Detecting relevant changes in time series models

Most of the literature on change-point analysis by means of hypothesis testing considers hypotheses of the form H0 : \theta_1 = \theta_2 vs. H1 : \theta_1 != \theta_2, where \theta_1 and \theta_2 denote parameters of the process before and after a change point. This paper takes a different perspective and investigates the null hypotheses of no relevant changes, i.e. H0 : ||\theta_1 - \theta_2|| ? \leq \Delta?, where || \cdot || is an appropriate norm. This formulation of the testing problem is motivated by the fact that in many applications a modification of the statistical analysis might not be necessary, if the difference between the parameters before and after the change-point is small. A general approach to problems of this type is developed which is based on the CUSUM principle. For the asymptotic analysis weak convergence of the sequential empirical process has to be established under the alternative of non-stationarity, and it is shown that the resulting test statistic is asymptotically normal distributed. Several applications of the methodology are given including tests for relevant changes in the mean, variance, parameter in a linear regression model and distribution function among others. The finite sample properties of the new tests are investigated by means of a simulation study and illustrated by analyzing a data example from economics.Comment: Keywords: change-point analysis, CUSUM, relevant changes, precise hypotheses, strong mixing, weak convergence under the alternative AMS Subject Classification: 62M10, 62F05, 62G1

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 non-trivial 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 US.Cramer-von Mises distance, quantile regression, distributional regression, location-scale model, bootstrap, wage distribution

An endogeneity correction based on a nonparametric control function approach

This paper considers a linear regression model with an endogenous regressor which is not normally distributed. It is shown that the corresponding coefficient can be consistently estimated without external instruments by adding a rank-based transformation of the regressor to the model and performing standard OLS estimation. In contrast to other approaches, our nonparametric control function approach does not rely on a conformably specified copula. Furthermore, the approach allows for the presence of additional exogenous regressors which may be (linearly) correlated with the endogenous regressor(s). Consistency and further asymptotic properties of the estimator are considered and the estimator is compared with copula based approaches by means of Monte Carlo simulations. An empirical application on wage data of the US current population survey demonstrates the usefulness of our method

Automated Portfolio Optimization Based on a New Test for Structural Breaks

We present a completely automated optimization strategy which combines the classical Markowitz mean-variance portfolio theory with a recently proposed test for structural breaks in covariance matrices. With respect to equity portfolios, global minimum-variance optimizations, which base solely on the covariance matrix, yield considerable results in previous studies. However, financial assets cannot be assumed to have a constant covariance matrix over longer periods of time. Hence, we estimate the covariance matrix of the assets by respecting potential change points. The resulting approach resolves the issue of determining a sample for parameter estimation. Moreover, we investigate if this approach is also appropriate for timing the reoptimizations. Finally, we apply the approach to two datasets and compare the results to relevant benchmark techniques by means of an out-of-sample study. It is shown that the new approach outperforms equally weighted portfolios and plain minimum-variance portfolios on average

A completely automated optimization strategy for global minimum-variance portfolios based on a new test for structural breaks

We present a completely automated optimization strategy which combines the classical Markowitz mean-variance portfolio theory with a recently proposed test for structural breaks in co- variance matrices. With respect to equity portfolios, global minimum-variance optimizations, which base solely on the covariance matrix, yield considerable results in previous studies. However, nancial assets cannot be assumed to have a constant covariance matrix over longer periods of time. Hence, we estimate the covariance matrix of the assets by respecting potential change points. The resulting approach resolves issues like timing or determining a sample for parameter estimation. Moreover, we apply the approach to two datasets and compare the results to relevant benchmark techniques by means of an out-of-sample study. It is shown that the new approach outperforms equally weighted portfolios and plain minimum-variance portfolios on average

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 directional and non-directional testing and is thus able to test separately whether a VaR-model is too conservative or underestimates the actual risk exposure. Second, we stress the importance of testing the property of independent and identically distributed (i.i.d.) VaRexceedances 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. In addition, the empirical analysis of a unique data set consisting of asset returns of an asset manager’s portfolios underline the usefulness of our new backtests especially in times of market turmoil

A fluctuation test for constant Spearman’s rho

We propose a CUSUM type test for constant correlation that goes beyond a previously suggested correlation constancy test by considering Spearman's rho in arbitrary dimensions. By using copula-based expressions, we simultaneously extend a previously suggested copula constancy test. We calculate the asymptotic null distribution 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. We give a local power result and analyse the test's behaviour in small samples