conteos
dc.creator.fl_str_mv	Betancur Rodríguez, Daniel
dc.contributor.advisor.none.fl_str_mv	Cabarcas Jaramillo, Daniel Gonzáles Alvarez, Nelfi Gertrudis
dc.contributor.author.none.fl_str_mv	Betancur Rodríguez, Daniel
dc.subject.ddc.spa.fl_str_mv	510 - Matemáticas::519 - Probabilidades y matemáticas aplicadas
topic	510 - Matemáticas::519 - Probabilidades y matemáticas aplicadas Análisis de series de tiempo Procesos de Poisson Redes neuronales (computadores) Aprendizaje automático (inteligencia artificial) Modelos lineales generalizados predicción datos de conteos regresión Poisson series de tiempo redes neuronales recurrentes transformers Generalized lineal models Prediction Count data Poisson regression Statespace models Time series Reuronal networks Recurrent neuronal networks Transformers
dc.subject.lemb.none.fl_str_mv	Análisis de series de tiempo Procesos de Poisson Redes neuronales (computadores) Aprendizaje automático (inteligencia artificial)
dc.subject.proposal.spa.fl_str_mv	Modelos lineales generalizados predicción datos de conteos regresión Poisson series de tiempo redes neuronales recurrentes transformers
dc.subject.proposal.ita.fl_str_mv	Generalized lineal models
dc.subject.proposal.eng.fl_str_mv	Prediction Count data Poisson regression Statespace models Time series Reuronal networks Recurrent neuronal networks Transformers
description	Ilustraciones
publishDate	2024
dc.date.accessioned.none.fl_str_mv	2024-04-16T15:44:15Z
dc.date.available.none.fl_str_mv	2024-04-16T15:44:15Z
dc.date.issued.none.fl_str_mv	2024-04-16
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
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status_str	acceptedVersion
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dc.identifier.instname.spa.fl_str_mv	Universidad Nacional de Colombia
dc.identifier.reponame.spa.fl_str_mv	Repositorio Institucional Universidad Nacional de Colombia
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url	https://repositorio.unal.edu.co/handle/unal/85925 https://repositorio.unal.edu.co/
identifier_str_mv	Universidad Nacional de Colombia Repositorio Institucional Universidad Nacional de Colombia
dc.language.iso.spa.fl_str_mv	spa
language	spa
dc.relation.indexed.spa.fl_str_mv	LaReferencia
dc.relation.references.spa.fl_str_mv	Aghababaei Jazi, M., & Alamatsaz, M. (2012). Two new thinning operators and their appli cations. Global Journal of Pure and Applied Mathematics, 8, 13-28 Allende, H., Moraga, C., & Salas, R. (2002). Artificial neural networks in time series fore casting: a comparative analysis. Kybernetika, 38(6), 685-707 Ba, J. L., Kiros, J. R., & Hinton, G. E. (2016). Layer Normalization Bahdanau, D., Cho, K., & Bengio, Y. (2016a). Neural Machine Translation by Jointly Lear ning to Align and Translate Bahdanau, D., Cho, K., & Bengio, Y. (2016b). Neural Machine Translation by Jointly Lear ning to Align and Translate Bandara, K., Shi, P., Bergmeir, C., Hewamalage, H., Tran, Q., & Seaman, B. (2019). Sales Demand Forecast in E-commerce Using a Long Short-Term Memory Neural Network Methodology. En T. Gedeon, K. W. Wong & M. Lee (Eds.), Neural Information Processing (pp. 462-474). Springer International Publishing Byrd, R. H., Schnabel, R. B., & Shultz, G. A. (1987). A Trust Region Algorithm for Non linearly Constrained Optimization. SIAM Journal on Numerical Analysis, 24(5), 1152-1170. Consultado el 7 de mayo de 2023, desde http://www.jstor.org/stable/ 2157645 Chollet, F. (2017). Deep Learning with Python (1st). Manning Publications Co Christou, V., & Fokianos, K. (2015). On count time series prediction. Journal of Statistical Computation and Simulation, 85(2), 357-373. https://doi.org/10.1080/00949655. 2013.823612 Davis, R. A., Fokianos, K., Holan, S. H., Joe, H., Livsey, J., Lund, R., Pipiras, V., & Ravishanker, N. (2021). Count Time Series: A methodological Review. Journal of the American Statistical Association, 116, 1533-1547. https://doi.org/10.1080/01621459. 2021.1904957 Dufour, J.-M. (2008). Estimation of ARMA models by maximum likelihood. https:// jeanmariedufour.github.io/ResE/Dufour 2008 C TS ARIMA Estimation.pdf Dunsmuir, W. T. (2016). Generalized Linear Autoregressive Moving Average Models. En R. A. Davis, S. H. Holan, R. Lund & N. Ravishanker (Eds.). CRC Press Excoffier, M., Gicquel, C., & Jouini, O. (2016). A joint chance-constrained programming approach for call center workforce scheduling under uncertain call arrival forecasts. Computers & Industrial Engineering, 96, 16-30. https://doi.org/https://doi.org/10. 1016/j.cie.2016.03.013 Farsani, R., Pazouki, E., & Jecei, J. (2021). A Transformer Self-Attention Model for Time Series Forecasting. Journal of Electrical and Computer Engineering Innovations, 9, 1-10. https://doi.org/10.22061/JECEI.2020.7426.391 Fearnhead, P. (2011). MCMC for State Space Models. En S. Brooks, A. Gelman, G. Jones & X.-L. Meng (Eds.). Chapman; HALL/CRC Feng, C., Li, L., & Sadeghpour, A. (2020). A comparison of residual diagnosis tools for diagnosing regression models for count data. BMC Medical Research Methodology, 20, 1-21. https://doi.org/10.1186/s12874-020-01055-2 Ferland, R., Latour, A., & Oraichi, D. (2006). Integer-Valued GARCH Process. Journal of Time Series Analysis, 27(6), 923-942. https://doi.org/https://doi.org/10.1111/j. 1467-9892.2006.00496.x Fokianos, K. (2012). Count Time Series Models. Handbook of Statistics, 30, 315-347. https: //doi.org/10.1016/B978-0-444-53858-1.00012-0 Fokianos, K., Rahbek, A., & Tjøstheim, D. (2009). Poisson Autoregression. Journal of the American Statistical Association, 104(488), 1430-1439. Consultado el 15 de marzo de 2023, desde http://www.jstor.org/stable/40592351 Fokianos, K., & Tjøstheim, D. (2011). Log-linear Poisson autoregression. Journal of Multi variate Analysis, 102(3), 563-578. https://doi.org/https://doi.org/10.1016/j.jmva. 2010.11.002 Gamerman, D., Abanto-Valle, C., Silva, R., & Martins, T. (2016). Dynamic Bayesian Mo dels for Discrete-Valued Time Series. En R. A. Davis, S. H. Holan, R. Lund & N. Ravishanker (Eds.). CRC Pess Goodfellow, I., Bengio, Y., & Courville, A. (2016). Deep Learning [http://www.deeplearningbook. org]. MIT Press He, K., Zhang, X., Ren, S., & Sun, J. (2016). Deep Residual Learning for Image Recogni tion. 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 770-778. https://doi.org/10.1109/CVPR.2016.90 Hewamalage, H., Bergmeir, C., & Bandara, K. (2022). Global models for time series forecas ting: A Simulation study. Pattern Recognition, 124, 108441. https://doi.org/https: //doi.org/10.1016/j.patcog.2021.108441 Hoppe, R. W. (2006). Chapter 4 Sequential Quadratic Programming. https://www.math. uh.edu/∼rohop/fall 06/Chapter4.pdf Hyndman, R. J. Focused Workshop: Synthetic Data — Generating time series. En: 2021. https://www.youtube.com/watch?v=F3lWECtFa44&ab channel=AustralianDataScienceNetwok Hyndman, R. J., & Athanasopoulos, G. (2021). Forecasting: Principles and Practice (3rd). OTexts. Hyndman, R. J., Kang, Y., Montero-Manso, P., O’Hara-Wild, M., Talagala, T., Wang, E., & Yang, Y. (2023). tsfeatures: Time Series Feature Extraction [https://pkg.robjhyndman.com/tsfeatures/, https://github.com/robjhyndman/tsfeatures] Hyndman, R. J., & Koehler, A. B. (2006). Another look at measures of forecast accuracy. International Journal of Forecasting, 22(4), 679-688. https://doi.org/https://doi. org/10.1016/j.ijforecast.2006.03.001 Jia, Y. (2018). Some Models for Count TimeSeries (Tesis doctoral). Clemson University. 105 Sikes Hall, Clemson, SC 29634, Estados Unidos. https://tigerprints.clemson. edu/all dissertations/2213 Kang, Y., Hyndman, R. J., & Li, F. (2020). GRATIS: GeneRAting TIme Series with diverse and controllable characteristics. Statistical Analysis and Data Mining: The ASA Data Science Journal, 13(4), 354-376. https://doi.org/10.1002/sam.11461 Liboschik, T., Fokianos, K., & Fried, R. (2017). tscount: An R Package for Analysis of Count Time Series Following Generalized Linear Models. Journal of Statistical Software, 82(5), 1-51. https://doi.org/10.18637/jss.v082.i05 Lund, R., & Livsey, J. (2016). Renewal-Based Count Time Series. En R. A. Davis, S. H. Holan, R. Lund & N. Ravishanker (Eds.). CRC Press Makridakis, S. (1993). Accuracy measures: theoretical and practical concerns. International Journal of Forecasting, 9(4), 527-529. https://doi.org/https://doi.org/10.1016/0169 2070(93)90079-3 Makridakis, S., Spiliotis, E., & Assimakopoulos, V. (2018). Statistical and Machine Learning forecasting methods: Concerns and ways forward. Plos One. https://doi.org/10.1371/ journal.pone.0194889 Makridakis, S., Spiliotis, E., & Assimakopoulos, V. (2020). The M4 Competition: 100,000 time series and 61 forecasting methods [M4 Competition]. International Journal of Forecasting, 36(1), 54-74. https://doi.org/https://doi.org/10.1016/j.ijforecast.2019. 04.014 Mart´ ın Abadi, Ashish Agarwal, Paul Barham, Eugene Brevdo, Zhifeng Chen, Craig Citro, Greg S. Corrado, Andy Davis, Jeffrey Dean, Matthieu Devin, Sanjay Ghemawat, Ian Goodfellow, Andrew Harp, Geoffrey Irving, Michael Isard, Jia, Y., Rafal Jozefo wicz, Lukasz Kaiser, Manjunath Kudlur, ... Xiaoqiang Zheng. (2015). TensorFlow: Large-Scale Machine Learning on Heterogeneous Systems [Software available from tensorflow.org]. https://www.tensorflow.org/ McCulloch, W. S., & Pitts, W. (1943). A logical calculus of the ideas immanent in ner vous activity. The bulletin of mathematical biophysics, 5. https://doi.org/10.1007/ BF02478259 Mikolov, T., Chen, K., Corrado, G., & Dean, J. (2013). Efficient Estimation of Word Repre sentations in Vector Space Montero-Manso, P., & Hyndman, R. J. (2021). Principles and algorithms for forecasting groups of time series: Locality and globality. International Journal of Forecasting, 37(4), 1632-1653. https://doi.org/https://doi.org/10.1016/j.ijforecast.2021.03.004 Nariswari, R., & Pudjihastuti, H. (2019). Bayesian Forecasting for Time Series of Count Data [The 4th International Conference on Computer Science and Computational Intelligence (ICCSCI 2019) : Enabling Collaboration to Escalate Impact of Research Results for Society]. Procedia Computer Science, 157, 427-435. https://doi.org/https: //doi.org/10.1016/j.procs.2019.08.235 Nelder, J. A., & Wedderburn, R. W. M. (1972). Generalized Linear Models. Journal of the Royal Statistical Society. Series A (General), 135(3), 370-384. Consultado el 13 de enero de 2024, desde http://www.jstor.org/stable/2344614 Ng, A. Y., Katanforoosh, K., & Mourri, Y. B. (2023). Neural Networks and Deep Learning [MOOC]. Coursera. https://www.coursera.org/learn/neural-networks-deep-learning Nie, Y., Nguyen, N. H., Sinthong, P., & Kalagnanam, J. (2023). A Time Series is Worth 64 Words: Long-term Forecasting with Transformers Nielsen, M. A. (2015). Neural Networks and Deep Learning. Determination Press. of Transportation, N. D. (2017). Bicycle Counts for East River Bridges (Historical) [Daily total of bike counts conducted monthly on the Brooklyn Bridge, Manhattan Brid ge, Williamsburg Bridge, and Queensboro Bridge. https://data.cityofnewyork.us/ Transportation/Bicycle-Counts-for-East-River-Bridges-Historical-/gua4-p9wg] Parr, T., & Howard, J. (2018). The Matrix Calculus You Need For Deep Learning Pedregosa, F., Varoquaux, G., Gramfort, A., Michel, V., Thirion, B., Grisel, O., Blondel, M., Prettenhofer, P., Weiss, R., Dubourg, V., Vanderplas, J., Passos, A., Cournapeau, D., Brucher, M., Perrot, M., & Duchesnay, E. (2011). Scikit-learn: Machine Learning in Python. Journal of Machine Learning Research, 12, 2825-2830 Phuong, M., & Hutter, M. (2022). Formal Algorithms for Transformers R Core Team. (2023). R: A Language and Environment for Statistical Computing. R Foun dation for Statistical Computing. Vienna, Austria. https://www.R-project.org/ Ruder, S. (2016). An overview of gradient descent optimization algorithms. CoRR, abs/1609.04747. http://arxiv.org/abs/1609.04747 Rue, H., Martino, S., & Chopin, N. (2009). Approximate Bayesian Inference for Latent Gaussian models by using Integrated Nested Laplace Approximations. Journal of the Royal Statistical Society Series B: Statistical Methodology, 71(2), 319-392. https: //doi.org/10.1111/j.1467-9868.2008.00700.x Sathish, V., Mukhopadhyay, S., & Tiwari, R. (2020). ARMA Models for Zero Inflated Count Time Series. https://doi.org/10.48550/ARXIV.2004.10732 Schmidhuber, J. (2015). Deep learning in neural networks: An overview. Neural Networks, 61, 85-117. https://doi.org/10.1016/j.neunet.2014.09.003 Seabold, S., & Perktold, J. (2010). statsmodels: Econometric and statistical modeling with python. 9th Python in Science Conference Shenstone, L., & Hyndman, R. J. (2005). Stochastic models underlying Croston’s method for intermittent demand forecasting. Journal of Forecasting, 24(6), 389-402. https: //doi.org/https://doi.org/10.1002/for.963 Shmueli, G., Bruce, P. C., Yahav, I., Patel, N. R., & Lichtendahl Jr., K. C. (2018). Data mining for business analytics. Wiley Shmueli, G., & Lichtebdahl, K. C. (2018). Practical time series forecasting with R. Axelrod Schnall Publishers Shrivastava, S. (2020). Cross Validation in Time Series. https://medium.com/@soumyachess1496/ cross-validation-in-time-series-566ae4981ce4 Smith, T. G. (2017). pmdarima: ARIMA estimators for Python Srivastava, N., Hinton, G., Krizhevsky, A., Sutskever, I., & Salakhutdinov, R. (2014). Dro pout: A Simple WaytoPrevent Neural Networks from Overfitting. Journal of Machine Learning Research, 15(56), 1929-1958. http://jmlr.org/papers/v15/srivastava14a. html Terven, J., Cordova-Esparza, D. M., Ramirez-Pedraza, A., & Chavez-Urbiola, E. A. (2023). Loss Functions and Metrics in Deep Learning Vaswani, A., Shazeer, N., Parmar, N., Uszkoreit, J., Jones, L., Gomez, A. N., Kaiser, L., & Polosukhin, I. (2017). Attention is all you need. Advances in neural information processing systems, 5998-6008. http://arxiv.org/abs/1706.03762 Virtanen, P., Gommers, R., Oliphant, T. E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., van der Walt, S. J., Brett, M., Wilson, J., Millman, K. J., Mayorov, N., Nelson, A. R. J., Jones, E., Kern, R., Larson, E., ... SciPy 1.0 Contributors. (2020). SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods, 17, 261-272. https://doi.org/ 10.1038/s41592-019-0686-2 Wen, Q., Zhou, T., Zhang, C., Chen, W., Ma, Z., Yan, J., & Sun, L. (2023). Transformers in Time Series: A Survey Zeng, A., Chen, M.-H., Zhang, L., & Xu, Q. (2022). Are Transformers Effective for Ti me Series Forecasting? AAAI Conference on Artificial Intelligence. https://api. semanticscholar.org/CorpusID:249097444 Zhang, A., Lipton, Z. C., Li, M., & Smola, A. J. (2021). Dive into Deep Learning. arXiv preprint arXiv:2106.11342
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dc.format.extent.spa.fl_str_mv	1 recursos en línea (167 páginas)
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dc.publisher.spa.fl_str_mv	Universidad Nacional de Colombia
dc.publisher.program.spa.fl_str_mv	Medellín - Ciencias - Maestría en Ciencias - Estadística
dc.publisher.faculty.spa.fl_str_mv	Facultad de Ciencias
dc.publisher.place.spa.fl_str_mv	Medellín, Colombia
dc.publisher.branch.spa.fl_str_mv	Universidad Nacional de Colombia - Sede Medellín
institution	Universidad Nacional de Colombia
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spelling	Atribución-NoComercial 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Cabarcas Jaramillo, Daniel9523b5dcc283edd60a465e234d239f3cGonzáles Alvarez, Nelfi Gertrudis3957256ebf7d9d41633c63e4d946876fBetancur Rodríguez, Danielb6bcfbc58553fd8a6ebf508e9eac3b5b2024-04-16T15:44:15Z2024-04-16T15:44:15Z2024-04-16https://repositorio.unal.edu.co/handle/unal/85925Universidad Nacional de ColombiaRepositorio Institucional Universidad Nacional de Colombiahttps://repositorio.unal.edu.co/IlustracionesEl pronóstico de series de tiempo de conteos es un caso particular de interés para la asignación óptima de capacidades e inventarios acorde a la demanda esperada, entre otras aplicaciones. Para abordar el pronóstico de las series de tiempo de conteos se han propuesto modelos estadísticos como los modelos autorregresivos para series de conteo o los modelos dinámicos generalizados. Por otro lado, se han aplicado metodologías basadas en algoritmos de machine learning apalancándose en la creciente potencia computacional, como las redes neuronales recurrentes y las arquitecturas basadas en algoritmos de atención, llamadas Transformers. El presente trabajo explora el problema del pronóstico paralelo de múltiples series de conteo, aplicando metodologías propias de la estadística y el machine learning en diversos escenarios de simulación en los cuales se compara la calidad de pronóstico, el tiempo computacional demandado y el esfuerzo para adaptar las metodologías a casos reales (texto tomado de la fuente)Forecasting time series of counts, with support on non-negative integers, is a particular case of interest for optimal job assigment and inventory allocation according to expected demand, among other applications. To address the problem of forecasting time series of counts, statiscal models such as autorregresive models for count data or dynamic generalized models have been proposed. On the other side, methodologies based on machine learning algorithms have been applied, leveraging on the increasing computational power, such as recurrent neuronal netwroks, LSTM networks architecures and architectures based in attention algorithms called Transformers. This study explores the problem of parallel forecasting multiple time series of counts, applying statistical and machine learning methodologies to various simulation scenarios in which the forecasting performance, demanded computational time, and the effort to adapt each methodology to real cases are comparedMaestríaMagíster en EstadísticaAnalíticaProcesos estocásticosÁrea Curricular Estadística1 recursos en línea (167 páginas)application/pdfspaUniversidad Nacional de ColombiaMedellín - Ciencias - Maestría en Ciencias - EstadísticaFacultad de CienciasMedellín, ColombiaUniversidad Nacional de Colombia - Sede Medellín510 - Matemáticas::519 - Probabilidades y matemáticas aplicadasAnálisis de series de tiempoProcesos de PoissonRedes neuronales (computadores)Aprendizaje automático (inteligencia artificial)Modelos lineales generalizadosprediccióndatos de conteosregresión Poissonseries de tiemporedes neuronales recurrentestransformersGeneralized lineal modelsPredictionCount dataPoisson regressionStatespace modelsTime seriesReuronal networksRecurrent neuronal networksTransformersAnálisis comparativo de metodologías de pronóstico para múltiples series de tiempo de conteosComparative analysis of forecasting methodologies for multiple time series of countsTrabajo de grado - Maestríainfo:eu-repo/semantics/masterThesisinfo:eu-repo/semantics/acceptedVersionTexthttp://purl.org/redcol/resource_type/TMLaReferenciaAghababaei Jazi, M., & Alamatsaz, M. (2012). Two new thinning operators and their appli cations. Global Journal of Pure and Applied Mathematics, 8, 13-28Allende, H., Moraga, C., & Salas, R. (2002). Artificial neural networks in time series fore casting: a comparative analysis. Kybernetika, 38(6), 685-707Ba, J. L., Kiros, J. R., & Hinton, G. E. (2016). Layer NormalizationBahdanau, D., Cho, K., & Bengio, Y. (2016a). Neural Machine Translation by Jointly Lear ning to Align and TranslateBahdanau, D., Cho, K., & Bengio, Y. (2016b). Neural Machine Translation by Jointly Lear ning to Align and TranslateBandara, K., Shi, P., Bergmeir, C., Hewamalage, H., Tran, Q., & Seaman, B. (2019). Sales Demand Forecast in E-commerce Using a Long Short-Term Memory Neural Network Methodology. En T. Gedeon, K. W. Wong & M. Lee (Eds.), Neural Information Processing (pp. 462-474). Springer International PublishingByrd, R. H., Schnabel, R. B., & Shultz, G. A. (1987). A Trust Region Algorithm for Non linearly Constrained Optimization. SIAM Journal on Numerical Analysis, 24(5), 1152-1170. Consultado el 7 de mayo de 2023, desde http://www.jstor.org/stable/ 2157645Chollet, F. (2017). Deep Learning with Python (1st). Manning Publications CoChristou, V., & Fokianos, K. (2015). On count time series prediction. Journal of Statistical Computation and Simulation, 85(2), 357-373. https://doi.org/10.1080/00949655. 2013.823612Davis, R. A., Fokianos, K., Holan, S. H., Joe, H., Livsey, J., Lund, R., Pipiras, V., & Ravishanker, N. (2021). Count Time Series: A methodological Review. Journal of the American Statistical Association, 116, 1533-1547. https://doi.org/10.1080/01621459. 2021.1904957Dufour, J.-M. (2008). Estimation of ARMA models by maximum likelihood. https:// jeanmariedufour.github.io/ResE/Dufour 2008 C TS ARIMA Estimation.pdfDunsmuir, W. T. (2016). Generalized Linear Autoregressive Moving Average Models. En R. A. Davis, S. H. Holan, R. Lund & N. Ravishanker (Eds.). CRC PressExcoffier, M., Gicquel, C., & Jouini, O. 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Dive into Deep Learning. arXiv preprint arXiv:2106.11342AdministradoresEstudiantesInvestigadoresMaestrosLICENSElicense.txtlicense.txttext/plain; charset=utf-85879https://repositorio.unal.edu.co/bitstream/unal/85925/1/license.txteb34b1cf90b7e1103fc9dfd26be24b4aMD51ORIGINAL1152456210.2024.pdf1152456210.2024.pdfTesis Maestría en Ciencias - Estadísticaapplication/pdf3388421https://repositorio.unal.edu.co/bitstream/unal/85925/3/1152456210.2024.pdf4c0201ec036c147f883503770c2e8d78MD53THUMBNAIL1152456210.2024.pdf.jpg1152456210.2024.pdf.jpgGenerated Thumbnailimage/jpeg4343https://repositorio.unal.edu.co/bitstream/unal/85925/4/1152456210.2024.pdf.jpga19e8cf205a6c1f8e28a665691dfb85eMD54unal/85925oai:repositorio.unal.edu.co:unal/859252024-08-23 23:12:18.156Repositorio Institucional Universidad Nacional de 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