Related papers: An autoregressive model leading to stable distribu…
We consider a family of multivariate autoregressive stochastic sequences that restart when hit a neighbourhood of the origin, and study their distributional limits when the autoregressive coefficient tends to one, the noise scaling…
We investigate a stationary random coefficient autoregressive process. Using renewal type arguments tailor-made for such processes, we show that the stationary distribution has a power-law tail. When the model is normal, we show that the…
A nearly unstable sequence of stationary spatial autoregressive processes is investigated, when the sum of the absolute values of the autoregressive coefficients tends to one. It is shown that after an appropriate norming the least squares…
Stability is a fundamental property of dynamical systems, yet to this date it has had little bearing on the practice of recurrent neural networks. In this work, we conduct a thorough investigation of stable recurrent models. Theoretically,…
We consider stationary autoregressive processes with coefficients restricted to an ellipsoid, which includes autoregressive processes with absolutely summable coefficients. We provide consistency results under different norms for the…
The aim of this paper is to provide conditions which ensure that the affinely transformed partial sums of a strictly stationary process converge in distribution to an infinite variance stable distribution. Conditions for this convergence to…
A random coefficient autoregressive process is deeply investigated in which the coefficients are correlated. First we look at the existence of a strictly stationary causal solution, we give the second-order stationarity conditions and the…
Models characterized by autoregressive structure and random coefficients are powerful tools for the analysis of high-frequency, high-dimensional and volatile time series. The available literature on such models is broad, but also sectorial,…
Stochastic processes generated by non-stationary distributions are difficult to represent with conventional models such as Gaussian processes. This work presents Recurrent Autoregressive Flows as a method toward general stochastic process…
In sustained growth with random dynamics stationary distributions can exist without detailed balance. This suggests thermodynamical behavior in fast growing complex systems. In order to model such phenomena we apply both a discrete and a…
We consider network autoregressive models for count data with a non-random neighborhood structure. The main methodological contribution is the development of conditions that guarantee stability and valid statistical inference for such…
The family of semi-stable laws is shown to be semi-selfdecomposable. Thus they qualify to model stationary first order autoregressive schemes. A connection between these autoregressive schemes with semi-stable marginals and semi-selfsimilar…
A useful sampling-reconstruction model should be stable with respect to different kind of small perturbations, regardless whether they result from jitter, measurement errors, or simply from a small change in the model assumptions. In this…
For a stationary sequence that is regularly varying and associated we give conditions which guarantee that partial sums of this sequence, under normalization related to the exponent of regular variation, converge in distribution to a…
We investigate a family of distributions having a property of stability-under-addition, provided that the number $\nu$ of added-up random variables in the random sum is also a random variable. We call the corresponding property a…
Here we develop a first order autoregressive model {Xn} that is marginally stationary where Xn is the sum/ extreme of k i.i.d observations. We prove that stationary solutions to these models are either semi-selfdecomposable/…
We consider regression in which one predicts a response $Y$ with a set of predictors $X$ across different experiments or environments. This is a common setup in many data-driven scientific fields and we argue that statistical inference can…
We consider maximum likelihood estimation for both causal and noncausal autoregressive time series processes with non-Gaussian $\alpha$-stable noise. A nondegenerate limiting distribution is given for maximum likelihood estimators of the…
We revisit processes generated by iterated random functions driven by a stationary and ergodic sequence. Such a process is called strongly stable if a random initialization exists, for which the process is stationary and ergodic, and for…
The inverse problem of backward diffusion is known to be ill-posed and highly unstable. Backward diffusion processes appear naturally in image enhancement and deblurring applications. It is therefore greatly desirable to establish a…