Related papers: Asymmetric GARCH modelling without moment conditio…
We propose a statistical-stochastic surrogate modeling approach to predict the response of the mean and variance statistics under various initial conditions and external forcing perturbations. The proposed modeling framework extends the…
Models with latent factors recently attract a lot of attention. However, most investigations focus on linear regression models and thus cannot capture nonlinearity. To address this issue, we propose a novel Factor Augmented Single-Index…
This paper studies the joint inference on conditional volatility parameters and the innovation moments by means of bootstrap to test for the existence of moments for GARCH(p,q) processes. We propose a residual bootstrap to mimic the joint…
Recently there is a large amount of work devoted to the study of Markov chain stochastic gradient methods (MC-SGMs) which mainly focus on their convergence analysis for solving minimization problems. In this paper, we provide a…
Statistical models that possess symmetry arise in diverse settings such as random fields associated to geophysical phenomena, exchangeable processes in Bayesian statistics, and cyclostationary processes in engineering. We formalize the…
This paper derives the rate of convergence and asymptotic distribution for a class of Kolmogorov-Smirnov style test statistics for conditional moment inequality models for parameters on the boundary of the identified set under general…
Uniform stability is a notion of algorithmic stability that bounds the worst case change in the model output by the algorithm when a single data point in the dataset is replaced. An influential work of Hardt et al. (2016) provides strong…
The autoregressive (AR) model is a widely used model to understand time series data. Traditionally, the innovation noise of the AR is modeled as Gaussian. However, many time series applications, for example, financial time series data, are…
The tuning of stochastic gradient algorithms (SGAs) for optimization and sampling is often based on heuristics and trial-and-error rather than generalizable theory. We address this theory--practice gap by characterizing the large-sample…
We combine geometric data analysis and stochastic modeling to describe the collective dynamics of complex systems. As an example we apply this approach to financial data and focus on the non-stationarity of the market correlation structure.…
We consider a stationary linear $AR(p)$ model with zero mean. The autoregression parameters as well as the distribution function (d.f.) $G(x)$ of innovations are unknown. We consider two situations. In the first situation the observations…
We propose a set of dependence measures that are non-linear, local, invariant to a wide range of transformations on the marginals, can show tail and risk asymmetries, are always well-defined, are easy to estimate and can be used on any…
In this paper some methods to use the empirical bootstrap approach for stochastic gradient descent (SGD) to minimize the empirical risk over a separable Hilbert space are investigated from the view point of algorithmic stability and…
A nonparametric procedure to estimate the conditional probability that a nonstationary geostatistical process exceeds a certain threshold value is proposed. The method consists of a bootstrap algorithm that combines conditional simulation…
The existence of generalized steady states (GSSs) in nonlinear mechanical systems under moderate temporally aperiodic forcing has only been shown recently. Here we derive systematic expansions for such GSSs and construct a numerical…
In extracting time series data from various sources, it is inevitable to compile variables measured at varying frequencies as this is often dependent on the source. Modeling from these data can be facilitated by aggregating high frequency…
The celebrated Kuramoto model provides an analytically tractable framework to study spontaneous collective synchronization and comprises globally coupled limit-cycle oscillators interacting symmetrically with one another. The…
We develop a theory of evolutionary spectra for heteroskedasticity and autocorrelation robust (HAR) inference when the data may not satisfy second-order stationarity. Nonstationarity is a common feature of economic time series which may…
This paper investigates the stability and convergence properties of asynchronous stochastic approximation (SA) algorithms, with a focus on extensions relevant to average-reward reinforcement learning. We first extend a stability proof…
We introduce a general class of autoregressive models for studying the dynamic of multivariate binary time series with stationary exogenous covariates. Using a high-level set of assumptions, we show that existence of a stationary path for…