In most macroeconomic models, the stability of the solution path implies that the system is covariancestationary and hence admits a Wold representation. The ability to estimate this Wold representation semi-parametrically by local projections (Jordà, 2005), even when the process for the solution path is unknown or unconventional, can be exploited to estimate the model’s parameters by minimum di...

This paper presents a multiparameter tissue characterization system based on the features obtained from the Weld decomposition algorithm when applied on red breast images. The Weld decomposition features quantify parameters of the tissue structure. This model ww applied to a large database of real ultrasound images of the breast. The features obtained were used to classify tissue pathology. To ...

Based on a Wold decomposition for families of partial isometries and projections of Cuntz-Krieger-Toeplitz-type, we extend several fundamental theorems from the case of single vertex graphs to the general case of countable directed graphs with no sinks. We prove a Szego-type factorization theorem for CKT families, which leads to information on the structure of the unit ball in free semigroupoid...

This paper considers the importance of moving average errors for the Johansen trace test of cointegrating rank based upon approximating vector autoregressions (VARs). Two cases are emphasized and explored, both taking as their starting point the Wold decomposition. Though each case defined satisfies the same cointegrating vector, one is a case of multicointegration while the other, based on res...

The restauration and preservation of ancient documents is becoming an interesting application in document image analysis. This paper introduces a top-down approach aimed at segmenting the graphical part in historical heritage called lettrine. The research principle was established on the concept of human visual perception and invariant texture analysis (co-occurrence and run-length matrices, au...

This article presents the theoretical basis for modeling univariate traffic condition data streams as seasonal autoregressive integrated moving average processes. This foundation rests on the Wold decomposition theorem and on the assertion that a one-week lagged first seasonal difference applied to discrete interval traffic condition data will yield a weakly stationary transformation. Moreover,...

This paper considers the achievable accuracy in jointly estimating the parameters of a real-valued twodimensional (2-D) homogeneous random field with mixed spectral distribution, from a single observed realization of it. On the basis of a 2-D Wold-like decomposition, the field is represented as a sum of mutually orthogonal components of three types: purely indeterministic, harmonic, and evanesc...

A.1 Gaussian MERS Solution We first consider the purely nondeterministic case; the result is easily extended to arbitrary stationary and ergodic Gaussian processes using the Wold decomposition. Let X and X̃ be two discrete-time stationary and ergodic purely nondeterministic univariate Gaussian processes, with spectral power density functions RX ( e ) and RX̃ ( e ) respectively. These are by neces...