Related papers: Order 1 autoregressive process of finite length

There exist important stochastic physical processes involving infinite mean waiting times. The mean divergence has dramatic consequences on the process dynamics. Fractal time random walks, a diffusion process, and subrecoil laser cooling, a…

Binomial time series in which the logit of the probability of success is modelled as a linear function of observed regressors and a stationary latent Gaussian process are considered. Score tests are developed to first test for the existence…

Processes controlled by stochastic synthesis and degradation (SSD) are widespread in biology but their reaction kinetics are not well understood. Using methods borrowed from the theory of resetting processes, we determine the first-passage…

Classical first passage under resetting is a paradigm in the search process. Despite its multitude of applications across interdisciplinary sciences, experimental realizations of such resetting processes posit practical challenges in…

We investigate the statistics of recurrences to finite size intervals for chaotic dynamical systems. We find that the typical distribution presents an exponential decay for almost all recurrence times except for a few short times affected…

We consider regression scenarios where it is natural to impose an order constraint on the coefficients. We propose an order-constrained version of L1-regularized regression for this problem, and show how to solve it efficiently using the…

Conditions are obtained for a Gaussian vector autoregressive time series of order $k$, VAR($k$), to have univariate margins that are autoregressive of order $k$ or lower-dimensional margins that are also VAR($k$). This can lead to…

Fluctuations in stochastic systems are usually characterized by the full counting statistics, which analyzes the distribution of the number of events taking place in the fixed time interval. In an alternative approach, the distribution of…

The time of the first occurrence of a threshold crossing event in a stochastic process, known as the first passage time, is of interest in many areas of sciences and engineering. Conventionally, there is an implicit assumption that the…

A family of continuous-time generalized autoregressive conditionally heteroscedastic processes, generalizing the $\operatorname {COGARCH}(1,1)$ process of Kl\"{u}ppelberg, Lindner and Maller [J. Appl. Probab. 41 (2004) 601--622], is…

A statistical model of discrete finite length random processes with negative power law spectral densities is presented. The definition of terms is followed by a description of the spectral density trend. An algorithmic construction of…

We introduce a method for reconstructing macroscopic models of one-dimensional stochastic processes with long-range correlations from sparsely sampled time series by combining fractional calculus and discrete-time Langevin equations. The…

For each of (i) arbitrary stochastic reset, (ii) deterministic reset with arbitrary period, (iii) reset at arbitrary constant rate, and then in the sense of either (a) first-order stochastic dominance or (b) expectation (i.e. for each of…

In this paper, we study the asymptotic relation between the first crossing point and the last exit time for Gaussian order statistics which are generated by stationary weakly and strongly dependent Gaussian sequences. It is shown that the…

Recently noticed ability of restart to reduce the expected completion time of first-passage processes allows appealing opportunities for performance improvement in a variety of settings. However, complex stochastic processes often exhibit…

First passage of stochastic processes under resetting has recently been an active research topic in the field of statistical physics. However, most of previous studies mainly focused on the systems with continuous time and space. In this…

In this paper, we consider a Banach space valued random coefficient autoregressive process. Our studies on this process involve existence, weak law of large numbers, strong law of large numbers, some exponential inequalities, central limit…

Investigating the relationship, particularly the lead-lag effect, between time series is a common question across various disciplines, especially when uncovering biological process. However, analyzing time series presents several…

The persistence of a stochastic variable is the probability that it does not cross a given level during a fixed time interval. Although persistence is a simple concept to understand, it is in general hard to calculate. Here we consider zero…

In this paper we suggest two continuous-time models which exhibit an autoregressive structure. We obtain existence and uniqueness results and study the structure of the solution processes. One of the models, which corresponds to general…