Related papers: Geometric Infinitely Divisible Autoregressive Mode…

Generative modeling of high-dimensional data is a key problem in machine learning. Successful approaches include latent variable models and autoregressive models. The complementary strengths of these approaches, to model global and local…

Data consisting of time-indexed distributions of cross-sectional or intraday returns have been extensively studied in finance, and provide one example in which the data atoms consist of serially dependent probability distributions.…

In this paper we propose an identification method for latent-variable graphical models associated to autoregressive (AR) Gaussian stationary processes. The identification procedure exploits the approximation of AR processes through…

Due to the skessed distribution, high peak and thick tail and asymmetry of financial return data, it is difficult to describe the traditional distribution. In recent years, generalized autoregressive score (GAS) has been used in many fields…

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…

We study infinitely divisible (ID) distributions on the nonnegative half-line $\mathbb{R}_+$. The L\'{e}vy-Khintchine representation of such distributions is well-known. Our primary contribution is to cast the probabilistic objects and the…

We study a statistical model for infinite dimensional Gaussian random variables with unknown parameters. For this model we derive linear estimators for the mean and the variance of the Gaussian distribution. Furthermore, we construct…

When considering the problem of forecasting a continuous-time stochastic process over an entire time-interval in terms of its recent past, the notion of Autoregressive Hilbert space processes (ARH) arises. This model can be seen as a…

INteger Auto-Regressive (INAR) processes are usually defined by specifying the innovations and the operator, which often leads to difficulties in deriving marginal properties of the process. In many practical situations, a major modeling…

It is known that backward iterations of independent copies of a contractive random Lipschitz function converge almost surely under mild assumptions. By a sieving (or thinning) procedure based on adding to the functions time and space…

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…

Standard autoregressive seq2seq models are easily trained by max-likelihood, but tend to show poor results under small-data conditions. We introduce a class of seq2seq models, GAMs (Global Autoregressive Models), which combine an…

Here we develop a first order autoregressive model {Xn} that is marginally stationary where Xn is the sum/ extreme of k i.i.d observations. We prove that stationary solutions to these models are either semi-selfdecomposable/…

The autoregressive (AR) models are used to represent the time-varying random process in which output depends linearly on previous terms and a stochastic term (the innovation). In the classical version, the AR models are based on normal…

The spherical-radial decomposition (SRD) is an efficient method for estimating probabilistic functions and their gradients defined over finite-dimensional elliptical distributions. In this work, we generalize the SRD to infinite stochastic…

We define a number of natural (from geometric and combinatorial points of view) deformation spaces of valuations on finite graphs, and study functions over these deformation spaces. These functions include both direct metric invariants…

Conditional auto-regressive (CAR) distributions are widely used to induce spatial dependence in the geographic analysis of areal data. These distributions establish multivariate dependence networks by defining conditional relationships…

We develop a framework for generalized variational inference in infinite-dimensional function spaces and use it to construct a method termed Gaussian Wasserstein inference (GWI). GWI leverages the Wasserstein distance between Gaussian…

We introduce Autoregressive Diffusion Models (ARDMs), a model class encompassing and generalizing order-agnostic autoregressive models (Uria et al., 2014) and absorbing discrete diffusion (Austin et al., 2021), which we show are special…

In a recent paper Birke and Bissantz (2008) considered the problem of nonparametric estimation in inverse regression models with convolution-type operators. For multivariate predictors nonparametric methods suffer from the curse of…