The paper is concerned with the estimation of the long memory parameter in a conditionally heteroskedastic model proposed by Giraitis et al. (1999b). We consider estimation methods based on the partial sums of the squared observations, which are similar in spirit to the classical R/S analysis, as well as spectral domain approximate maximum likelihood… (More)
We suggest a rescaled variance type test for stationarity (null hypothesis) against deter-ministic trends and unit roots. The asymptotic (parameter free) distribution of the test is derived and critical values tabulated by simulations for a wide class of stationary errors with short, long or negative dependence structure. The proposed test detects a… (More)
We consider the long memory and leverage properties of a model for the conditional variance V 2 t of an observable stationary sequence X t , where V 2 t is the square of an inhomogeneous linear combination of Xs, s < t, with square summable weights bj. This model, which we call linear ARCH (LARCH), specializes, when V 2 t depends only on Xt−1, to the… (More)
The paper studies the aggregation/disaggregation problem of random parameter AR(1) processes and its relation to the long memory phenomenon. We give a characterization of a subclass of aggre-gated processes which can be obtained from simpler, " elementary " , cases. In particular cases of the mixture densities, the structure (moving average representation)… (More)
In this paper, following , the equivalence of the tail probabilities for the maximum and the sum with heavy-tailed summands under the negative dependence structure is investigated. Applications to some risk models with financial and insurance risks are provided. The Monte-Carlo simulation study illustrates the results.
The paper concerns the asymptotic distribution of the mixture density estimator, proposed by Leipus et al. (2006), in the aggrega-tion/disaggregation problem of random parameter AR(1) process. We prove that, under mild conditions on the (semiparametric) form of the mixture density, the estimator is asymptotically normal. The proof is based on the limit… (More)
This paper considers the real-valued random variables X