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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)

- Dmitrij Celov, Remigijus Leipus, Anne Philippe
- 2008

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)

- Dmitrij Celov, Remigijus Leipus, Anne Philippe
- 2008

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)

- Yang Yang, Remigijus Leipus, Jonas Siaulys
- J. Computational Applied Mathematics
- 2012

- Remigijus Leipus, Yang Yang, Lina Dindiene
- ITC
- 2015

In this paper, following [1], 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.

- Aldona Aleškevičienė, Remigijus Leipus, Jonas Šiaulys
- 2007

The paper considers the compound renewal model risk earlier introduced by Tang et al. [8]. We study the tail behavior of the finite-time ruin probability, ψ(x, t), in the case where the distribution of individual claims has consistent variation. The asymptotic relation, as initial capital x increases, holds uniformly for t in a corresponding region related… (More)

- R Leipus, A Philippe, D Puplinskait, D Surgailis
- 2013

It is well-known that the aggregated time series might have very different properties from those of the individual series, in particular, long memory. At the present time, aggregation has become one of the main tools for modelling of long memory processes. We review recent work on contempora-neous aggregation of random-coefficient AR(1) and related models,… (More)