Related papers: The functional AR(1) process with a unit root
The functional autoregressive model is a Markov model taylored for data of functional nature. It revealed fruitful when attempting to model samples of dependent random curves and has been widely studied along the past few years. This…
Closed-form generating functions for counting one-face rooted hypermaps with a known number of darts by number of vertices and edges is found, using matrix integral expressions relating to the reduced density operator of a bipartite quantum…
Functional principal component analysis has been shown to be invaluable for revealing variation modes of longitudinal outcomes, which serves as important building blocks for forecasting and model building. Decades of research have advanced…
For positive integers d, r, and M, we consider the class of rational functions on real d-dimensional space whose denominators are products of at most r functions of the form 1+Q(x) where each Q is a quadratic form with eigenvalues bounded…
A monolithic process is a single recursive equation with data parameters, which only uses non-determinism, action prefixing, and recursion. We present a technique that decomposes such a monolithic process into multiple processes where each…
We present an improved version of commutator methods for unitary operators under a weak regularity condition. Once applied to a unitary operator, the method typically leads to the absence of singularly continuous spectrum and to the local…
This paper discusses semiparametric inference on hypotheses on the cointegration and the attractor spaces for $I(1)$ linear processes with moderately large cross-sectional dimension. The approach is based on empirical canonical correlations…
This paper focuses on the problem of reconstructing a vector of rational functions given some evaluations, or more generally given their remainders modulo different polynomials. The special case of rational functions sharing the same…
We propose a flexible dual functional factor model for modelling high-dimensional functional time series. In this model, a high-dimensional fully functional factor parametrisation is imposed on the observed functional processes, whereas a…
It is argued that for certain meromorphic functions $u:\cal{R}\rightarrow\cal{R}$ and analytic function $ A_1$ and for any integrable function $F$, as long as it converges as a Cauchy Principal Value,, $$\int_{-\infty}^{\infty}A_1(x)F[u(x)]…
Motivated by partition regularity problems of homogeneous quadratic equations, we prove multiple recurrence and convergence results for multiplicative measure preserving actions with iterates given by rational sequences involving…
We study regression using functional predictors in situations where these functions contain both phase and amplitude variability. In other words, the functions are misaligned due to errors in time measurements, and these errors can…
We unify and generalize different notions of local units and local projectivity. We investigate the connection between these properties by constructing elementary algebras from locally projective modules. Dual versions of these…
In this article we consider functions $f$ meromorphic in the unit disk. We give an elementary proof for a condition that is sufficient for the univalence of such functions. This condition simplifies and generalizes known conditions. We…
A correspondence between arbitrary Fourier series and certain analytic functions on the unit disk of the complex plane is established. The expression of the Fourier coefficients is derived from the structure of complex analysis. The…
Functional Principal Component Analysis is a reference method for dimension reduction of curve data. Its theoretical properties are now well understood in the simplified case where the sample curves are fully observed without noise.…
In this note we describe the theory of functional asynchronous networks and one of the main results, the Modularization of Dynamics Theorem, which for a large class of functional asynchronous networks gives a factorization of dynamics in…
In functional analysis it is well known that every linear functional defined on the dual of a locally convex vector space which is continuous for the weak topology is the evaluation at a uniquely determined point of the given vector space.…
We consider the problem of characterizing all functions $f$ defined on the set of integers modulo $n$ with the property that an average of some $n$th roots of unity determined by $f$ is always an algebraic integer. Examples of such…
In the analysis of binary longitudinal data, it is of interest to model a dynamic relationship between a response and covariates as a function of time, while also investigating similar patterns of time-dependent interactions. We present a…