Dominik Wied

TESTING FOR A CHANGE IN CORRELATION AT AN UNKNOWN POINT IN TIME USING AN EXTENDED FUNCTIONAL DELTA METHOD

We propose a new test against a change in correlation at an unknown point in time based on cumulated sums of empirical correlations. The test does not require that inputs are independent and identically distributed under the null. We derive its limiting null distribution using a new functional delta method argument, provide a formula for its local power for particular types of structural changes, give some Monte Carlo evidence on its finite-sample behavior, and apply it to recent stock returns.

Misspecification Testing in a Class of Conditional Distributional Models

We propose a specification test for a wide range of parametric models for the conditional distribution function of an outcome variable given a vector of covariates. The test is based on the Cramer–von Mises distance between an unrestricted estimate of the joint distribution function of the data and a restricted estimate that imposes the structure implied by the model. The procedure is straightforward to implement, is consistent against fixed alternatives, has nontrivial power against local deviations of order n − 1/2 from the null hypothesis, and does not require the choice of smoothing parameters. In an empirical application, we use our test to study the validity of various models for the conditional distribution of wages in the United States.

Multiple break detection in the correlation structure of random variables

Correlations between random variables play an important role in applications, e.g. in financial analysis. More precisely, accurate estimates of the correlation between financial returns are crucial in portfolio management. In particular, in periods of financial crisis, extreme movements in asset prices are found to be more highly correlated than small movements. It is precisely under these conditions that investors are extremely concerned about changes on correlations. A binary segmentation procedure to detect the number and position of multiple change points in the correlation structure of random variables is proposed. The procedure assumes that expectations and variances are constant and that there are sudden shifts in the correlations. It is shown analytically that the proposed algorithm asymptotically gives the correct number of change points and the change points are consistently estimated. It is also shown by simulation studies and by an empirical application that the algorithm yields reasonable results.

A New Set of Improved Value-at-Risk Backtests

We propose a new set of formal backtests for VaR-forecasts that significantly improve upon existing backtesting procedures. Our new test of unconditional coverage can be used for both one-sided and two-sided testing, which leads to a significantly increased power. Second, we stress the importance of testing the property of independent and identically distributed (i.i.d.) VaR-exceedances and propose a simple approach that explicitly tests for the presence of clusters in VaR-violation processes. Results from a simulation study indicate that our tests significantly outperform competing backtests in several distinct settings.

A fluctuation test for constant Spearman's rho with nuisance-free limit distribution

A CUSUM type test for constant correlation that goes beyond a previously suggested correlation constancy test by considering Spearmans rho in arbitrary dimensions is proposed. Since the new test does not require the existence of any moments, the applicability on usually heavy-tailed financial data is greatly improved. The asymptotic null distribution is calculated using an invariance principle for the sequential empirical copula process. The limit distribution is free of nuisance parameters and critical values can be obtained without bootstrap techniques. A local power result and an analysis of the behavior of the test in small samples are provided.

A Nonparametric Test for a Constant Correlation Matrix

We propose a nonparametric procedure to test for changes in correlation matrices at an unknown point in time. The new test requires constant expectations and variances, but only mild assumptions on the serial dependence structure, and has considerable power in finite samples. We derive the asymptotic distribution under the null hypothesis of no change as well as local power results and apply the test to stock returns.

CUSUM‐Type Testing for Changing Parameters in a Spatial Autoregressive Model for Stock Returns

The article suggests a CUSUM‐type test for time‐varying parameters in a recently proposed spatial autoregressive model for stock returns and derives its asymptotic null distribution as well as local power properties. As can be seen from Euro Stoxx 50 returns, a combination of spatial modelling and change point tests might allow for superior risk forecasts in portfolio management.

Nonparametric tests for constant tail dependence with an application to energy and finance

New tests for detecting structural breaks in the tail dependence of multivariate time series using the concept of tail copulas are presented. To obtain asymptotic properties, we derive a new limit result for the sequential empirical tail copula process. Moreover, consistency of both the tests and a break-point estimator are proven. We analyze the finite sample behavior of the tests by Monte Carlo simulations. Finally, and crucial from a risk management perspective, we apply the new findings to datasets from energy and financial markets.

Testing for changes in Kendall’s tau

For a bivariate time series

Testing for Structural Breaks in Correlations: Does it Improve Value-at-Risk Forecasting?

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