Josef Steinebach

ON LEAST SQUARES ESTIMATES OF AN EXPONENTIAL TAIL COEFFICIENT

Consider a sample Zi,...,Z„ of i.i.d r.v.s with tail behavior P{Zi > z) = r(z)exp(—Äz), where r( ) is an (unknown) regularly varying function as z —• oo, and R is a constant. Least squares estimators are proposed here for the problem of estimating the exponential tail coefiicient R. We mainly prove consistency of the proposed estimators. Some Simulation results are presented as well in order to illustrate the finite sample behavior. Herein, adaptive methods are suggested to determine the number k = k„ of upper order statistics, which should be taken into account for estimation. Without loss of generality we shall assume positivity of the random variables Zi

Estimation in Random Coefficient Autoregressive Models

We propose the quasi-maximum likelihood method to estimate the parameters of an RCA(1) process, i.e. a random coefficient autoregressive time series of order 1. The strong consistency and the asymptotic normality of the estimators are derived under optimal conditions. Copyright 2006 Blackwell Publishing Ltd.

SEQUENTIAL TESTING FOR THE STABILITY OF HIGH-FREQUENCY PORTFOLIO BETAS

Despite substantial criticism, variants of the capital asset pricing model (CAPM) remain to this day the primary statistical tools for portfolio managers to assess the performance of financial assets. In the CAPM, the risk of an asset is expressed through its correlation with the market, widely known as the beta. There is now a general consensus among economists that these portfolio betas are time-varying and that, consequently, any appropriate analysis has to take this variability into account. Recent advances in data acquisition and processing techniques have led to an increased research output concerning high-frequency models. Within this framework, we introduce here a modified functional CAPM and sequential monitoring procedures to test for the constancy of the portfolio betas. As our main results we derive the large-sample properties of these monitoring procedures. In a simulation study and an application to S&P 100 data we show that our method performs well in finite samples.

Testing for changes in the mean or variance of a stochastic process under weak invariance

Asymptotic CUSUM tests are derived for detecting changes in the mean or variance of a stochastic process for which a weak invariance principle is available. Conditions for the consistency of these tests are also discussed.

Exact convergence rates in strong approximation laws for large increments of partial sums

SummaryConsider partial sumsSn of an i.i.d. sequenceX1X2, ..., of centered random variables having a finite moment generating function ϕ in a neighborhood of zero. The asymptotic behaviour of

On the estimation of the adjustment coefficient in risk theory via intermediate order statistics

U_n = \mathop {\max }\limits_{0 \leqq k \leqq n - b_n } (S_{k - b_n } - S_k )

On a semiparametric regression model whose errors form a linear process with negatively associated innovations

is investigated, where 1≦bn≦n denotes an integer sequence such thatbn/logn→∞ asn→∞. In particular, ifbn=o(logpn) asn→∞ for somep>1, the exact convergence rate ofUn/bnαn=1 +0 (1) is determined, where αn depends uponbn and the distribution ofX1. In addition, a weak limit law forUn is derived. Finally, it is shown how strong invariance takes over if