Related papers: Partial autocorrelation parameterisation of models…

The Al-Salam-Chihara polynomials are an important family of orthogonal polynomials in one variable $x$ depending on 3 parameters $\alpha$, $\beta$ and $q$. They are closely connected to a model from statistical mechanics called the…

Let F_{n+m} be the free group of rank n+m, with generators x_1,...,x_{n+m}. An automorphism \phi of F_{n+m} is called partially symmetric if for each 1 \le i \le m, \phi(x_i) is conjugate to x_j or x_j^{-1} for some 1 \le j \le m. Let…

Random matrix theory allows one to deduce the eigenvalue spectrum of a large matrix given only statistical information about its elements. Such results provide insight into what factors contribute to the stability of complex dynamical…

We propose an $L^2$ norm for stationary Autoregressive Moving Average (ARMA) models. We look at ARMA models within the Hilbert space of the past with present of a true purely linearly non-deterministic stationary process $X_t$, and compute…

Correlation matrices are the sub-class of positive definite real matrices with all entries on the diagonal equal to unity. Earlier work has exhibited a parametrisation of the corresponding Cholesky factorisation in terms of partial…

Modelling physical data with linear discrete time series, namely Fractionally Integrated Autoregressive Moving Average (ARFIMA), is a technique which achieved attention in recent years. However, these models are used mainly as a statistical…

In many atmospheric and earth sciences, it is of interest to identify dominant spatial patterns of variation based on data observed at $p$ locations and $n$ time points with the possibility that $p>n$. While principal component analysis…

Automatic machine learning (\AML) is a family of techniques to automate the process of training predictive models, aiming to both improve performance and make machine learning more accessible. While many recent works have focused on aspects…

A nearly unstable sequence of stationary spatial autoregressive processes is investigated, when the sum of the absolute values of the autoregressive coefficients tends to one. It is shown that after an appropriate norming the least squares…

Automorphisms of algebras $R$ from a very large axiomatic class of quantum nilpotent algebras are studied using techniques from noncommutative unique factorization domains and quantum cluster algebras. First, the Nakayama automorphism of…

This work is devoted to functional ARMA$(p, q)$ processes and approximating vector models based on functional PCA in the context of prediction. After deriving sufficient conditions for the existence of a stationary solution to both the…

We propose a novel cointegrated autoregressive model for matrix-valued time series, with bi-linear cointegrating vectors corresponding to the rows and columns of the matrix data. Compared to the traditional cointegration analysis, our…

We present an autodifferentiable rejection sampling algorithm termed Rejection Sampling with Autodifferentiation (RSA). In conjunction with reweighting, we show that RSA can be used for efficient parameter estimation and model exploration.…

In this paper, we propose a novel and efficient two-stage variable selection approach for sparse GLARMA models, which are pervasive for modeling discrete-valued time series. Our approach consists in iteratively combining the estimation of…

Radars provide robust perception of vehicle surroundings by effectively functioning in poor light and adverse weather conditions. Synthetic aperture radar (SAR) algorithms are employed to address the limited angular resolution of radars by…

The General Automated Machine learning Assistant (GAMA) is a modular AutoML system developed to empower users to track and control how AutoML algorithms search for optimal machine learning pipelines, and facilitate AutoML research itself.…

Modeling the ratio of two dependent components as a function of covariates is a frequently pursued objective in observational research. Despite the high relevance of this topic in medical studies, where biomarker ratios are often used as…

In the present paper we study properties of roots of characteristic polynomials for the linear recurrent formulae (LRF) that govern time series. We also investigate how the values of these roots affect Singular Spectrum Analysis…

One considers a system on $\mathbb{C}^2$ close to an invariant curve which can be viewed as a generalization of the semi-standard map to a trigonometric polynomial with many Fourier modes. The radius of convergence of an analytic…

There has been an enormous interest in analysing and modelling periodic time series. The research on periodically integrated autoregressive (PIAR) models which capture the periodic structure and the presence of unit roots is widely applied…