The forecasting of univariate time series poses challenges in industrial applications if the seasonality varies. Typically, a non-varying is treated with model based on Fourier theory or aggregation forecasts from multiple resolution levels. If changes time, various wavelet approaches for are proposed promising potential but without accessible software systematic evaluation different models com...

‎Let $G$ be a locally compact abelian group‎. ‎The concept of a generalized multiresolution structure (GMS) in $L^2(G)$ is discussed which is a generalization of GMS in $L^2(mathbb{R})$‎. ‎Basically a GMS in $L^2(G)$ consists of an increasing sequence of closed subspaces of $L^2(G)$ and a pseudoframe of translation type at each level‎. ‎Also‎, ‎the construction of affine frames for $L^2(G)$ bas...

In the present paper we find new constructions of orthonormal multiresolution analyses on the triangle ∆. In the first one, we describe a direct method to define an orthonormal multiresolution analysis R which is adapted for the study of the Sobolev spaces H 0(∆) (s ∈ N). In the second one, we add boundary conditions for constructing an orthonormal multiresolution analysis which is adapted for ...

The notion of a weak multiresolution analysis is defined over an arbitrary field in terms of cyclic modules for a certain affine group ring. In this setting the basic properties of weak multiresolution analyses are established, including characterizations of their submodules and quotient modules, the existence and uniqueness of reduced scaling equations, and the existence of wavelet bases. Thes...

In recent years, multiresolution techniques are increasingly being applied to image processing problems. Global features are quickly and e ciently extracted from images through these techniques. In this paper, we describe a robust image segmentation scheme that analyzes the histogram of a grayscale image using the idea of multiresolution. Our approach is di erent from most conventional multires...

Gabardo and Nashed have studied nonuniform multiresolution analysis based on the theory of spectral pairs in a series of papers, see Refs. 4 and 5. Farkov,3 has extended the notion of multiresolution analysis on locally compact Abelian groups and constructed the compactly supported orthogonal p-wavelets on L(R+). We have considered the nonuniform multiresolution analysis on positive half-line. ...