A note of kernel smoothing of an estimator of a periodic function in the multiplicative intensity model

The estimator obtained by the kernel regularization of the sieve-based maximum likelihood estimator (MLE) of a periodic function in the multiplicative intensity model is considered. Under some regularity assumptions it is shown that this estimator is L1 consistent and asymptotically normal. The paper generalizes the result of Leskow (1988) obtained for a histogram estimator in this model.kernel method sieve-based maximum likelihood estimator periodic function mixing property

Ergodic behavior and estimation for periodically correlated processes

A complex second-order stochastic process {X(t); t [set membership, variant] } is periodically correlated (PC) when its mean function m(t) and covariance R(s, t) are periodic with the period T. In the following note the relationship between the hierarchy of chaos and estimation for the stochastic process is investigated. The results are based on the Correspondence Principle for the PC processes.Periodically correlated process [phi]-mixing spectral density estimation

Subsampling for APC stochastic processes

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Histogram maximum likelihood estimator in the multiplicative intensity model

In the paper the maximum likelihood estimator of a deterministic function of the stochastic intensity of a point process is derived by the method of sieves. Consistency and asymptotic normality of this estimator are proved.point process maximum likelihood estimator sieve method [psi]-mixing

MODELING STNOCK MARKET INDEXES WITH COPULA FUNCTIONS (Zastosowanie funkcji kopuli w modelowaniu indeksów gieldowych)

Contemporary financial risk management is significantly based on the analysis of time series of returns. One of the most significant errors frequently committed by analysts is the predominant use of normal distributions when it is clear that the returns are not normal. Copula models and models for non-normal multivariate distributions provide new tools to solve the problem because the obtained results are immediately applicable in portfolio management, option pricing and measuring risk without assuming normality. Therefore, both a theoretician and a practitioner are interested in multivariate models for returns and copula functions. The copula function models provide an effective and interesting technique of constructing multivariate distribution starting from marginal ones. Due to Sklar's result established in 1959, we can present any multivariate distribution with a help of corresponding marginal distributions and a selected copula function. In this work we present an application of copula function to construct multivariate conditional distributions of times series. In the last part of this paper dynamic models such as DCC-MVGARCH and conditional copula are analyzed. Moreover, we also present an application of bootstrap in the context of copula function. This work is appended by examples showing practical application of our work

Central limit theorem in the functional approach

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Subsampling for continuous-time almost periodically correlated processes

International audienceIn this work we investigate the problem of consistency of subsampling procedure for estimators in continuous time nonstationary stochastic processes with periodic or almost periodic covariance structure. The motivation for this work comes from the difficulty associated with handling the asymptotic distributions corresponding to estimates of second order characteristics for such nonstationary processes. It is shown that an appropriately normalized estimator has a consistent subsampling version provided that some mild regularity conditions are fulfilled. We also prove the mean square and almost everywhere consistency of our subsampling procedure. As a result of the research, we are able to construct the subsampling-based confidence intervals for the relevant characteristics of such nonstationary processes. We show that our results can be generalized to other nonstationary continuous time processes. At the end of the paper, simulations and real data applications are considered