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Forecasting time series with multivariate copulas

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Słowa kluczowe
Kategorie tematyczne
Wydawca
Czasopismo
Rocznik
Tom
3
Numer
1
Opis fizyczny
Daty
otrzymano
2014-08-17
zaakceptowano
2015-05-15
online
2015-05-28
Twórcy
  • Department of Mathematics and Statistics, Université de Montréal
  • Department of Decision Sciences, HEC Montréal
Bibliografia
  • [1] Aas, K., Czado, C., Frigessi, A., and Bakken, H. (2009). Pair-copula constructions of multiple dependence. Insurance Math.Econom., 44(2), 182–198.
  • [2] Akaike, H. (1974). A new look at the statistical model identification. IEEE Trans. Automatic Control, AC-19(6), 716–723.
  • [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] 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]
  • [5] Beare, B. (2010). Copulas and temporal dependence. Econometrica, 78(1), 395–410.[WoS][Crossref]
  • [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]
  • [7] Brockwell, P. J. and Davis, R. A. (1991). Time Series: Theory and Methods. Springer-Verlag, New York, second edition.
  • [8] Bush, T., Christensen, B., and M.Ø., N. (2011). The role of implied volatility in forecasting future realized volatility and jumpsin foreign exchange, stock, and bond markets. J. Econometrics, 60(1), 48–57.[Crossref]
  • [9] Chen, X. and Fan, Y. (2006). Estimation of copula-based semiparametric model time series models. J. Econometrics, 130(2),307–335.
  • [10] Corsi, F. (2009). A simple approximate long-memory model of realized volatility. J. Financ. Econ., 7(2), 174–196.
  • [11] Diebold, F. X. and Mariano, R. S. (1995). Comparing predictive accuracy. J. Bus. Econom. Statist., 13(3), 253–263.
  • [12] Duchesne, P., Ghoudi, K., and Rémillard, B. (2012). On testing for independence between the innovations of several timeseries. Canad. J. Statist., 40(3), 447–479.
  • [13] Engle, R. F. and Kroner, K. F. (1995). Multivariate simultaneous generalized ARCH. Economet. Theor., 11(1),122–150.[Crossref]
  • [14] Erhardt, T. M., Czado, C., and Schepsmeier, U. (2014). R-vine models for spatial time series with an application to daily meantemperature. Biometrics, to appear. DOI:10.1111/biom.12279[WoS][Crossref]
  • [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]
  • [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] Genest, C. and Rémillard, B. (2004). Tests of independence or randomness based on the empirical copula process. Test,13(2), 335–369.[Crossref]
  • [18] Ghoudi, K. and Rémillard, B. (2004). Empirical processes based on pseudo-observations. II. The multivariate case. InAsymptotic Methods in Stochastics, 381–406. Amer. Math. Soc., Providence, RI.
  • [19] Kurowicka, D. and Joe, H., editors (2011). Dependence Modeling. Vine Copula Handbook. World Scientific, Hackensack, NJ.
  • [20] Martens, M. and van Dijk, D. (2006). Measuring volatility with the realized range. J. Econometrics, 138(1), 181–207.[WoS]
  • [21] Nelsen, R. B. (1999). An introduction to copulas. Springer-Verlag, New York.
  • [22] Rémillard, B. (2013). Statistical Methods For Financial Engineering. CRC Press, Boca Raton, FL.
  • [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]
  • [24] Rio, E. (2000). Théorie asymptotique des processus aléatoires faiblement dépendants. Springer-Verlag, Berlin.
  • [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] Sokolinskiy, O. and Van Dijk, D. (2011). Forecasting volatility with copula-based time series models. Technical report,Tinbergen Institute Discussion Paper.
  • [27] Soustra, F. (2006). Pricing of synthetic CDO tranches, analysis of base correlations and an introduction to dynamic copulas.Master thesis, HEC Montréal.
  • [28] Zhang, L., Mykland, P., and Aït-Sahalia, Y. (2005). A tale of two time scales: Determining integrated volatility with noisyhigh-frequency data. J. Amer. Statist. Assoc., 100(472), 1394–1414.[Crossref]
  • [29] Zhou, B. (1996). High-frequency data and volatility in foreign-exchange rates. J. Bus. Econom. Statist., 14(1), 45–52.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_1515_demo-2015-0005
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