Forecasting time series with multivariate copulas

Clarence Simard; Bruno Rémillard

Dependence Modeling (2015)

  • Volume: 3, Issue: 1, page 59-82, electronic only
  • ISSN: 2300-2298

Abstract

top
In this paper we present a forecasting method for time series using copula-based models for multivariate time series. We study how the performance of the predictions evolves when changing the strength of the different possible dependencies, as well as the structure of the dependence. We also look at the impact of the marginal distributions. The impact of estimation errors on the performance of the predictions is also considered. In all the experiments, we compare predictions from our multivariate method with predictions from the univariate version which has been introduced in the literature recently. To simplify implementation, a test of independence between univariate Markovian time series is proposed. Finally, we illustrate the methodology by a practical implementation with financial data.

How to cite

top

Clarence Simard, and Bruno Rémillard. "Forecasting time series with multivariate copulas." Dependence Modeling 3.1 (2015): 59-82, electronic only. <http://eudml.org/doc/271015>.

@article{ClarenceSimard2015,
abstract = {In this paper we present a forecasting method for time series using copula-based models for multivariate time series. We study how the performance of the predictions evolves when changing the strength of the different possible dependencies, as well as the structure of the dependence. We also look at the impact of the marginal distributions. The impact of estimation errors on the performance of the predictions is also considered. In all the experiments, we compare predictions from our multivariate method with predictions from the univariate version which has been introduced in the literature recently. To simplify implementation, a test of independence between univariate Markovian time series is proposed. Finally, we illustrate the methodology by a practical implementation with financial data.},
author = {Clarence Simard, Bruno Rémillard},
journal = {Dependence Modeling},
keywords = {Copulas; time series; forecasting; realized volatility; copulas},
language = {eng},
number = {1},
pages = {59-82, electronic only},
title = {Forecasting time series with multivariate copulas},
url = {http://eudml.org/doc/271015},
volume = {3},
year = {2015},
}

TY - JOUR
AU - Clarence Simard
AU - Bruno Rémillard
TI - Forecasting time series with multivariate copulas
JO - Dependence Modeling
PY - 2015
VL - 3
IS - 1
SP - 59
EP - 82, electronic only
AB - In this paper we present a forecasting method for time series using copula-based models for multivariate time series. We study how the performance of the predictions evolves when changing the strength of the different possible dependencies, as well as the structure of the dependence. We also look at the impact of the marginal distributions. The impact of estimation errors on the performance of the predictions is also considered. In all the experiments, we compare predictions from our multivariate method with predictions from the univariate version which has been introduced in the literature recently. To simplify implementation, a test of independence between univariate Markovian time series is proposed. Finally, we illustrate the methodology by a practical implementation with financial data.
LA - eng
KW - Copulas; time series; forecasting; realized volatility; copulas
UR - http://eudml.org/doc/271015
ER -

References

top
  1. [1] Aas, K., Czado, C., Frigessi, A., and Bakken, H. (2009). Pair-copula constructions of multiple dependence. Insurance Math. Econom., 44(2), 182–198. Zbl1165.60009
  2. [2] Akaike, H. (1974). A new look at the statistical model identification. IEEE Trans. Automatic Control, AC-19(6), 716–723. Zbl0314.62039
  3. [3] Andersen, T., Bollerslev, T., and Diebold, F. (2007). Roughing it up: Including jump components in the measurement, modeling, and forecasting of return volatility. Rev. Econ. Stat., 89(4), 701–720. [Crossref] 
  4. [4] Andersen, T., Bollerslev, T., Diebold, F., and Labys, P. (2001). The distribution of realized exchange rate volatility. J. Amer. Statist. Assoc., 96(453), 42–55. [Crossref] Zbl1015.62107
  5. [5] Beare, B. (2010). Copulas and temporal dependence. Econometrica, 78(1), 395–410. [WoS][Crossref] Zbl1202.91271
  6. [6] Beare, B. K. and Seo, J. (2015). Vine copula specifications for stationary multivariate Markov chains. J. Time. Ser. Anal., 36, 228–246. [WoS][Crossref] Zbl1320.62224
  7. [7] Brockwell, P. J. and Davis, R. A. (1991). Time Series: Theory and Methods. Springer-Verlag, New York, second edition. Zbl0709.62080
  8. [8] Bush, T., Christensen, B., and M.Ø., N. (2011). The role of implied volatility in forecasting future realized volatility and jumps in foreign exchange, stock, and bond markets. J. Econometrics, 60(1), 48–57. [Crossref] 
  9. [9] Chen, X. and Fan, Y. (2006). Estimation of copula-based semiparametric model time series models. J. Econometrics, 130(2), 307–335. Zbl1337.62201
  10. [10] Corsi, F. (2009). A simple approximate long-memory model of realized volatility. J. Financ. Econ., 7(2), 174–196. 
  11. [11] Diebold, F. X. and Mariano, R. S. (1995). Comparing predictive accuracy. J. Bus. Econom. Statist., 13(3), 253–263. 
  12. [12] Duchesne, P., Ghoudi, K., and Rémillard, B. (2012). On testing for independence between the innovations of several time series. Canad. J. Statist., 40(3), 447–479. Zbl1333.62208
  13. [13] Engle, R. F. and Kroner, K. F. (1995). Multivariate simultaneous generalized ARCH. Economet. Theor., 11(1),122–150. [Crossref] 
  14. [14] Erhardt, T. M., Czado, C., and Schepsmeier, U. (2014). R-vine models for spatial time series with an application to daily mean temperature. Biometrics, to appear. DOI:10.1111/biom.12279 [WoS][Crossref] Zbl06528641
  15. [15] Fang, H.-B., Fang, K.-T., and Kotz, S. (2002). The meta-elliptical distributions with given marginals. J. Multivariate Anal., 82(1), 1–16. [Crossref] Zbl1002.62016
  16. [16] Genest, C., Gendron, M., and Bourdeau-Brien, M. (2009). The advent of copula in finance. Europ. J. Financ., 15(7-8), 609–618. 
  17. [17] Genest, C. and Rémillard, B. (2004). Tests of independence or randomness based on the empirical copula process. Test, 13(2), 335–369. [Crossref] Zbl1069.62039
  18. [18] Ghoudi, K. and Rémillard, B. (2004). Empirical processes based on pseudo-observations. II. The multivariate case. In Asymptotic Methods in Stochastics, 381–406. Amer. Math. Soc., Providence, RI. Zbl1079.60024
  19. [19] Kurowicka, D. and Joe, H., editors (2011). Dependence Modeling. Vine Copula Handbook. World Scientific, Hackensack, NJ. 
  20. [20] Martens, M. and van Dijk, D. (2006). Measuring volatility with the realized range. J. Econometrics, 138(1), 181–207. [WoS] Zbl06577509
  21. [21] Nelsen, R. B. (1999). An introduction to copulas. Springer-Verlag, New York. Zbl0909.62052
  22. [22] Rémillard, B. (2013). Statistical Methods For Financial Engineering. CRC Press, Boca Raton, FL. Zbl1273.91010
  23. [23] Rémillard, B., Papageorgiou, N., and Soustra, F. (2012). Copula-based semiparametric models for multivariate time series. J. Multivariate Anal., 110, 30–42. [WoS][Crossref] Zbl1281.62136
  24. [24] Rio, E. (2000). Théorie asymptotique des processus aléatoires faiblement dépendants. Springer-Verlag, Berlin. 
  25. [25] Smith, M. (2015). Copula modelling of dependence in multivariate time series. Int. J. Forecasting, to appear. DOI:10.1016/j.ijforecast.2014.04.003 [WoS][Crossref] 
  26. [26] Sokolinskiy, O. and Van Dijk, D. (2011). Forecasting volatility with copula-based time series models. Technical report, Tinbergen Institute Discussion Paper. 
  27. [27] Soustra, F. (2006). Pricing of synthetic CDO tranches, analysis of base correlations and an introduction to dynamic copulas. Master thesis, HEC Montréal. 
  28. [28] Zhang, L., Mykland, P., and Aït-Sahalia, Y. (2005). A tale of two time scales: Determining integrated volatility with noisy high-frequency data. J. Amer. Statist. Assoc., 100(472), 1394–1414. [Crossref] Zbl1117.62461
  29. [29] Zhou, B. (1996). High-frequency data and volatility in foreign-exchange rates. J. Bus. Econom. Statist., 14(1), 45–52. 

NotesEmbed ?

top

You must be logged in to post comments.