Models characterized by autoregressive structure and random coefficients are powerful tools for the analysis of high-frequency, high-dimensional volatile time series. The available literature on such models is broad, but also sector-specific, overlapping, confusing. Most focus one property data, while much can be gained combining strength various their sources heterogeneity. We present a struct...

In this article, normal inverse Gaussian (NIG) autoregressive model is introduced. The parameters of the are estimated using expectation maximization (EM) algorithm. efficacy EM algorithm shown simulated and real-world financial data. It that NIG fit very well on considered data hence could be useful in modelling various real-life time-series

We show that, under suitable conditions, an operator acting like a shift on some sequence space has frequently hypercyclic random vector whose distribution is strongly mixing for the operator. This result will be applied to chaotic weighted shifts. also apply it every satisfying Frequent Hypercyclicity Criterion, recovering of Murillo and Peris.

be the set of k observations. Finding xak, the estimate or analysis of the state space xk, given Zk and the initial conditions is called the filtering problem. When the dynamic model for the process, f(·), and for the measurements, h(·), are linear, and the random components x0, wk, vk are uncorrelated Gaussian random vectors, then the solution is given by the classical Kalman filter equations ...

In one-bit compressed sensing, previous results state that sparse signals may be robustly recovered when the measurements are taken using Gaussian random vectors. In contrast to standard compressed sensing, these results are not extendable to natural non-Gaussian distributions without further assumptions, as can be demonstrated by simple counter-examples involving extremely sparse signals. We s...

This paper considers the problem of estimating the parameters of two-dimensional (2-D) moving average random (MA) fields. We first address the problem of expressing the covariance matrix of nonsymmetrical half-plane, noncausal, and quarter-plane MA random fields in terms of the model parameters. Assuming the random field is Gaussian, we derive a closedform expression for the Cramér–Rao lower bo...

Dimension reduction provides an important tool for preprocessing large scale data sets. A possible model for dimension reduction is realized by projecting onto the non-Gaussian part of a given multivariate recording. We prove that the subspaces of such a projection are unique given that the Gaussian subspace is of maximal dimension. This result therefore guarantees that projection algorithms un...

Following Södergren, we consider a collection of random variables on the space Xn unimodular lattices in dimension n: normalizations angles between N=N(n) shortest vectors lattice, and volumes spheres with radii equal to lengths these vectors. We investigate expected values certain functions (whose support depends parameter K=K(n)) evaluated at regime where K N are allowed tend infinity n rate ...