Combining Interval Time Series Forecasts. A First Step in a Long Way (Research Agenda)

• Autores: Carlos G. Maté
• Localización: Revista Colombiana de Estadística, ISSN-e 2389-8976, ISSN 0120-1751, Vol. 44, Nº. 1, 2021, págs. 123-157
• Idioma: inglés
• DOI: 10.15446/rce.v44n1.85116
• Títulos paralelos:
  • La combinación de predicciones de series temporales de intervalo (STI)
• Enlaces
  • Texto completo
• Resumen
  • español

    Resumen Cada día observamos un mundo más complejo, incierto y con mayor riesgo que el mundo de ayer. Luego, tener pronósticos precisos en economía, finanzas, energía, salud, turismo, etc.; es más crítico que nunca. Además, existe un requisito creciente de proporcionar otro tipo de pronósticos más allá de los puntuales, como los pronósticos de intervalos. Después de más de 50 años de investigación, hay dos consensos, "combinar pronósticos reduce el error de pronóstico final" y "un promedio simple de varios pronósticos a menudo supera complicados esquemas de ponderación", que se denominó "rompecabezas de combinación de pronósticos (FCP)". La introducción de los conceptos de series de tiempo de intervalo (ITS) y varios métodos de pronóstico se han propuesto y dan respuestas a algunos desafíos de los grandes datos. Entonces, un problema es cómo combinar varios pronósticos obtenidos para una ITS. Este documento propone algunos esquemas combinados con un par o varios pronósticos ITS. Algunos extienden esquemas previos para datos puntuales, incorporando como novedad la U de Theil. El FCP en el marco de pronósticos ITS se analizará con diferentes medidas de exactitud y se proporcionarán algunas pautas. Se describirá una agenda para futuras investigaciones en la combinación de pronósticos obtenidos para ITS.

  • English

    Abstract We observe every day a world more complex, uncertain, and riskier than the world of yesterday. Consequently, having accurate forecasts in economics, finance, energy, health, tourism, and so on; is more critical than ever. Moreover, there is an increasing requirement to provide other types of forecasts beyond point ones such as interval forecasts. After more than 50 years of research, there are two consensuses, "combining forecasts reduces the final forecasting error" and "a simple average of several forecasts often outperforms complicated weighting schemes", which was named "forecast combination puzzle (FCP)". The introduction of interval-valued time series (ITS) concepts and several forecasting methods has been proposed in different papers and gives answers to some big data challenges. Hence, one main issue is how to combine several forecasts obtained for one ITS. This paper proposes some combination schemes with a couple or various ITS forecasts. Some of them extend previous crisp combination schemes incorporating as a novelty the use of Theil's U. The FCP under the ITS forecasts framework will be analyzed in the context of different accuracy measures and some guidelines will be provided. An agenda for future research in the field of combining forecasts obtained for ITS will be outlined.

• Referencias bibliográficas
  • Adhikari, R.,Agrawal, R. (2014). 'A combination of artificial neural network and random walk models for financial time series forecasting'....
  • Aladag, C. H.,Egrioglu, E.,Yolcu, U. (2010). 'Forecast combination by using artificial neural networks'. Neural Processing Letters....
  • Armstrong, J. S. (2001). Combined forecasts. In Principies of Forecasting: A Handbook for Researchers and Practitioners. Kluwer Academic Publishers....
  • Arroyo, J.,Espínola, R.,Maté, C. (2011). 'Different approaches to forecast interval time series: a comparison in finance'. Computational...
  • Arroyo, J.,Espínola, R.,Maté, C. (2011). 'Different approaches to forecast interval time series: a comparison in finance'. Computational...
  • Arroyo, J.,González-Rivera, G.,Maté, C. (2010). 'Forecasting with interval and histogram data. some financial applications'. Handbook...
  • Arroyo, J.,Maté, C. (2006). Introducing interval time series: accuracy measures, in 'Compstat, proceedings in computational statistics'....
  • Arroyo, J.,Maté, C. (2009). 'Forecasting histogram time series with k-nearest neighbours methods'. International Journal of Forecasting....
  • Atiya, A. F. (2020). 'Why does forecast combination work so well?'. International Journal of Forecasting. 36. 197-200
  • Avci, E.,Ketter, W.,van Heck, E. (2018). 'Managing electricity price modeling risk via ensemble forecasting: The case of turkey'....
  • Bassetti, F.,Casarin, R.,Ravazzolo, F. (2020). 'Macroeconomic Forecasting in the Era of Big Data'. Springer.
  • Bates, J. M.,Granger, C. W. (1969). 'The combination of forecasts'. Journal of the Operational Research Society. 20. 451
  • Billard, L.,Diday, E. (2003). 'From the statistics of data to the statistics of knowledge: Symbolic data analysis'. Journal of the...
  • Billard, L.,Diday, E. (2006). Symbolic Data Analysis: Conceptual Statistics and Data Mining John Wiley. Chichester.
  • Blanco-Fernández, A.,Corral, N.,González-Rodríguez, G. (2011). 'Estimation of a flexible simple linear model for interval data based on...
  • Buansing, T. T.,Golan, A.,Ullah, A. (2020). 'An information-theoretic approach for forecasting interval-valued sp500 daily returns'....
  • Chen, Y.,Chen, H.,Gorkhali, A.,Lu, Y.,Ma, Y.,Li, L. (2016). 'Big data analytics and big data science: a survey'. Journal of Management...
  • Clemen, R. T. (1989). 'Combining forecasts: A review and annotated bibliography'. International Journal of Forecasting. 5. 559
  • de Menezes, L.,Bunn, D.,Taylor, J. (2000). 'Review of guidelines for the use of combined forecasts'. European Journal of Operational...
  • den Butter, F. A.,Jansen, P. W. (2013). 'Beating the random walk: a performance assessment of long-term interest rate forecasts'....
  • Dickinson, J. (1975). 'Some comments on the combination of forecasts'. Journal of the Operational Research Society. 26. 205
  • Diebold, F. X.,Mariano, R. S. (1995). 'Comparing predictive accuracy'. Journal of Business & Economic Statistics. 13. 253
  • Fama, E. F. (1995). 'Random walks in stock market prices'. Financial Analysts Journal. 51. 75-80
  • Fama, E. F.,Blume, M. E. (1966). 'Filter rules and stock-market trading'. The Journal of Business. 39. 226
  • Galicia, A.,Talavera-Llames, R.,Troncoso, A.,Koprinska, I.,Martínez-Álvarez, F. (2019). 'Multi-step forecasting for big data time series...
  • Gao, Y.,Shang, H. L.,Yang, Y. (2019). 'High-dimensional functional time series forecasting: An application to age-specific mortality rates'....
  • García-Ascanio, C.,Maté, C. (2010). 'Electric power demand forecasting using interval time series: A comparison between var and imlp'....
  • Genre, V.,Kenny, G.,Meyler, A.,Timmermann, A. (2013). 'Combining expert forecasts: Can anything beat the simple average?'. International...
  • Gibbs, C. G. (2017). 'Forecast combination, non-linear dynamics, and the macroeconomy. Economic Theory. 63. 653
  • Glennon, D.,Kiefer, H.,Mayock, T. (2018). 'Measurement error in residential property valuation: An application of forecast combination'....
  • Gneiting, T. (2011). 'Making and evaluating point forecasts'. Journal of the American Statistical Association. 106. 746
  • Gneiting, T.,Katzfuss, M. (2014). 'Probabilistic forecasting'. Annual Review of Statistics and Its Application. 1. 125
  • Hallman, J.,Kamstra, M. (1989). 'Combining algorithms based on robust estimation techniques and co-integrating restrictions'. Journal...
  • Han, A.,Hong, Y.,Lai, K.,Wang, S. (2008). 'Interval time series analysis with an application to the sterling-dollar exchange rate'....
  • Han, A.,Lai, K. K.,Wang, S.,Xu, S. (2012). 'An interval method for studying the relationship between the australian dollar exchange rate...
  • Hendry, D. F.,Clements, M. P. (2004). 'Pooling of forecasts'. The Econometrics Journal. 7. 1-31
  • Hsu, H.-L.,Wu, B. (2008). 'Evaluating forecasting performance for interval data'. Computers & Mathematics with Applications. 56....
  • Hyndman, R. J.,Koehler, A. B. (2006). 'Another look at measures of forecast accuracy'. International Journal of Forecasting. 22. 679
  • Hyndman, R. J.,Shang, H. L. (2009). 'Forecasting functional time series'. Journal of the Korean Statistical Society. 38. 199
  • Irpino, A.,Verde, R. (2008). 'Dynamic clustering of interval data using a wasserstein-based distance'. Pattern Recognition Letters....
  • Kao, C.-H.,Nakano, J.,Shieh, S.-H.,Tien, Y.-J.,Wu, H.-M.,Yang, C.-K.,Chen, C.-h. (2014). 'Exploratory data analysis of interval-valued...
  • Kourentzes, N.,Barrow, D.,Petropoulos, F. (2019). 'Another look at forecast selection and combination: Evidence from forecast pooling'....
  • Kubica, B. J.,Malinowski, K. (2006). 'SMPS'. Springer.
  • Kwiatkowski, D.,Phillips, P.,Schmidt, P.,Shin, Y. (1992). 'Testing the null hypothesis of stationarity against the alternative of a unit...
  • Le-Rademacher, J.,Billard, L. (2012). 'Symbolic covariance principal component analysis and visualization for interval-valued data'....
  • Li, H.,Wang, J.,Lu, H.,Guo, Z. (2018). 'Research and application of a combined model based on variable weight for short term wind speed...
  • Lima Neto, E.,De Carvalho, F. (2010). 'Constrained linear regression models for symbolic interval-valued variables'. Computational...
  • Maia, A. L. S.,de Carvalho, F. d. A. (2011). 'Holts exponential smoothing and neural network models for forecasting interval-valued time...
  • Maia, A. L. S.,de Carvalho, F. d. A.,Ludermir, T. B. (2008). 'Forecasting models for interval-valued time series'. Neurocomputing....
  • Makridakis, S.,Spiliotis, E.,Assimakopoulos, V. (2020). 'The m4 competition: 100,000 time series and 61 forecasting methods'. International...
  • Maté, C. (2012). 'The bayesian model averaging approach for interval-valued data. 3 rd workshop in symbolic data analysis. 47
  • Maté, C. G. (2011). 'A multivariate analysis approach to forecasts combination. application to foreign exchange (fx) markets'. Revista...
  • Moral-Benito, E. (2015). 'Model averaging in economics: An overview'. Journal of Economic Surveys. 29. 46-75
  • Muñoz, A.,Maté, C.,Arroyo, J.,Sarabia, A. (2007). 'iMLP: applying multilayer perceptrons to interval-valued data'. Neural Processing...
  • Naseer, M.,bin Tariq, Y.. (2015). 'The efficient market hypothesis: A critical review of the literature'. IUP Journal of Financial...
  • Nelson, C. R.,Plosser, C. R. (1982). 'Trends and random walks in macroeconomic time series: some evidence and implications'. Journal...
  • Noirhomme-Fraiture, M.,Brito, P. (2011). 'Far beyond the classical data models: symbolic data analysis'. Statistical Analysis and...
  • Ordiano, J. Á. G.,Bartschat, A.,Ludwig, N.,Braun, E.,Waczowicz, S.,Renkamp, N.,Peter, N.,Düpmeier, C.,Mikut, R.,Hagenmeyer, V. (2018). 'Concept...
  • Phillips, P. C.,Perron, P. (1988). 'Testing for a unit root in time series regression'. Biometrika. 75. 335
  • Ramos-Guajardo, A. B.,González-Rodríguez, G.,Colubi, A. (2020). 'Testing the degree of overlap for the expected value of random intervals'....
  • Rapach, D.,Zhou, G. (2013). 'Handbook of economic forecasting'. Elsevier.
  • Riddington, G. (1993). 'Time varying coefficient models and their forecasting performance'. Omega. 21. 573
  • Rodrigues, P. M.,Salish, N. (2015). 'Modeling and forecasting interval time series with threshold models'. Advances in Data Analysis...
  • Sarno, L.,Valente, G. (2005). 'Empirical exchange rate models and currency risk: Some evidence from density forecasts'. Journal of...
  • Shaub, D. (2020). 'Fast and accurate yearly time series forecasting with forecast combinations'. International Journal of Forecasting....
  • Sinova, B.,Casals, M. R.,Colubi, A.,Gil, M. Á. (2010). The median of a random interval, in 'Combining Soft Computing and Statistical Methods...
  • Sinova, B.,Colubi, A.,González-Rodri, G.. (2012). 'Interval arithmetic-based simple linear regression between interval data: Discussion...
  • Sinova, B.,Van Aelst, S. (2015). 'On the consistency of a spatial-type interval-valued median for random intervals. Statistics & Probability...
  • Smith, J.,Wallis, K. F. (2009). 'A simple explanation of the forecast combination puzzle'. Oxford Bulletin of Economics and Statistics....
  • Song, H.,Liu, H. (2017). 'Analytics in smart tourism design'. Springer.
  • Stock, J. H.,Watson, M. W. (2004). 'Combination forecasts of output growth in a seven-country data set'. Journal of Forecasting. 23....
  • Stock, J. H.,Watson, M. W. (2006). 'Forecasting with many predictors'. Handbook of economic forecasting. 1. 515
  • Tay, A. S.,Wallis, K. F. (2000). 'Density forecasting: a survey'. Journal of Forecasting. 19. 235
  • Thomson, M. E.,Pollock, A. C.,Õnkal, D.,Gõnül, M. S. (2019). 'Combining forecasts: Performance and coherence'. International Journal...
  • Timmermann, A. (2006). 'Forecast combinations'. Handbook of economic forecasting. 1. 135
  • Wang, J.,Wu, J. J. (2012). 'The taylor rule and forecast intervals for exchange rates'. Journal of Money, Credit and banking. 44....
  • Winkler, R. L.,Clemen, R. T. (1992). 'Sensitivity of weights in combining forecasts'. Operations Research. 40. 609
  • Zhang, W.,Liu, J.,Cho, C.,Han, X. (2015). 'A hybrid parameter identification method based on bayesian approach and interval analysis for...