Table of Contents Author Guidelines Submit a Manuscript
Mathematical Problems in Engineering
Volume 2014, Article ID 823046, 8 pages
http://dx.doi.org/10.1155/2014/823046
Research Article

Long Memory Models to Generate Synthetic Hydrological Series

Department of Electrical Engineering, Pontifical Catholic University of Rio de Janeiro (PUC-Rio), 22451-900 Rio de Janeiro, RJ, Brazil

Received 21 April 2014; Revised 19 June 2014; Accepted 27 June 2014; Published 17 July 2014

Academic Editor: Nazim I. Mahmudov

Copyright © 2014 Guilherme Armando de Almeida Pereira and Reinaldo Castro Souza. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. B. H. Dias, A. L. M. Marcato, R. C. Souza et al., “Stochastic dynamic programming applied to hydrothermal power systems operation planning based on the convex hull algorithm,” Mathematical Problems in Engineering, vol. 2010, Article ID 390940, 20 pages, 2010. View at Publisher · View at Google Scholar
  2. A. L. M. Marcato, Hybrid representation of equivalents and individualized systems for the avegare stated period operation planning of power systems of great size [D.S. thesis], DEE, PUC, Rio, Brazil, 2002.
  3. H. A. Thomas and M. B. Fiering, “Mathematical synthesis of streamflow sequences for the analysis of river basins by simulation,” in Design Water Resource Systems, A. Mass, Ed., pp. 459–463, Harvard University Press, Cambrigde, Mass, USA, 1962. View at Google Scholar
  4. A. I. McLeod, “Parsimony, model adequacy and periodic correlation in time series forecasting,” International Statistical Review, vol. 61, no. 3, pp. 387–393, 1993. View at Google Scholar
  5. A. I. McLeod, “Diagnostic checking of periodic autoregression models with application,” Journal of Time Series Analysis, vol. 15, no. 2, pp. 221–233, 1994. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. F. L. C. Oliveira, P. G. C. Ferreira, and R. C. Souza, “A parsimonious bootstrap method to model natural inflow energy series,” Mathematical Problems in Engineering, vol. 2014, Article ID 158689, 10 pages, 2014. View at Publisher · View at Google Scholar
  7. F. L. C. Oliveira and R. C. Souza, “A new approach to identify the structural order of par (p) models,” Pesquisa Operacional, vol. 31, pp. 487–498, 2011. View at Publisher · View at Google Scholar
  8. L. C. D. Campos, Periodic stochastic model based on neural networks [Ph.D. thesis], DEE, PUC-Rio, Rio de Janeiro, Brazil, 2010.
  9. R. M. Souza, Modeling of periodic series via PAR(p) structures utilizing wavelet shrinkage [Ph.D. thesis], DEE, PUC-Rio, Rio de Janeiro, Brazil, 2014.
  10. P. G. C. Ferreira, The stochasticity associated with Brazilian Electrical Sector and a new approach to generate natural inflow energy via periodic gama model, [D.Sc. Thesis], DEE, PUC-Rio, Rio de Janeiro, Brazil, 2013.
  11. J. R. M. Hosking, “Fractional differencing,” Biometrika, vol. 68, no. 1, pp. 165–176, 1981. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. V. A. Reisen, “Estimation of the fractional difference parameter in the ARIMA(p,d,q) model using the smoothed periodogram,” Journal of Time Series Analysis, vol. 15, no. 3, pp. 335–350, 1994. View at Publisher · View at Google Scholar · View at MathSciNet
  13. P. Doukham, G. Oppeenhein, and M. S. Taqqu, Theory and Applications of Long-Range Dependence, Birkhäuser, Basel, Switzerland, 2003. View at MathSciNet
  14. W. Palma, Long-Memory Time Series: Theory and Methods, Wiley Series in Probability and Statistics, John Wiley & Sons, Hoboken, NJ, USA, 2007. View at Publisher · View at Google Scholar · View at MathSciNet
  15. G. C. Franco and V. A. Reisen, “Bootstrap approaches and confidence intervals for stationary and nonstationary long-range dependence processes,” Physica A, vol. 375, pp. 546–562, 2007. View at Google Scholar
  16. C. W. J. Granger and R. Joyeux, “An introduction to long-memory time series models and fractional differencing,” Journal of Time Series Analysis, vol. 1, no. 1, pp. 15–29, 1980. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  17. F. Sowell, “Maximum likelihood estimation of stationary univariate fractionally integrated time series models,” Journal of Econometrics, vol. 53, no. 1–3, pp. 165–188, 1992. View at Publisher · View at Google Scholar · View at MathSciNet
  18. R. Fox and M. S. Taqqu, “Large-sample properties of parameter estimates for strongly dependent stationary Gaussian time series,” The Annals of Statistics, vol. 14, no. 2, pp. 517–532, 1986. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  19. J. Geweke and S. Porter-Hudak, “The estimation and application of long memory time series models,” Journal of Time Series Analysis, vol. 4, no. 4, pp. 221–238, 1983. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  20. P. M. Robinson, “Semiparametric analysis of long-memory time series,” The Annals of Statistics, vol. 22, no. 1, pp. 515–539, 1994. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  21. B. Efron, “Bootstrap methods: another look at the jackknife,” The Annals of Statistics, vol. 7, no. 1, pp. 1–26, 1979. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  22. B. Efron and R. J. Tibshirani, An Introduction to the Bootstrap, Chapman & Hall, New York, NY, USA, 1993.
  23. G. C. Franco and V. A. Reisen, “Bootstrap techniques in semiparametric estimation models for ARFIMA models: a comparison study,” Computational Statistics, vol. 19, no. 2, pp. 243–259, 2004. View at Publisher · View at Google Scholar · View at MathSciNet
  24. G. C. Franco, V. A. Reisen, and F. A. Alves, “Bootstrap tests for fractional integration and cointegration: a comparison study,” Mathematics and Computers in Simulation, vol. 87, pp. 19–29, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  25. D. D. J. Penna, efinition of the streamflow scenario tree to long-term operation planning, DEE, PUC-Rio, Rio de Janeiro, Brazil, 2009.