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Asymptotic normality of randomized periodogram for estimating quadratic variation in mixed Brownian–fractional Brownian model

Ehsan Azmoodeh Tommi Sottinen Lauri Viitasaari

https://doi.org/10.15559/15-VMSTA24

Pub. online: 11 May 2015 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications Volume 2, Issue 1 (2015), pp. 29–49

Abstract

We study asymptotic normality of the randomized periodogram estimator of quadratic variation in the mixed Brownian–fractional Brownian model. In the semimartingale case, that is, where the Hurst parameter H of the fractional part satisfies $H\in (3/4,1)$, the central limit theorem holds. In the nonsemimartingale case, that is, where $H\in (1/2,3/4]$, the convergence toward the normal distribution with a nonzero mean still holds if $H=3/4$, whereas for the other values, that is, $H\in (1/2,3/4)$, the central convergence does not take place. We also provide Berry–Esseen estimates for the estimator.

Asymptotic normality of randomized periodogram for estimating quadratic variation in mixed Brownian–fractional Brownian model

Ehsan Azmoodeh Tommi Sottinen Lauri Viitasaari

https://doi.org/10.15559/15-MSTA24

Pub. online: 11 May 2015 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications* Volume 2, Issue 1 (2015), pp. 29–49

Abstract

The rate of convergence to the normal law in terms of pseudomoments

Yuliya Mishura Yevheniya Munchak Petro Slyusarchuk

https://doi.org/10.15559/15-VMSTA23

Pub. online: 21 Apr 2015 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications Volume 2, Issue 2 (2015), pp. 95–106

Abstract

We establish the rate of convergence of distributions of sums of independent identically distributed random variables to the Gaussian distribution in terms of truncated pseudomoments by implementing the idea of Yu. Studnyev for getting estimates of the rate of convergence of the order higher than ${n}^{-1/2}$.

The rate of convergence to the normal law in terms of pseudomoments

Yuliya Mishura Yevheniya Munchak Petro Slyusarchuk

https://doi.org/10.15559/15-MSTA23

Pub. online: 21 Apr 2015 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications* Volume 2, Issue 2 (2015), pp. 95–106

Abstract

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.

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

Luca Di Persio

https://doi.org/10.15559/15-MSTA22

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

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.

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

Kostiantyn Ralchenko

https://doi.org/10.15559/15-MSTA21

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.

Nonparametric Bayesian inference for multidimensional compound Poisson processes

Shota Gugushvili Frank van der Meulen Peter Spreij

https://doi.org/10.15559/15-MSTA20

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

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