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Autoregressive approaches to import–export time series I: basic techniques

Luca Di Persio

https://doi.org/10.15559/15-VMSTA22

Pub. online: 20 Apr 2015 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications Volume 2, Issue 1 (2015), pp. 51–65

Abstract

This work is the first part of a project dealing with an in-depth study of effective techniques used in econometrics in order to make accurate forecasts in the concrete framework of one of the major economies of the most productive Italian area, namely the province of Verona. In particular, we develop an approach mainly based on vector autoregressions, where lagged values of two or more variables are considered, Granger causality, and the stochastic trend approach useful to work with the cointegration phenomenon. Latter techniques constitute the core of the present paper, whereas in the second part of the project, we present how these approaches can be applied to economic data at our disposal in order to obtain concrete analysis of import–export behavior for the considered productive area of Verona.

Asymptotic normality of discretized maximum likelihood estimator for drift parameter in homogeneous diffusion model

Kostiantyn Ralchenko

https://doi.org/10.15559/15-VMSTA21

Pub. online: 13 Apr 2015 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications Volume 2, Issue 1 (2015), pp. 17–28

Abstract

We prove the asymptotic normality of the discretized maximum likelihood estimator for the drift parameter in the homogeneous ergodic diffusion model.

Nonparametric Bayesian inference for multidimensional compound Poisson processes

Shota Gugushvili Frank van der Meulen Peter Spreij

https://doi.org/10.15559/15-VMSTA20

Pub. online: 13 Mar 2015 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications Volume 2, Issue 1 (2015), pp. 1–15

Abstract

Given a sample from a discretely observed multidimensional compound Poisson process, we study the problem of nonparametric estimation of its jump size density $r_{0}$ and intensity $\lambda _{0}$. We take a nonparametric Bayesian approach to the problem and determine posterior contraction rates in this context, which, under some assumptions, we argue to be optimal posterior contraction rates. In particular, our results imply the existence of Bayesian point estimates that converge to the true parameter pair $(r_{0},\lambda _{0})$ at these rates. To the best of our knowledge, construction of nonparametric density estimators for inference in the class of discretely observed multidimensional Lévy processes, and the study of their rates of convergence is a new contribution to the literature.

2010 Mathematics Subject Classification index

https://doi.org/10.15559/15-VMSTA12MI

Pub. online: 12 Feb 2015 Type: 2010 Mathematics Subject Classification Index

Journal: Modern Stochastics: Theory and Applications Volume 1, Issue 2 (2014), pp. 215–217

Subject index

https://doi.org/10.15559/15-VMSTA12SI

Pub. online: 12 Feb 2015 Type: Subject Index

Journal: Modern Stochastics: Theory and Applications Volume 1, Issue 2 (2014), pp. 213–214

Author index

https://doi.org/10.15559/15-VMSTA12AI

Pub. online: 12 Feb 2015 Type: Author Index

Journal: Modern Stochastics: Theory and Applications Volume 1, Issue 2 (2014), p. 211

Testing hypotheses on moments by observations from a mixture with varying concentrations

Alexey Doronin Rostyslav Maiboroda

https://doi.org/10.15559/15-VMSTA19

Pub. online: 4 Feb 2015 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications Volume 1, Issue 2 (2014), pp. 195–209

Abstract

A mixture with varying concentrations is a modification of a finite mixture model in which the mixing probabilities (concentrations of mixture components) may be different for different observations. In the paper, we assume that the concentrations are known and the distributions of components are completely unknown. Nonparametric technique is proposed for testing hypotheses on functional moments of components.

Asymptotics for functionals of powers of a periodogram

Lyudmyla Sakhno

https://doi.org/10.15559/15-VMSTA15

Pub. online: 4 Feb 2015 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications Volume 1, Issue 2 (2014), pp. 181–194

Abstract

We present large sample properties and conditions for asymptotic normality of linear functionals of powers of the periodogram constructed with the use of tapered data.

Practical approaches to the estimation of the ruin probability in a risk model with additional funds

Yuliya Mishura Olena Ragulina Oleksandr Stroyev

https://doi.org/10.15559/15-VMSTA18

Pub. online: 2 Feb 2015 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications Volume 1, Issue 2 (2014), pp. 167–180

Abstract

We deal with a generalization of the classical risk model when an insurance company gets additional funds whenever a claim arrives and consider some practical approaches to the estimation of the ruin probability. In particular, we get an upper exponential bound and construct an analogue to the De Vylder approximation for the ruin probability. We compare results of these approaches with statistical estimates obtained by the Monte Carlo method for selected distributions of claim sizes and additional funds.

A martingale bound for the entropy associated with a trimmed filtration on

R^{d}

Alexei Kulik Taras Tymoshkevych

https://doi.org/10.15559/15-VMSTA16

Pub. online: 2 Feb 2015 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications Volume 1, Issue 2 (2014), pp. 151–165

Abstract

Using martingale methods, we provide bounds for the entropy of a probability measure on ${\mathbb{R}}^{d}$ with the right-hand side given in a certain integral form. As a corollary, in the one-dimensional case, we obtain a weighted log-Sobolev inequality.

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