Analyzing Dependent Data with Vine Copulas

Czado, Claudia; Diggle, P.; Zeger, SL

doi:10.1007/978-3-030-13785-4

Cited by 196 publications

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“…Ass et al [56] shows that these copulae are able to catch the tail dependence of financial data. For a deeper discussion on the copulae described next, the reader is referred to [57]. In this section we will show that HP performances properly in the case of these copula models.…”

Section: Copula Relationshipmentioning

confidence: 91%

An Alternative Approach to Measure Co-Movement between Two Time Series

2020

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The study of the dependences between different assets is a classic topic in financial literature. To understand how the movements of one asset affect to others is critical for derivatives pricing, portfolio management, risk control, or trading strategies. Over time, different methodologies were proposed by researchers. ARCH, GARCH or EGARCH models, among others, are very popular to model volatility autocorrelation. In this paper, a new simple method called HP is introduced to measure the co-movement between two time series. This method, based on the Hurst exponent of the product series, is designed to detect correlation, even if the relationship is weak, but it also works fine with cointegration as well as non linear correlations or more complex relationships given by a copula. This method and different variations thereaof are tested in statistical arbitrage. Results show that HP is able to detect the relationship between assets better than the traditional correlation method. 2 of 24 multivariate GARCH, to estimate large covariance matrices, and Hafner [26] developed the GDCC model which is able to capture the asset-specific heterogeneity in the correlation structure.In this paper, an alternative way to look at correlations and co-movements is proposed by using the Hurst exponent. Along the paper, correlations, co-movements, etc. refer to cross-correlation, i.e., correlation between two different series (or assets). Introducing the HP of Two Series Hurst Exponent of a Time SeriesHurst exponent can be used to measure persistence as well as mean reversion properties in a time series. Introduced by H.E. Hurst in 1951 [27] to study the frequency of rain and drought in order to size the Nile River Dam, its application was extended not only to social sciences (see [28] for an interesting review) but also to meteorology [29], astrophysics [30], geography [31], medicine [32] or culturomics [33]. The first method to estimate the Hurst exponent was the R/S analysis [34]. However, as a consequence of a lack of accuracy of this methodology claimed by several authors [35-38] and its limited validity mainly for fractional Brownian motions [39], there has been an effort in the literature to provide new algorithms to improve the estimation. Some of these techniques are the Hudaks Semiparametric Method (GPH) [40], the Quasi Maximum Likelihood analysis (QML) [41], the Generalized Hurst Exponent (GHE) [42], Wavelets [43], the Centered Moving Average (CMA) [44], the Multifractal Detrended Fluctuation Analysis (MF-DFA) [45], the Lyapunov Exponent [46,47], Geometric Method-Based Procedures (GM) [48] and Fractal Dimension Algorithms (FD) [49].Among all of them, in this paper we will use the GHE algorithm, because it does not require to calculate ranges, it is not biased when applied to short series [49,50] and the calculation is simple.The GHE algorithm is based on the scaling properties of the following statistic [50]:

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Section: Copula Relationshipmentioning

confidence: 91%

An Alternative Approach to Measure Co-Movement between Two Time Series

2020

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“…For automated model selection and pair copula estimation, we employ Algorithm 3.1 of [8], referred to as "The Dißmann Algorithm" in Section 8.3 of [4]. This algorithm delivers an estimateV of the vine structure V underlying the data, as well as an estimateĈ of the family C of pair copulae underlying the construction in (5).…”

Section: Main Contributions Proposed Methodologymentioning

confidence: 99%

“…Here, we collect some essential de nitions and properties of (regular) vines and vine copulae. For more details, see Chapter 5 in [4] and the references therein.…”

Section: Vine Copulaementioning

confidence: 99%

“…In the present work, we contribute to copula-based multiple testing by demonstrating how vine copula models (cf. [4] and references therein) can be used to optimize e ective numbers of tests (in the sense of [7]) for control of the FWER. Assuming that the dependency structure among the test statistics is a nuisance parameter (of potentially in nite dimension), we propose to t a regular vine copula model to the observed data.…”

Section: Introductionmentioning

confidence: 99%

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Optimizing effective numbers of tests by vine copula modeling

Steffen

Dickhaus

2020

Dependence Modeling

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In the multiple testing context, we utilize vine copulae for optimizing the effective number of tests. It is well known that for the calibration of multiple tests for control of the family-wise error rate the dependencies between the marginal tests are of utmost importance. It has been shown in previous work, that positive dependencies between the marginal tests can be exploited in order to derive a relaxed Šidák-type multiplicity correction. This correction can conveniently be expressed by calculating the corresponding „effective number of tests“ for a given (global) significance level. This methodology can also be applied to blocks of test statistics so that the effective number of tests can be calculated by the sum of the effective numbers of tests for each block. In the present work, we demonstrate how the power of the multiple test can be optimized by taking blocks with high inner-block dependencies. The determination of those blocks will be performed by means of an estimated vine copula model. An algorithm is presented which uses the information of the estimated vine copula to make a data-driven choice of appropriate blocks in terms of (estimated) dependencies. Numerical experiments demonstrate the usefulness of the proposed approach.

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“…Having obtained the standardized residuals (z j ), we estimate the dependence structure of the stock markets. To compare the different vine structures, we use the mixed versions of the C-vine, D-vine, and R-vine copulas (Czado, 2019). In these mixed versions, we allow for selection of pairwise copulas from all the families listed in Table A.1 based on the sequential estimations suggested in Brechmann et al (2013) and Dissmann et al (2013).…”

Section: Vine Copulamentioning

confidence: 99%

Portfolio Optimization Based on Forecasting Models Using Vine Copulas: An Empirical Assessment for the Financial Crisis

Sahamkhadam

Stephan

2019

SSRN Journal

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We employ and examine vine copulas in modeling symmetric and asymmetric dependency structures and forecasting financial returns. We analyze the asset allocations performed during the 2008-2009 financial crisis and test different portfolio strategies such as maximum Sharpe ratio, minimum variance, and minimum conditional Value-at-Risk. We then specify the regular, drawable, and canonical vine copulas, such as the Student−t, Clayton, Frank, Joe, Gumbel, and mixed copulas, and analyze both in-sample and out-of-sample portfolio performances. Out-of-sample portfolio back-testing shows that vine copulas reduce portfolio risk better than simple copulas. Our econometric analysis of the outcomes of the various models shows that in terms of reducing conditional Value-at-Risk, D-vines appear to be better than R-and C-vines. Overall, we find that the Student−t drawable vine copula models perform best with regard to risk reduction, both for the entire period 2005-2012 as well as during the financial crisis. targeted sample and estimate portfolio measures that capture the utility function maximization, including conditional Value-at-Risk (CVaR), Sharpe ratio (SR) and standard deviation. This allows for a better understanding of the copulabased portfolio strategies' performance over a short-term investment horizon during the global financial crisis. Finally, using these measures, we perform a regression analysis on the effect of copula families and vine structures on the portfolio out-of-sample performance.Out-of-sample portfolio back-testing shows that vine copulas are better at reducing portfolio risk than simple copulas. In the case of portfolio out-of-sample CVaR, Frank and Student−t vine copulas result in lower downside risk.Our short-term investment analyses reveal gains obtained from vine copula-based SR portfolios. Although most of the model fails to pass the downside risk back-testing, asymmetric copulas (e.g., Clayton) are better able to forecast the downside risk. Copula families capturing no tail dependence (Frank) and upper tail dependence (Joe and Gumbel) lead to higher terminal portfolio values over the financial crisis. The econometric analysis of the target measures from the various optimal portfolio models reveals that D-vines, in general, reduce downside risk measured by CVaR better than R-or C-vines, and that the Student-t D-vine copula is overall best both for the entire period and during the financial crisis. However, the simple Gumbel copula model shows better effects regarding increasing the Sharpe ratio in both periods. Somewhat surprisingly, mixed vines do not show better performance in terms of risk reduction compared to the less flexible single family vine copula models.The remainder of this paper is structured as follows. Section 2 presents a short review of the previous studies.Empirical methods such as copula modeling and portfolio optimization are discussed in Section 3. The data used are presented in Section 4. Section 5 presents our empirical analysis. Finally, Section 6 discusses the main conc...

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Analyzing Dependent Data with Vine Copulas

Cited by 196 publications

References 0 publications

An Alternative Approach to Measure Co-Movement between Two Time Series

An Alternative Approach to Measure Co-Movement between Two Time Series

Optimizing effective numbers of tests by vine copula modeling

Portfolio Optimization Based on Forecasting Models Using Vine Copulas: An Empirical Assessment for the Financial Crisis

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