Related papers: Nearly Unstable Integer-Valued ARCH Process and Un…
We develop a monitoring procedure to detect changes in a large approximate factor model. Letting $r$ be the number of common factors, we base our statistics on the fact that the $\left( r+1\right) $-th eigenvalue of the sample covariance…
Markov chain Monte Carlo (MCMC) is a commonly used method for approximating expectations with respect to probability distributions. Uncertainty assessment for MCMC estimators is essential in practical applications. Moreover, for…
This paper considers the problem of testing if a sequence of means $(\mu_t)_{t =1,\ldots ,n }$ of a non-stationary time series $(X_t)_{t =1,\ldots ,n }$ is stable in the sense that the difference of the means $\mu_1$ and $\mu_t$ between the…
The volatility modeling for autoregressive univariate time series is considered. A benchmark approach is the stationary ARCH model of Engle (1982). Motivated by real data evidence, processes with non constant unconditional variance and ARCH…
We consider the problem of testing a null hypothesis defined by equality and inequality constraints on a statistical parameter. Testing such hypotheses can be challenging because the number of relevant constraints may be on the same order…
We implement a computer-assisted approach that, under appropriate conditions, allows the bifurcation analysis of the coarse dynamic behavior of microscopic simulators without requiring the explicit derivation of closed macroscopic equations…
We consider a complex-valued linear mixture model, under discrete weakly stationary processes. We recover latent components of interest, which have undergone a linear mixing. We study asymptotic properties of a classical unmixing estimator,…
In this paper we investigate how the bootstrap can be applied to time series regressions when the volatility of the innovations is random and non-stationary. The volatility of many economic and financial time series displays persistent…
We present a new framework to address the non-convex robust hypothesis testing problem, wherein the goal is to seek the optimal detector that minimizes the maximum of worst-case type-I and type-II risk functions. The distributional…
Electricity systems are experiencing increased effects of randomness and variability due to emerging stochastic assets. The increased effects introduce new uncertainties into power systems that can impact system operability and reliability.…
This paper considers nonparametric estimation and inference in first-order autoregressive (AR(1)) models with deterministically time-varying parameters. A key feature of the proposed approach is to allow for time-varying stationarity in…
This paper proposes a novel conditional heteroscedastic time series model by applying the framework of quantile regression processes to the ARCH(\infty) form of the GARCH model. This model can provide varying structures for conditional…
In this paper, we study random dissipative weak solutions of the compressible Euler equations in the Kelvin-Helmholtz (KH) instability. Motivated by the fact that weak entropy solutions are not unique and can be viewed as inviscid limits of…
This paper considers the effect of least squares procedures for nearly unstable linear time series with strongly dependent innovations. Under a general framework and appropriate scaling, it is shown that ordinary least squares procedures…
We demonstrate the effectiveness of an adaptive explicit Euler method for the approximate solution of the Cox-Ingersoll-Ross model. This relies on a class of path-bounded timestepping strategies which work by reducing the stepsize as…
This paper proposes self-normalized tests for multistep conditional predictive ability in forecast comparison. By normalizing the sample mean of the transformed loss differential using functionals of its cumulative sum (CUSUM) process,…
We numerically address the stability analysis of linear age-structured population models with nonlocal diffusion, which arise naturally in describing dynamics of infectious diseases. Compared to Laplace diffusion, models with nonlocal…
A novel data-driven method for formal verification is proposed to study complex systems operating in safety-critical domains. The proposed approach is able to formally verify discrete-time stochastic dynamical systems against temporal logic…
The stability of solutions to evolution equations with respect to small stochastic perturbations is considered. The stability of a stochastic dynamical system is characterized by the local stability index. The limit of this index with…
We provide finite sample properties of sparse multivariate ARCH processes, where the linear representation of ARCH models allows for an ordinary least squares estimation. Under the restricted strong convexity of the unpenalized loss…