Structural Constant Conditional Correlation

A small strand of recent literature is occupied with identifying simultaneity in multiple equation systems through autoregressive conditional heteroscedasticity. Since this approach assumes that the structural innovations are uncorrelated, any contemporaneous connection of the endogenous variables needs to be exclusively explained by mutual spillover effects. In contrast, this paper allows for instantaneous covariances, which become identifiable by imposing the constraint of structural constant conditional correlation (SCCC). In this, common driving forces can be modelled in addition to simultaneous transmission effects. The new methodology is applied to the Dow Jones and Nasdaq Composite indexes in a small empirical example, illuminating scope and functioning of the SCCC model.Simultaneity, Identification, EGARCH, CCC

A generalized Dynamic Conditional Correlation Model for Portfolio Risk Evaluation

We propose a generalization of the Dynamic Conditional Correlation multivariate GARCH model of Engle (2002) and of the Asymmetric Dynamic Conditional Correlation model of Cappiello et al. (2006). The model we propose introduces a block structure in parameter matrices that allows for interdependence with a reduced number of parameters. Our model nests the Flexible Dynamic Conditional Correlation model of Billio et al. (2006) and is named Quadratic Flexible Dynamic Conditional Correlation Multivariate GARCH. In the paper, we provide conditions for positive definiteness of the conditional correlations. We also present an empirical application to the Italian stock market comparing alternative correlation models for portfolio risk evaluation.Dynamic correlations, Block-structures, Flexible correlation models

Testing conditional independence using maximal nonlinear conditional correlation

In this paper, the maximal nonlinear conditional correlation of two random vectors $X$ and $Y$ given another random vector $Z$, denoted by $\rho_1(X,Y|Z)$, is defined as a measure of conditional association, which satisfies certain desirable properties. When $Z$ is continuous, a test for testing the conditional independence of $X$ and $Y$ given $Z$ is constructed based on the estimator of a weighted average of the form $\sum_{k=1}^{n_Z}f_Z(z_k)\rho^2_1(X,Y|Z=z_k)$, where $f_Z$ is the probability density function of $Z$ and the $z_k$'s are some points in the range of $Z$. Under some conditions, it is shown that the test statistic is asymptotically normal under conditional independence, and the test is consistent.Comment: Published in at http://dx.doi.org/10.1214/09-AOS770 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Correlation dynamics between Asia-Pacific, EU and US stock returns

This paper investigates the correlation dynamics in the equity markets of 13 Asia-Pacific countries, Europe and the US using the asymmetric dynamic conditional correlation GARCH model (AG-DCC-GARCH) introduced by Cappiello, Engle and Sheppard (2006). We find significant variation in correlation between markets through time. Stocks exhibit asymmetries in conditional correlations in addition to conditional volatility. Yet asymmetry is less apparent in less integrated markets. The Asian crisis acts as a structural break, with correlations increasing markedly between crisis countries during this period though the bear market in the early 2000s is a more significant event for correlations with developed markets. Our findings also provide further evidence consistent with increasing global market integration. The documented asymmetries and correlation dynamics have important implications for international portfolio diversification and asset allocation.dynamic conditional correlation; asymmetry; international portfolio diversification

A Multivariate GARCH Model with Time-Varying Correlations

In this paper we propose a new multivariate GARCH model with time-varying correlations. We adopt the vech representation based on the conditional variances and the conditional correlations. While each conditional-variance term is assumed to follow a univariate GARCH formulation, the conditional-correlation matrix is postulated to follow an autoregressive moving average type of analogue. By imposing some suitable restrictions on the conditional-correlation-matrix equation, we manage to construct a MGARCH model in which the conditional-correlation matrix is guaranteed to be positive definite during the optimisation. Thus, our new model retains the intuition and interpretation of the univariate GARCH model and yet satisfies the positive-definite condition as found in the constant-correlation and BEKK models. We report some Monte Carlo results on the finite-sample distributions of the QMLE of the varying-correlation MGARCH model. The new model is applied to some real data sets. It is found that extending the constant-correlation model to allow for time-varying correlations provides some interesting time histories that are not available in a constant-correlation model.

Structural Conditional Correlation

A small strand of recent literature is occupied with identifying simultaneity in multiple equation systems through autoregressive conditional heteroscedasticity. Since this approach assumes that the structural innovations are uncorrelated, any contemporaneous connection of the endogenous variables needs to be exclusively explained by mutual spillover effects. In contrast, this paper allows for instantaneous covariances, which become identifiable by imposing the constraint of structural constant / dynamic conditional correlation (SCCC / SDCC). In this, common driving forces can be modelled in addition to simultaneous transmission effects. The methodology is applied to the Dow Jones and Nasdaq Composite indexes, illuminating scope and functioning of the new models.Simultaneity; Identification; EGARCH; Conditional Correlation

Correlated Binomial Models and Correlation Structures

We discuss a general method to construct correlated binomial distributions by imposing several consistent relations on the joint probability function. We obtain self-consistency relations for the conditional correlations and conditional probabilities. The beta-binomial distribution is derived by a strong symmetric assumption on the conditional correlations. Our derivation clarifies the 'correlation' structure of the beta-binomial distribution. It is also possible to study the correlation structures of other probability distributions of exchangeable (homogeneous) correlated Bernoulli random variables. We study some distribution functions and discuss their behaviors in terms of their correlation structures.Comment: 12 pages, 7 figure

Dynamic Conditional Correlation with Elliptical Distributions

The Dynamic Conditional Correlation model of Engle has made the estimation of multivariate GARCH models feasible for reasonably big vectors of securities’ returns. In the present paper we show how Engle’s twosteps estimate of the model can be easily extended to elliptical conditional distributions and apply different leptokurtic DCC models to some stocks listed at the Milan Stock Exchange. A free software written by the authors to carry out all the required computations is presented as well.Multivariate GARCH, Dynamic conditional correlation, Generalized method of moments

A local dynamic conditional correlation model

This paper introduces the idea that the variances or correlations in financial returns may all change conditionally and slowly over time. A multi-step local dynamic conditional correlation model is proposed for simultaneously modelling these components. In particular, the local and conditional correlations are jointly estimated by multivariate kernel regression. A multivariate k-NN method with variable bandwidths is developed to solve the curse of dimension problem. Asymptotic properties of the estimators are discussed in detail. Practical performance of the model is illustrated by applications to foreign exchange rates.Local and conditional correlations; multivariate nonparametric ARCH; multivariate kernel regression; multivariate k-NN method

Structural Dynamic Conditional Correlation

In the literature of identifcation through autoregressive conditional heteroscedasticity, Weber (2008) developed the structural constant conditional correlation (SCCC) model. Besides determining linear simultaneous in uences between several variables, this model considers interaction in the structural innovations. Even though this allows for common fundamental driving forces, these cannot explain time variation in correlations of observed variables, which still have to rely on causal transmission eects. In this context, the present paper extends the analysis to structural dynamic conditional correlation (SDCC). The additional fexibility is shown to make an important contribution in the estimation of empirical real-data examples.Simultaneity, Identifcation, EGARCH, DCC