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Prediction intervals and regions for multivariate time series models with sieve bootstrap

Różański R., Chłapiński G., Hławka M., Jamróz K., Kawecki M., Zagdański A.

Probability and Mathematical Statistics

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2018

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Vol. 38, Fasc. 2

317--357

EN

In the paper, the construction of unconditional bootstrap prediction intervals and regions for some class of second order stationary multivariate linear time series models is considered. Our approach uses the sieje bootstrap procedure introduced by Kreiss (1992) and Bühlmann (1997). Basic theoretical results concerning consistency of the bootstrap replications and the bootstrap prediction regions are proved. We present a simulation study comparing the proposed bootstrap methods with the Box-Jenkins approach.

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On estimation in the multiplicative intensity model via histogram sieve

Różański R., Zagdański A.

Probability and Mathematical Statistics

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2001

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Vol. 21, Fasc. 1

89--99

EN

In the paper we consider the problem of estimating stochastic intensity of a point process from multiplicative intensity model using the method of sieves of Grenander [6]. Basic properties of the histogram sieve estimator including consistency and asymptotic normality are proved. Our approach extends results obtained in Leśkow and Różański [13].

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On the application of the method of sieves in estimation of the intensity of multiplicative point processes

Zagdański A.

Prace Naukowe Instytutu Matematyki Politechniki Wrocławskiej. Konferencje

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2001

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Vol. 24, nr 3

129-136

EN

We consider the problem of estimation the stochastic intensity of point processes with multiplicative intensity model. For this purpose Grenander's [5] method of sieves is used. Results concerned with consistency and asymptotic normality of the sieve estimator are formulated. Proposed method of estimation is generalized to the case of multivariate point processes.

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Prediction intervals for stationary time series using the sieve bootstrap metod

Zagdański A.

Demonstratio Mathematica

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2001

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Vol. 34, nr 2

469-481

EN

We consider the problem of constructing prediction intervals for future observations of stationary time series. Our approach relies on the sieve bootstrap procedure introduced by Blihimann (1997, 1998) which is asymptotically valid for the rich class of linear stationary processes which can be inverted and represented as an autoregressive processes of order infinity (AR(oo)). We extend the results obtained earlier by Stine (1987) for autoregressive time series of known order. A more traditional Gaussian strategy is also presented. We verify accuracy of the proposed methods via numerical comparison including both Gaussian and non-Gaussian data.