Related papers: Asymmetric GARCH modelling without moment conditio…
This paper addresses the problem of fitting a known distribution to the innovation distribution in a class of stationary and ergodic time series models. The asymptotic null distribution of the usual Kolmogorov--Smirnov test based on the…
A challenging problem in estimating high-dimensional graphical models is to choose the regularization parameter in a data-dependent way. The standard techniques include $K$-fold cross-validation ($K$-CV), Akaike information criterion (AIC),…
We propose a Bayesian non-parametric approach for modeling the distribution of multiple returns. In particular, we use an asymmetric dynamic conditional correlation (ADCC) model to estimate the time-varying correlations of financial returns…
This paper has two main goals: (a) establish several statistical properties---consistency, asymptotic distributions, and convergence rates---of stationary solutions and values of a class of coupled nonconvex and nonsmoothempirical risk…
Stability analysis and control of linear impulsive systems is addressed in a hybrid framework, through the use of continuous-time time-varying discontinuous Lyapunov functions. Necessary and sufficient conditions for stability of impulsive…
Adaptive gradient methods have been widely adopted in training large-scale deep neural networks, especially large foundation models. Despite the huge success in practice, their theoretical advantages over classical gradient methods with…
We establish two concentration inequalities for nonlinear stochastic system under time-varying contraction conditions. The key to our approach is an energy function termed Averaged Moment Generating Function (AMGF). By combining it with…
We study inference on the common stochastic trends in a non-stationary, $N$-variate time series $y_{t}$, in the possible presence of heavy tails. We propose a novel methodology which does not require any knowledge or estimation of the tail…
This paper presents a novel estimator of orthogonal GARCH models, which combines (eigenvalue and -vector) targeting estimation with stepwise (univariate) estimation. We denote this the spectral targeting estimator. This two-step estimator…
We consider the asymmetric random average process which is a one-dimensional stochastic lattice model with nearest neighbour interaction but continuous and unbounded state variables. First, the explicit functional representations, so-called…
Generalized autoregressive conditionally heteroskedastic (GARCH) processes are widely used for modelling features commonly found in observed financial returns. The extremal properties of these processes are of considerable interest for…
This paper presents the first sufficient conditions that guarantee the stability and almost sure convergence of multi-timescale stochastic approximation (SA) iterates. It extends the existing results on one-timescale and two-timescale SA…
This paper provides an entire inference procedure for the autoregressive model under (conditional) heteroscedasticity of unknown form with a finite variance. We first establish the asymptotic normality of the weighted least absolute…
In this paper, we study the performance of a large family of SGD variants in the smooth nonconvex regime. To this end, we propose a generic and flexible assumption capable of accurate modeling of the second moment of the stochastic…
Extreme events and the heavy tail distributions driven by them are ubiquitous in various scientific, engineering and financial research. They are typically associated with stochastic instability caused by hidden unresolved processes.…
Machine learning has made tremendous progress in recent years, with models matching or even surpassing humans on a series of specialized tasks. One key element behind the progress of machine learning in recent years has been the ability to…
The Lyapounov exponent and sharp conditions for geometric ergodicity are determined of a time series model with both a threshold autoregression term and threshold autoregressive conditional heteroscedastic (ARCH) errors. The conditions…
Stochastic optimization has found wide applications in minimizing objective functions in machine learning, which motivates a lot of theoretical studies to understand its practical success. Most of existing studies focus on the convergence…
State space models contain time-indexed parameters, termed states, as well as static parameters, simply termed parameters. The problem of inferring both static parameters as well as states simultaneously, based on time-indexed observations,…
Although stochastic volatility and GARCH (generalized autoregressive conditional heteroscedasticity) models have successfully described the volatility dynamics of univariate asset returns, extending them to the multivariate models with…