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

CUSUM-Type testing for changing parameters in a spatial autoregressive model of stock returns

The paper 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 allows for superior risk forecasts in portfolio management

A generalized functional delta method

We develop a generalized functional delta method, where the considered random function is not multiplied by a scalar, but by another function. It bases on a generalized Hadamard differentiability between special function spaces. For a certain class of functions, we calculate the Hadamard differential explicitely. We give an example, where the method allows for calculations that are not possible with previous methods

Monitoring stationarity and cointegration

We propose a monitoring procedure to detect a structural change from stationary to integrated behavior. When the procedure is applied to the residuals of a relationship between integrated series it thus monitors a structural change from a cointegrating relationship to a spurious relationship. The cointegration monitoring procedure is based on residuals from modified least squares estimation, using either Fully Modifi ed, Dynamic or Integrated Modified OLS. The procedure is inspired by Chu et al. (1996) in that it is based on parameter estimation on a pre-break \calibration" period only rather than being based on sequential estimation over the full sample. We investigate the asymptotic behavior of the procedures under the null, for ( fixed and local) alternatives and in case of parameter changes. We also study the finite sample performance via simulations. An application to credit default swap spreads illustrates the potential usefulness of the procedure

Separate estimation of spatial dependence parameters and variance parameters in a spatial model

This paper suggests a two step estimation procedure for a spatial model with different kinds of spatial dependence and heteroscedastic innovations. Since maximum likelihood estimation is cumbersome due to the large number of parameters, we use a generalized method of moments approach to estimate the parameters of spatial correlation which does not need the large number of variance parameters to be known. For illustration purposes, we apply our estimation procedure to daily stock returns of the Euro Stoxx 50 members. JEL subject classifications: C13, C51, G1

A simple and focused backtest of value at risk

We suggest a simple improvement of recent VaR-backtesting procedures based on time intervals between VaR-exceedances and show via Monte Carlo that our test has more power than its competitors against empirically relevant clustering alternatives

Monitoring correlation change in a sequence of random variables

We propose a monitoring procedure to test for the constancy of the correlation coefficient of a sequence of random variables. The idea of the method is that a historical sample is available and the goal is to monitor for changes in the correlation as new data become available. We introduce a detector which is based on the first hitting time of a CUSUM-type statistic over a suitably constructed threshold function. We derive the asymptotic distribution of the detector and show that the procedure detects a change with probability approaching unity as the length of the historical period increases. The method is illustrated by Monte Carlo experiments and the analysis of a real application with the log-returns of the Standard & Poor's 500 (S&P 500) and IBM stock assets

Dating multiple change points in the correlation matrix

We propose a nonparametric procedure for detecting and dating multiple change points in the correlation matrix of a sequence of random variables. The procedure is based on a test for changes in correlation matrices at an unknown point in time recently proposed by Wied (2014). Although the procedure requires constant expectations and variances, only mild assumptions on the serial dependence structure are assumed. We show the validity of the procedure including the convergence rate of the change point estimators. Moreover, we illustrate its performance in finite samples by means of a simulation study and the analysis of a real data example with financial returns. These examples show that the proposed algorithm has large power in finite samples