Copula Methods for Forecasting Multivariate Time Series

Patton, Andrew J.

doi:10.1016/b978-0-444-62731-5.00016-6

Cited by 237 publications

(232 citation statements)

References 107 publications

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“…The above equation is at the origin of the increasing use of copulas for modeling multivariate distributions with continuous margins in many areas such as quantitative risk management (McNeil, Frey and Embrechts [31]), econometric modeling (Patton [35]), environmental modeling (Salvadori, De Michele and Kottegoda [41]), to name a very few.…”

Section: Introductionmentioning

confidence: 99%

A dependent multiplier bootstrap for the sequential empirical copula process under strong mixing

Bücher¹,

Kojadinovic²

2016

Bernoulli

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Two key ingredients to carry out inference on the copula of multivariate observations are the empirical copula process and an appropriate resampling scheme for the latter. Among the existing techniques used for i.i.d. observations, the multiplier bootstrap of Rémillard and Scaillet (J. Multivariate Anal. 100 (2009) 377-386) frequently appears to lead to inference procedures with the best finite-sample properties. Bücher and Ruppert (J. Multivariate Anal. 116 (2013) 208-229) recently proposed an extension of this technique to strictly stationary strongly mixing observations by adapting the dependent multiplier bootstrap of Bühlmann (The blockwise bootstrap in time series and empirical processes (1993) ETH Zürich, Section 3.3) to the empirical copula process. The main contribution of this work is a generalization of the multiplier resampling scheme proposed by Bücher and Ruppert along two directions. First, the resampling scheme is now genuinely sequential, thereby allowing to transpose to the strongly mixing setting many of the existing multiplier tests on the unknown copula, including nonparametric tests for change-point detection. Second, the resampling scheme is now fully automatic as a data-adaptive procedure is proposed which can be used to estimate the bandwidth parameter. A simulation study is used to investigate the finite-sample performance of the resampling scheme and provides suggestions on how to choose several additional parameters. As by-products of this work, the validity of a sequential version of the dependent multiplier bootstrap for empirical processes of Bühlmann is obtained under weaker conditions on the strong mixing coefficients and the multipliers, and the weak convergence of the sequential empirical copula process is established under many serial dependence conditions. Keywords: lag window estimator; multiplier central limit theorem; multivariate observations; partial-sum process; ranks; serial dependence This is an electronic reprint of the original article published by the ISI/BS in Bernoulli, 2016, Vol. 22, No. 2, 927-968. This reprint differs from the original in pagination and typographic detail.

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Section: Introductionmentioning

confidence: 99%

A dependent multiplier bootstrap for the sequential empirical copula process under strong mixing

Bücher¹,

Kojadinovic²

2016

Bernoulli

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“…Anatolyev(2009), Patton(2006 and Scotti(2011) applied this methodology to predict multiple economic events. Patton (2013) provided a recent survey on copula methods to forecasting multivariate time series.…”

Section: Roc and Non-linear Combination Methodology 21 A Copula-basementioning

confidence: 99%

A non-linear forecast combination procedure for binary outcomes

Lahiri

Liu²

2016

Studies in Nonlinear Dynamics &Amp; Econometrics

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Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. We develop a non-linear forecast combination rule based on copulas that incorporate the dynamic interaction between individual predictors. This approach is optimal in the sense that the resulting combined forecast produces the highest discriminatory power as measured by the receiver operating characteristic (ROC) curve. Under additional assumptions, this rule is shown to be equivalent to the quintessential linear combination scheme. To illustrate its usefulness, we apply this methodology to optimally aggregate two currently used leading indicators-the ISM new order diffusion index and the yield curve spread-to predict economic recessions in the United States. We also examine the sources of forecasting gains using a counterfactual experimental set up. Terms of use: Documents in

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“…Unlike some applications of the bootstrap, its use here does not lead to any asymptotic re…nements, rather it merely enables one to avoid having to compute large and 5 Inference methods for models with dynamic conditional copulas and nonparametric or semiparametric marginal distributions are not yet available in the literature, see Patton (2012), and so we are constrained to consider fully parametric marginal distributions. 6 It is possible to allow the conditional distribution of the standardized residuals to vary through time (e.g., to have time-varying higher-order moments), but for simplicity we do not consider this here.…”

Section: Estimation and Inferencementioning

confidence: 99%

“…Comparing the values of the loglikelihoods from that model with those in Table 2 con…rms the gains from including realized correlation in this speci…cation. 1 1 The linear correlation implied by a copula-based multivariate model is generally not a closed-form function of the parameters of the model, even when the copula has a "correlation" parameter, see Patton (2012). We use simple numerical integration to obtain the model-implied linear correlation.…”

Section: High Frequency Data and Dynamic Copula Modelsmentioning

confidence: 99%

Dynamic copula models and high frequency data

Salvatierra

Patton

2015

Journal of Empirical Finance

101

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This paper proposes a new class of dynamic copula models for daily asset returns that exploits information from high frequency (intra-daily) data. We augment the generalized autoregressive score (GAS) model of Creal, et al. (2012) with high frequency measures such as realized correlation to obtain a "GRAS" model. We …nd that the inclusion of realized measures signi…cantly improves the in-sample …t of dynamic copula models across a range of U.S. equity returns. Moreover, we …nd that out-of-sample density forecasts from our GRAS models are superior to those from simpler models. Finally, we consider a simple portfolio choice problem to illustrate the economic gains from exploiting high frequency data for modeling dynamic dependence.

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Copula Methods for Forecasting Multivariate Time Series

Cited by 237 publications

References 107 publications

A dependent multiplier bootstrap for the sequential empirical copula process under strong mixing

A dependent multiplier bootstrap for the sequential empirical copula process under strong mixing

A non-linear forecast combination procedure for binary outcomes

Dynamic copula models and high frequency data

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