Related papers: On non-stationary threshold autoregressive models
Non-linear renewal theory is extended to include random walks perturbed by both a slowly changing sequence and a stationary one. Main results include a version of the Key Renewal Theorem, a derivation of the limiting distribution of the…
Tiny Recursive Models (TRMs) have recently demonstrated remarkable performance on ARC-AGI, showing that very small models can compete against large foundation models through a two-step refinement mechanism that updates an internal reasoning…
In this paper, we consider the distributed estimation problem of a linear stochastic system described by an autoregressive model with exogenous inputs (ARX) when both the system orders and parameters are unknown. We design distributed…
In this paper, we derive asymptotic results for L^1-Wasserstein distance between the distribution function and the corresponding empirical distribution function of a stationary sequence. Next, we give some applications to dynamical systems…
This paper studies sparse covariance operator estimation for nonstationary processes with sharply varying marginal variance and small correlation lengthscale. We introduce a covariance operator estimator that adaptively thresholds the…
We propose a new class of models specifically tailored for spatio-temporal data analysis. To this end, we generalize the spatial autoregressive model with autoregressive and heteroskedastic disturbances, i.e. SARAR(1,1), by exploiting the…
Many researchers have investigated first hitting times as models for survival data. First hitting times arise naturally in many types of stochastic processes, ranging from Wiener processes to Markov chains. In a survival context, the state…
Strictly stationary INAR(1) ("integer-valued autoregressive processes of order 1") with Poisson innovations are "interlaced rho-mixing".
Recent cosmological observations hint at a deviation from the simple power-law form of the primordial spectrum of curvature perturbations. In this paper we show that in the presence of a tensor component, a turn-over in the initial spectrum…
A class of multivariate periodic autoregressive models is proposed where coupling between time series is achieved through linear mean functions. Various response distributions with quadratic mean-variance relationships fit into the…
We consider the estimation of a bounded regression function with nonparametric heteroscedastic noise and random design. We study the true and empirical excess risks of the least-squares estimator on finite-dimensional vector spaces. We give…
Convergence to non-minimal quasi-stationary distributions for one-dimensional diffusions is studied. We give a method of reducing the convergence to the tail behavior of the lifetime via a property which we call the first hitting…
We revisit classical asymptotics when testing for a structural break in linear regression models by obtaining the limit theory of residual-based and Wald-type processes. First, we establish the Brownian bridge limiting distribution of these…
The phase diagram of a novel two-dimensional frustrated Ising model with both anti-ferromagnetic and ferromagnetic couplings is studied using Tensor-Network Renormalization-Group techniques. This model can be seen as two anti-ferromagnetic…
We establish the asymptotic theory of least absolute deviation estimators for AR(1) processes with autoregressive parameter satisfying $n(\rho_n-1)\to\gamma$ for some fixed $\gamma$ as $n\to\infty$, which is parallel to the results of…
The fundamental task of general density estimation $p(x)$ has been of keen interest to machine learning. In this work, we attempt to systematically characterize methods for density estimation. Broadly speaking, most of the existing methods…
One-shot devices data represent an extreme case of interval censoring.Some kind of one-shot units do not get destroyed when tested, and so, survival units can continue within the test providing extra information about their lifetime.…
In this paper, non-linear time series models are used to describe volatility in financial time series data. To describe volatility, two of the non-linear time series are combined into form TAR (Threshold Auto-Regressive Model) with AARCH…
In this short letter, we rediscuss the model for non-commutative U(1) gauge theory presented in [arXiv:0912.2634] and argue that by treating the "soft-breaking terms" of that model in the realm of an extended BRST symmetry, a future…
Switching ARMA models greatly enhance the standard linear models to the extent that different ARMA model is allowed in a different regime, and the regime switching is typically assumed a Markov chain on the finite states of potential…