Regular multidimensional stationary time series

Beta Jacobi processes

We define and study a multidimensional process that generalizes the eigenvalues of matrix Jacobi processes on the one hand and whose stationary distribution is given by the beta Jacobi ensemble on the other hand.

Statistical inference of subcritical strongly stationary Galton--Watson processes with regularly varying immigration

We describe the asymptotic behavior of the conditional least squares estimator of the offspring mean for subcritical strongly stationary Galton--Watson processes with regularly varying immigration with tail index $α\in (1,2)$. The limit law is the ratio of two dependent stable random variables with indices $α/2$ and $2α/3$, respectively, and it has a continuously differentiable density function. We use point process technique in the proofs.

Semiparametric stationarity tests based on adaptive multidimensional increment ratio statistics

In this paper, we show that the adaptive multidimensional increment ratio estimator of the long range memory parameter defined in Bardet and Dola (2012) satisfies a central limit theorem (CLT in the sequel) for a large semiparametric class of Gaussian fractionally integrated processes with memory parameter $d \in (-0.5,1.25)$. Since the asymptotic variance of this CLT can be computed, tests of stationarity or nonstationarity distinguishing the assumptions $d<0.5$ and $d \geq 0.5$ are constructed. These tests are also consistent tests of unit root. Simulations done on a large benchmark of short…

Vector-valued Generalised Ornstein-Uhlenbeck Processes

Generalisations of the Ornstein-Uhlenbeck process defined through Langevin equation $dU_t = - ΘU_t dt + dG_t,$ such as fractional Ornstein-Uhlenbeck processes, have recently received a lot of attention in the literature. In particular, estimation of the unknown parameter $Θ$ is widely studied under Gaussian stationary increment noise $G$. Langevin equation is well-known for its connections to physics. In addition to that, motivation for studying Langevin equation with a general noise $G$ stems from the fact that the equation characterises all univariate stationary processes. Most of the litera…

非零均值平稳球不变随机过程的参数与半参数Fisher信息矩阵

On the parametric and semiparametric Fisher information matrix for non-zero mean stationary spherical invariant random processes

本文将Whittle公式推广至非零均值平稳复合高斯过程，在统一框架下推导出参数与半参数Fisher信息矩阵的闭式谱域表达式，支持重尾信号处理性能分析。

Suppression of random noise by the separation of frequencies

It is shown that a well-known theory of random stationary processes contain contradictions. Integral representations of correlation functions and random stationary processes are investigated further. The new method of struggle with handicaps is received on the basis of the carried out researches. Method of dealing with noise leads to a new method of identification of dynamic characteristics of control objects in a class of multidimensional linear stationary models. As an example, describe an algorithm for obtaining the differential equation-wire feed control aircraft pitch, taking into account…