Forecasts of climatological variables using the change point and Holt-Winters models.
Keywords:
Holt-Winters, precipitation, forecasts, change pointAbstract
This study analyzes a time series with daily historical data from January 1, 1989 to December 31, 2021 of the precipitation variable with a total of 12053 observations, these data are obtained from the Tunjuelito climatological station. For the research the records of the variable “precipitation” were taken into account, the objective was to analyze the trends, use the data up to December 31, 2020 to estimate a forecast for the year 2021 Holt-Winters method and the change point model, the observed data are compared with the predicted data. Finally, statistical tests are performed to contrast the degree of similarity of the data obtained from the forecasts with the observed data provided by the station. The results show that the data obtained from the change point model show higher accuracy and fit relatively well with the observed data. However, this study is considered preliminary and for the results to be considered conclusive they must be applied to a significant number of time series of meteorological variables.
Downloads
Download data is not yet available.
References
C. H. Sui, X. Li, and M. J. Yang, “On the definition of precipitation efficiency,” J. Atmos. Sci., vol. 64, no. 12, pp. 4506–4513, 2007, doi: 10.1175/2007JAS2332.1
A. Esquivel et al., “Predictability of seasonal precipitation across major crop growing areas in Colombia,” Clim. Serv., vol. 12, no. March, pp. 36–47, 2018, doi: 10.1016/j.cliser.2018.09.001.
H. Feidas, C. Noulopoulou, T. Makrogiannis, and E. Bora-Senta, “Trend analysis of precipitation time series in Greece and their relationship with circulation using surface and satellite data: 1955-2001,” Theor. Appl. Climatol., vol. 87, no. 1–4, pp. 155–177, 2007, doi: 10.1007/s00704-006-0200-5.
P. T. Nastos, A. G. Paliatsos, K. V. Koukouletsos, I. K. Larissi, and K. P. Moustris, “Artificial neural networks modeling for forecasting the maximum daily total precipitation at Athens, Greece,” Atmos. Res., vol. 144, pp. 141–150, 2014, doi: 10.1016/j.atmosres.2013.11.013
T. Li, C. Qiao, L. Wang, J. Chen, and Y. Ren, “An Algorithm for Precipitation Correction in Flood Season Based on Dendritic Neural Network,” Front. Plant Sci., vol. 13, no. May, pp. 1–13, 2022, doi: 10.3389/fpls.2022.862558
T. T. H. Phan, É. Poisson Caillault, and A. Bigand, “Comparative study on univariate forecasting methods for meteorological time series,” Eur. Signal Process. Conf., vol. 2018-Septe, pp. 2380–2384, 2018, doi: 10.23919/EUSIPCO.2018.8553576
A. J. M. Jacobs and N. Maat, “Numerical guidance methods for decision support in aviation meteorological forecasting,” Weather Forecast., vol. 20, no. 1, pp. 82–100, 2005, doi: 10.1175/WAF-827.1
J. Arroyo and C. Maté, “Forecasting histogram time series with k-nearest neighbours methods,” Int. J. Forecast., vol. 25, no. 1, pp. 192–207, 2009, doi: 10.1016/j.ijforecast.2008.07.003.
M. Heydari, H. B. Ghadim, M. Rashidi, and M. Noori, “Application of holt-winters time series models for predicting climatic parameters (Case study: Robat Garah-Bil station, Iran),” Polish J. Environ. Stud., vol. 29, no. 1, pp. 617–627, 2020, doi: 10.15244/pjoes/100496
M. V. Zhitlukhin and W. T. Ziemba, “Exit strategies in bubble-like markets using a changepoint model,” Quant. Financ. Lett., vol. 4, no. 1, pp. 47–52, 2016, doi: 10.1080/21649502.2015.1165918
M. J. Lenardon and A. Amirdjanova, “Interaction between stock indices via changepoint analysis,” pp. 573–586, 2006, doi: 10.1002/asmb
D. Barry and J. A. Hartigan, “A Bayesian Analysis for Change Point Problems,” J. Am. Stat. Assoc., vol. 88, no. 421, p. 309, 1993, doi: 10.2307/2290726
R. Cmejla, J. Rusz, P. Bergl, and J. Vokral, “Bayesian changepoint detection for the automatic assessment of fluency and articulatory disorders,” Speech Commun., vol. 55, no. 1, pp. 178–189, 2013, doi: https://doi.org/10.1016/j.specom.2012.08.003
C. Jeong and J. Kim, “Bayesian multiple structural change-points estimation in time series models with genetic algorithm,” J. Korean Stat. Soc., vol. 42, no. 4, pp. 459–468, Dec. 2013, doi: 10.1016/j.jkss.2013.02.001
S. Liu, M. Yamada, N. Collier, and M. Sugiyama, “Change-point detection in time-series data by relative density-ratio estimation.,” Neural Netw., vol. 43, pp. 72–83, Jul. 2013, doi: 10.1016/j.neunet.2013.01.012
S. Li and R. Lund, “Multiple Changepoint Detection via Genetic Algorithms,” J. Clim., vol. 25, no. 2, pp. 674–686, Jan. 2012, doi: 10.1175/2011JCLI4055.1
J. Chen and K. Gupta, Parametric Statistical Change Point Analysis, 2nd ed. Boston: Birkhäuser, Springer, 2012
F. A. Alawadhi and D. Alhulail, “Bayesian change points analysis for earthquakes body wave magnitude,” J. Appl. Stat., vol. 43, no. 9, pp. 1567–1582, 2016, doi: 10.1080/02664763.2015.1117585
D. Picard, “Testing and estimating change-points in time series,” vol. 17, no. 4, pp. 841–867, 2013
P. J. Plummer and B.S.E., “Decting Change–Points in a compound Poisson,” 2012
E. L. Lehmann, “On likelihood ratio tests,” Optimality, vol. 49, no. 2006, pp. 1–8, 2006, doi: 10.1214/074921706000000356
T. Wang, W. Tian, and W. Ning, “Likelihood ratio test change-point detection in the skew slash distribution,” Commun. Stat. Simul. Comput., vol. 0, no. 0, pp. 1–13, 2020, doi: 10.1080/03610918.2020.1755869
Y. Zhou, L. Fu, and B. Zhang, “Two non parametric methods for change-point detection in distribution,” Commun. Stat. - Theory Methods, vol. 46, no. 6, pp. 2801–2815, 2017, doi: 10.1080/03610926.2015.1048891
J. Vanegas and F. Vásquez, “[Multivariate Adaptive Regression Splines (MARS), an alternative for the analysis of time series].,” Gac. Sanit., no. xx, pp. 4–6, Dec. 2016, doi: 10.1016/j.gaceta.2016.10.003.
V. Grech and N. Calleja, “WASP (Write a Scientific Paper): Parametric vs. non-parametric tests,” Early Hum. Dev., no. xxxx, pp. 1–2, 2018, doi: 10.1016/j.earlhumdev.2018.04.014
S. Herrmann, H. Schwender, K. Ickstadt, and P. Müller, “A Bayesian changepoint analysis of ChIP-Seq data of Lamin B,” Biochim. Biophys. Acta - Proteins Proteomics, vol. 1844, no. 1 PART A, pp. 138–144, 2014, doi: 10.1016/j.bbapap.2013.09.001
L. O. Mesa, M. Rivera, and J. A. Romero, “Descripción general de la Inferencia Bayesiana y sus aplicaciones en los procesos de gestión,” La Simulación al Serv. la Acad., vol. 2, pp. 1–28, 2011
A. Contreras Juárez, C. Atziry Zuñiga, J. L. Martínez Flores, and D. Sánchez Partida, “Análisis de series de tiempo en el pronóstico de la demanda de almacenamiento de productos perecederos,” Estud. Gerenciales, vol. 32, no. 141, pp. 387–396, Oct. 2016, doi: 10.1016/j.estger.2016.11.002
G. Masterton, “What to do with a forecast?,” Synthese, vol. 191, no. 8, pp. 1881–1907, 2014, doi: 10.1007/s11229-013-0384-z
R. Ballou, Logística: Administración de la cadena de suministro, 5ta Ed. México, 2004
M. Mas-Machuca, M. Sainz, and C. Martinez-Costa, “A review of forecasting models for new products,” Intang. Cap., vol. 10, no. 1, pp. 1–25, 2014, doi: 10.3926/ic.482
D. J. Eck, “Bootstrapping for multivariate linear regression models,” Stat. Probab. Lett., vol. 134, pp. 141–149, 2018, doi: 10.1016/j.spl.2017.11.001
L. Ferbar Tratar, B. Mojškerc, and A. Toman, “Demand forecasting with four-parameter exponential smoothing,” Int. J. Prod. Econ., vol. 181, pp. 162–173, 2016, doi: 10.1016/j.ijpe.2016.08.004
J. W. Taylor, “Multi-item sales forecasting with total and split exponential smoothing,” J. Oper. Res. Soc., vol. 62, no. 3, pp. 555–563, 2011, doi: 10.1057/jors.2010.95
E. M. de Oliveira and F. L. Cyrino Oliveira, “Forecasting mid-long term electric energy consumption through bagging ARIMA and exponential smoothing methods,” Energy, vol. 144, pp. 776–788, 2018, doi: 10.1016/j.energy.2017.12.049
B. Heizer, J., & Render, Principios de administración de operaciones. Pearson Educación., 7ma Ed. Pearson, 2004
L. Frías-Paredes, F. Mallor, M. Gastón-Romeo, and T. León, “Dynamic mean absolute error as new measure for assessing forecasting errors,” Energy Convers. Manag., vol. 162, no. December 2017, pp. 176–188, 2018, doi: 10.1016/j.enconman.2018.02.030
M. V. Shcherbakov, A. Brebels, N. L. Shcherbakova, A. P. Tyukov, T. A. Janovsky, and V. A. evich Kamaev, “A survey of forecast error measures,” World Appl. Sci. J., vol. 24, no. 24, pp. 171–176, 2013, doi: 10.5829/idosi.wasj.2013.24.itmies.80032
“Precipitation,” Adv. Remote Sens., pp. 621–647, Jan. 2020, doi: 10.1016/B978-0-12-815826-5.00016-7
S. Michaelides, V. Levizzani, E. Anagnostou, P. Bauer, T. Kasparis, and J. E. Lane, “Precipitation: Measurement, remote sensing, climatology and modeling,” Atmos. Res., vol. 94, no. 4, pp. 512–533, 2009, doi: 10.1016/j.atmosres.2009.08.017
C. Kummerow, W. Barnes, T. Kozu, J. Shiue, and J. Simpson, “The Tropical Rainfall Measuring Mission (TRMM) sensor package,” J. Atmos. Ocean. Technol., vol. 15, no. 3, pp. 809–817, 1998
A. Esquivel et al., “Predictability of seasonal precipitation across major crop growing areas in Colombia,” Clim. Serv., vol. 12, no. March, pp. 36–47, 2018, doi: 10.1016/j.cliser.2018.09.001.
H. Feidas, C. Noulopoulou, T. Makrogiannis, and E. Bora-Senta, “Trend analysis of precipitation time series in Greece and their relationship with circulation using surface and satellite data: 1955-2001,” Theor. Appl. Climatol., vol. 87, no. 1–4, pp. 155–177, 2007, doi: 10.1007/s00704-006-0200-5.
P. T. Nastos, A. G. Paliatsos, K. V. Koukouletsos, I. K. Larissi, and K. P. Moustris, “Artificial neural networks modeling for forecasting the maximum daily total precipitation at Athens, Greece,” Atmos. Res., vol. 144, pp. 141–150, 2014, doi: 10.1016/j.atmosres.2013.11.013
T. Li, C. Qiao, L. Wang, J. Chen, and Y. Ren, “An Algorithm for Precipitation Correction in Flood Season Based on Dendritic Neural Network,” Front. Plant Sci., vol. 13, no. May, pp. 1–13, 2022, doi: 10.3389/fpls.2022.862558
T. T. H. Phan, É. Poisson Caillault, and A. Bigand, “Comparative study on univariate forecasting methods for meteorological time series,” Eur. Signal Process. Conf., vol. 2018-Septe, pp. 2380–2384, 2018, doi: 10.23919/EUSIPCO.2018.8553576
A. J. M. Jacobs and N. Maat, “Numerical guidance methods for decision support in aviation meteorological forecasting,” Weather Forecast., vol. 20, no. 1, pp. 82–100, 2005, doi: 10.1175/WAF-827.1
J. Arroyo and C. Maté, “Forecasting histogram time series with k-nearest neighbours methods,” Int. J. Forecast., vol. 25, no. 1, pp. 192–207, 2009, doi: 10.1016/j.ijforecast.2008.07.003.
M. Heydari, H. B. Ghadim, M. Rashidi, and M. Noori, “Application of holt-winters time series models for predicting climatic parameters (Case study: Robat Garah-Bil station, Iran),” Polish J. Environ. Stud., vol. 29, no. 1, pp. 617–627, 2020, doi: 10.15244/pjoes/100496
M. V. Zhitlukhin and W. T. Ziemba, “Exit strategies in bubble-like markets using a changepoint model,” Quant. Financ. Lett., vol. 4, no. 1, pp. 47–52, 2016, doi: 10.1080/21649502.2015.1165918
M. J. Lenardon and A. Amirdjanova, “Interaction between stock indices via changepoint analysis,” pp. 573–586, 2006, doi: 10.1002/asmb
D. Barry and J. A. Hartigan, “A Bayesian Analysis for Change Point Problems,” J. Am. Stat. Assoc., vol. 88, no. 421, p. 309, 1993, doi: 10.2307/2290726
R. Cmejla, J. Rusz, P. Bergl, and J. Vokral, “Bayesian changepoint detection for the automatic assessment of fluency and articulatory disorders,” Speech Commun., vol. 55, no. 1, pp. 178–189, 2013, doi: https://doi.org/10.1016/j.specom.2012.08.003
C. Jeong and J. Kim, “Bayesian multiple structural change-points estimation in time series models with genetic algorithm,” J. Korean Stat. Soc., vol. 42, no. 4, pp. 459–468, Dec. 2013, doi: 10.1016/j.jkss.2013.02.001
S. Liu, M. Yamada, N. Collier, and M. Sugiyama, “Change-point detection in time-series data by relative density-ratio estimation.,” Neural Netw., vol. 43, pp. 72–83, Jul. 2013, doi: 10.1016/j.neunet.2013.01.012
S. Li and R. Lund, “Multiple Changepoint Detection via Genetic Algorithms,” J. Clim., vol. 25, no. 2, pp. 674–686, Jan. 2012, doi: 10.1175/2011JCLI4055.1
J. Chen and K. Gupta, Parametric Statistical Change Point Analysis, 2nd ed. Boston: Birkhäuser, Springer, 2012
F. A. Alawadhi and D. Alhulail, “Bayesian change points analysis for earthquakes body wave magnitude,” J. Appl. Stat., vol. 43, no. 9, pp. 1567–1582, 2016, doi: 10.1080/02664763.2015.1117585
D. Picard, “Testing and estimating change-points in time series,” vol. 17, no. 4, pp. 841–867, 2013
P. J. Plummer and B.S.E., “Decting Change–Points in a compound Poisson,” 2012
E. L. Lehmann, “On likelihood ratio tests,” Optimality, vol. 49, no. 2006, pp. 1–8, 2006, doi: 10.1214/074921706000000356
T. Wang, W. Tian, and W. Ning, “Likelihood ratio test change-point detection in the skew slash distribution,” Commun. Stat. Simul. Comput., vol. 0, no. 0, pp. 1–13, 2020, doi: 10.1080/03610918.2020.1755869
Y. Zhou, L. Fu, and B. Zhang, “Two non parametric methods for change-point detection in distribution,” Commun. Stat. - Theory Methods, vol. 46, no. 6, pp. 2801–2815, 2017, doi: 10.1080/03610926.2015.1048891
J. Vanegas and F. Vásquez, “[Multivariate Adaptive Regression Splines (MARS), an alternative for the analysis of time series].,” Gac. Sanit., no. xx, pp. 4–6, Dec. 2016, doi: 10.1016/j.gaceta.2016.10.003.
V. Grech and N. Calleja, “WASP (Write a Scientific Paper): Parametric vs. non-parametric tests,” Early Hum. Dev., no. xxxx, pp. 1–2, 2018, doi: 10.1016/j.earlhumdev.2018.04.014
S. Herrmann, H. Schwender, K. Ickstadt, and P. Müller, “A Bayesian changepoint analysis of ChIP-Seq data of Lamin B,” Biochim. Biophys. Acta - Proteins Proteomics, vol. 1844, no. 1 PART A, pp. 138–144, 2014, doi: 10.1016/j.bbapap.2013.09.001
L. O. Mesa, M. Rivera, and J. A. Romero, “Descripción general de la Inferencia Bayesiana y sus aplicaciones en los procesos de gestión,” La Simulación al Serv. la Acad., vol. 2, pp. 1–28, 2011
A. Contreras Juárez, C. Atziry Zuñiga, J. L. Martínez Flores, and D. Sánchez Partida, “Análisis de series de tiempo en el pronóstico de la demanda de almacenamiento de productos perecederos,” Estud. Gerenciales, vol. 32, no. 141, pp. 387–396, Oct. 2016, doi: 10.1016/j.estger.2016.11.002
G. Masterton, “What to do with a forecast?,” Synthese, vol. 191, no. 8, pp. 1881–1907, 2014, doi: 10.1007/s11229-013-0384-z
R. Ballou, Logística: Administración de la cadena de suministro, 5ta Ed. México, 2004
M. Mas-Machuca, M. Sainz, and C. Martinez-Costa, “A review of forecasting models for new products,” Intang. Cap., vol. 10, no. 1, pp. 1–25, 2014, doi: 10.3926/ic.482
D. J. Eck, “Bootstrapping for multivariate linear regression models,” Stat. Probab. Lett., vol. 134, pp. 141–149, 2018, doi: 10.1016/j.spl.2017.11.001
L. Ferbar Tratar, B. Mojškerc, and A. Toman, “Demand forecasting with four-parameter exponential smoothing,” Int. J. Prod. Econ., vol. 181, pp. 162–173, 2016, doi: 10.1016/j.ijpe.2016.08.004
J. W. Taylor, “Multi-item sales forecasting with total and split exponential smoothing,” J. Oper. Res. Soc., vol. 62, no. 3, pp. 555–563, 2011, doi: 10.1057/jors.2010.95
E. M. de Oliveira and F. L. Cyrino Oliveira, “Forecasting mid-long term electric energy consumption through bagging ARIMA and exponential smoothing methods,” Energy, vol. 144, pp. 776–788, 2018, doi: 10.1016/j.energy.2017.12.049
B. Heizer, J., & Render, Principios de administración de operaciones. Pearson Educación., 7ma Ed. Pearson, 2004
L. Frías-Paredes, F. Mallor, M. Gastón-Romeo, and T. León, “Dynamic mean absolute error as new measure for assessing forecasting errors,” Energy Convers. Manag., vol. 162, no. December 2017, pp. 176–188, 2018, doi: 10.1016/j.enconman.2018.02.030
M. V. Shcherbakov, A. Brebels, N. L. Shcherbakova, A. P. Tyukov, T. A. Janovsky, and V. A. evich Kamaev, “A survey of forecast error measures,” World Appl. Sci. J., vol. 24, no. 24, pp. 171–176, 2013, doi: 10.5829/idosi.wasj.2013.24.itmies.80032
“Precipitation,” Adv. Remote Sens., pp. 621–647, Jan. 2020, doi: 10.1016/B978-0-12-815826-5.00016-7
S. Michaelides, V. Levizzani, E. Anagnostou, P. Bauer, T. Kasparis, and J. E. Lane, “Precipitation: Measurement, remote sensing, climatology and modeling,” Atmos. Res., vol. 94, no. 4, pp. 512–533, 2009, doi: 10.1016/j.atmosres.2009.08.017
C. Kummerow, W. Barnes, T. Kozu, J. Shiue, and J. Simpson, “The Tropical Rainfall Measuring Mission (TRMM) sensor package,” J. Atmos. Ocean. Technol., vol. 15, no. 3, pp. 809–817, 1998
Downloads
Published
2021-09-01
How to Cite
Valderrama-Balaguera, J. C., Castro-Silva, H. F., & Dávila Carrillo, C. A. (2021). Forecasts of climatological variables using the change point and Holt-Winters models. Mundo FESC Journal, 11(S2), 337–352. Retrieved from https://www.fesc.edu.co/Revistas/OJS/index.php/mundofesc/article/view/986
Issue
Section
Articulos
