Zuzana Prášková

Effect of dependence on statistics for determination of change

Abstract Quite a number of test statistics and estimators for detection of a change in the mean of a series of independent observations were proposed and studied. The purpose of this paper is to examine the behaviour of these statistics if the observations are dependent, particularly, if they form a linear process.

Delay time in monitoring jump changes in linear models

Along the lines of Hušková and Koubková [Sequential procedures for detection of changes in autoregressive sequences, in Proceedings of Prague Stochastics 2006, M. Hušková and M. Janžura, eds., MatfyzPress, Charles University, Prague, pp. 437–447], we further investigate a sequential procedure for monitoring jump changes in linear models. Our main result shows that, under the alternative, the suitably normalized stopping time of the procedure has a standard normal limiting distribution. A number of examples are discussed and the finite sample validity of the asymptotics is checked via a small simulation study.

Robust monitoring of CAPM portfolio betas II

Detection of instabilities in various models Marie Hušková Charles University Prague Czech Republic The talk focuses on two setups: • Structural breaks in some CAPM with functional data, sequential monitoring procedures. Mostly based based on the paper: Robust monitoring of CAPM portfolio betas II, couathors: Z.Praskova, J.Steinebach, O. Chochola, JMVA 132, 2014, 58 – 81. • Detection of changes connected with martingale hypothesis testing Based on the paper: FourierType Tests Involving Martingale Difference Processes, coauthors: S. Meintanis, C. Kirch, Z. Hlavka, Econometric Reviews 36, 2017, 468 – 492. Both parts contain introduction, theoretical results, simulations and applications.

On Testing Changes in Autoregressive Parameters of a VAR Model

The article deals with the problem of testing a change in autoregressive matrices of the p-th order vector autoregressive process, VAR(p). The proposed test statistics are based on the likelihood ratio concept and are studied under the null hypothesis of no change in parameters. Their asymptotic behavior is derived under minimal moment assumptions in both cases where the time point of possible change is known a priori and is undefined. The Gumbel-type approximation of the test statistic is also developed, which previous papers on VAR(p) models do not cover.

Rate of Convergence for Simple Estimate in the Rejective Sampling

In this paper, rejective sampling of size n from a population consisting of N units is considered and the rate of convergence of simple linear estimator of the population total based on this sampling design is studied. The rejective sampling is defined as conditional Poisson sampling and asymptotic relations between probabilities of inclusion in the rejective and Poisson sampling, respectively, are utilized.

Monitoring Changes in RCA Models

In the paper a sequential monitoring scheme is proposed to detect instability of parameters in a random coefficient autoregressive (RCA) time series model of general order p. A given set of historical stable observations is available that serves as a training sample. The proposed monitoring procedure is based on the quasi-likelihood scores and the quasi-maximum likelihood estimators of the respective parameters computed from the training sample, and it is designed so that the sequential test has a small probability of a false alarm and asymptotic power one as the size of the training sample is sufficiently large. The asymptotic distribution of the detector statistic is established under both the null hypothesis of no change as well as under the alternative that a change occurs.

Bootstrap Change Point Testing for Dependent Data

Critical values of change point tests in location and regression models are usually based on limit distribution of the respective test statistics under the null hypothesis. However, the limit distribution is very often a functional of some Gaussian processes depending on unknown quantities that cannot be easily estimated. In many situations, convergence to the asymptotic distribution is rather slow and the asymptotic critical values are not well applicable in small and moderate samples. It has appeared that resampling methods provide reasonable approximations for critical values of test statistics for detection changes in location and regression models. In this chapter dependent wild bootstrap procedure for testing changes in linear model with weakly dependent regressors and errors will be proposed and its validity verified. More specifically, the concept of \(L_p\)-m-approximability will be used.

On Bayes Inference in Contingency Tables

The multinomial sampling model for IxJ contingency table is considered. Assuming that the multinomial probabilities have certain prior distribution and utilizing the fact that the posterior distribution of the logarithmic interactions is asymptotically normal we construct credible intervals and simultaneous credible intervals for logarithmic interactions.The results are compared with those obtained by classical methods.