Related papers: Markov Switching Smooth Transition GARCH Model
Hawkes processes are often applied to model dependence and interaction phenomena in multivariate event data sets, such as neuronal spike trains, social interactions, and financial transactions. In the nonparametric setting, learning the…
In this paper, we use the results in Andrews and Cheng (2012), extended to allow for parameters to be near or at the boundary of the parameter space, to derive the asymptotic distributions of the two test statistics that are used in the…
In various industrial contexts, estimating the distribution of unobserved random vectors Xi from some noisy indirect observations H(Xi) + Ui is required. If the relation between Xi and the quantity H(Xi), measured with the error Ui, is…
The paper presents efficient approaches for evaluating convergence rate in total variation for finite and general linear Markov chains. The motivation for studying convergence rate in this metric is its usefulness in various limit theorems.…
Acyclic directed mixed graphs, also known as semi-Markov models represent the conditional independence structure induced on an observed margin by a DAG model with latent variables. In this paper we present the first method for fitting these…
Penalized spline smoothing of time series and its asymptotic properties are studied. A data-driven algorithm for selecting the smoothing parameter is developed. The proposal is applied to define a semiparametric extension of the well-known…
The first motivation of this paper is to study stationarity and ergodic properties for a general class of time series models defined conditional on an exogenous covariates process. The dynamic of these models is given by an autoregressive…
This paper provides a new unified framework for second-moment stability of discrete-time linear systems with stochastic dynamics. Relations of notions of second-moment stability are studied for the systems with general stochastic dynamics,…
The convergence rate of a Markov chain to its stationary distribution is typically assessed using the concept of total variation mixing time. However, this worst-case measure often yields pessimistic estimates and is challenging to infer…
We consider reinforcement learning in changing Markov Decision Processes where both the state-transition probabilities and the reward functions may vary over time. For this problem setting, we propose an algorithm using a sliding window…
In order to sample from a given target distribution (often of Gibbs type), the Monte Carlo Markov chain method consists in constructing an ergodic Markov process whose invariant measure is the target distribution. By sampling the Markov…
In Markov networks, measurement blackouts with unknown frequency compromise observations such that thermodynamic quantities can no longer be inferred reliably. In particular, the observed currents neither discern equilibrium from…
We introduce a new method to estimate the Markov equivalence class of a directed acyclic graph (DAG) in the presence of hidden variables, in settings where the underlying DAG among the observed variables is sparse, and there are a few…
This paper is devoted to the study of a stochastic process obtained by random switching between a finite collection of vector fields. Such processes have recently been the focus of much attention in the case where the switching times are…
In this paper, we derive some asymptotic theory for the extremogram and cross-extremogram of a bivariate GARCH(1,1) process. We show that the tails of the components of a bivariate GARCH(1,1) process may exhibit power law behavior but,…
The overall performance or expected excess risk of an iterative machine learning algorithm can be decomposed into training error and generalization error. While the former is controlled by its convergence analysis, the latter can be tightly…
We consider the task of learning a parametric Continuous Time Markov Chain (CTMC) sequence model without examples of sequences, where the training data consists entirely of aggregate steady-state statistics. Making the problem harder, we…
This paper studies the asymptotic behavior of processes with switching. More precisely, the stability under fast switching for diffusion processes and discrete state space Markovian processes is considered. The proofs are based on…
We consider a simple but important class of metastable discrete time Markov chains, which we call perturbed Markov chains. Basically, we assume that the transition matrices depend on a parameter $\varepsilon$, and converge as $\varepsilon$.…
This paper introduces a unified approach for modeling high-frequency financial data that can accommodate both the continuous-time jump-diffusion and discrete-time realized GARCH model by embedding the discrete realized GARCH structure in…