Detection of Changes in INAR Models

In the present paper we develop on-line procedures for detecting changes in the parameters of integer valued autoregressive models of order one. Tests statistics based on probability generating functions are constructed and studied. The asymptotic behavior of the tests under the null hypothesis as well as under certain alternatives is derived

Change Detection in INARCH Time Series of Counts

In the present paper we develop an online procedure for detecting changes in the parameters of integer ARCH models of order one. The test statistic utilizes the notion of the empirical probability generating function. The asymptotic behavior of the test under the null hypothesis is derived

On Distinguishing between Random Walk and Change in the Mean Alternatives

We study test procedures that detect structural breaks in underlying data sequences. In particular, we wish to discriminate between different reasons for these changes, such as (1) shifting means, (2) random walk behavior, and (3) constant means but innovations switching from stationary to difference stationary behavior. Almost all procedures presently available in the literature are Simultaneously sensitive to all three types of alternatives. The test statistics under investigation are based on functionals of the partial sums of observations. These Cumulative sum-type (CUSUM-type) statistics have limit distributions if the mean remains constant and the errors satisfy the central limit theorem but tend to infinity in the case when any of the alternatives (1), (2), or (3) holds. On removing the effect of the shifting mean, however, divergence of the test statistics will only occur under the random walk behavior, which in turn enables statisticians not only to detect structural breaks but also to specify their causes. The results are underlined by it simulation study and an application to returns of the German stock index DAX

Estimating a gradual parameter change in an AR(1)-process

We discuss the estimation of a change-point t(0) at which the parameter of a (non-stationary) AR(1)-process possibly changes in a gradual way. Making use of the observations X-1,..., X-n, we shall study the least squares estimator (t(0)) over cap for t(0), which is obtained by minimizing the sum of squares of residuals with respect to the given parameters. As a first result it can be shown that, under certain regularity and moment assumptions, (t(0)) over cap /n is a consistent estimator for t(0), where t(0) = left perpendicularn tau(0)right perpendicular, with 0 (P) tau(0) (n ->infinity). Based on the rates obtained in the proof of the consistency result, a first, but rough, convergence rate statement can immediately be given. Under somewhat stronger assumptions, a precise rate can be derived via the asymptotic normality of our estimator. Some results from a small simulation study are included to give an idea of the finite sample behaviour of the proposed estimator

Robust monitoring of CAPM portfolio betas II

In this work, we extend our study in Chochola et al. [7] and propose some robust sequential procedure for the detection of structural breaks in a Functional Capital Asset Pricing Model (FCAPM). The procedure is again based on M-estimates and partial weighted sums of M-residuals and robustifies the approach of Aue et al. [3], in which ordinary least squares (OLS) estimates have been used. Similar to Aue et al. [3], and in contrast to Chochola et al. [7], high-frequency data can now also be taken into account. The main results prove some null asymptotics for the suggested test as well as its consistency under local alternatives. In addition to the theoretical results, some conclusions from a small simulation study together with an application to a real data set are presented in order to illustrate the finite sample performance of our monitoring procedure. (C) 2014 Elsevier Inc. All rights reserved

A nonparametric model for analysis of the EURO bond market

The goal of this paper is to analyse by statistical methods the positions of individual countries within the EURO bond market. To this purpose we assume that each of the individual yield curves equals the sum of a common effect curve and of a country-specific one, interpreted as a spread. This allows to analyse the position of the countries by a two-stage nonparametric regression model. In addition, we provide a nonparametric bootstrap test. Both the estimated regression curves and the test indicate significant differences among European Monetary Union countries. A method for quantification of these differences is designed