Abstract An ARMA(n,m) model is uniquely determined by its n first covariances and m first cepstrum coefficients. However, there does not always exist a model matching an estimated set of these parameters. We propose a method determining an asymptotically stable minimum phase model that match the covariances exactly and the cepstrum parameters approximatively. A convex barrier term is used for t...

This paper concerns the characterisation of second order marginals for random sets in a discrete setting. Under the instance of unit covariances, this problem possesses a combinatorial symmetry, exploited jointly in the companion paper to give a heuristic procedure to check realisability. In particular we disprove Matheron’s conjecture, and explicit partially the structure of the convex body fo...

The use of linear filters, i.e. convolutions, inevitably introduces dependencies in the uncertainties of the filter outputs. Such non-vanishing covariances appear both between different positions and between the responses from different filters (even at the same position). This report describes how these covariances between the output of linear filters can be computed. We then examine the induc...

This article investigates correlational properties of two-dimensional chaotic maps on the unit circle. We give analytical forms of higher-order covariances. We derive the characteristic function of their simultaneous and lagged ergodic densities. We found that these characteristic functions are described by three types of two-dimensional Bessel functions. Higher-order covariances between x and ...

Integrated white noise disturbance models are included in advanced control strategies, such as Model Predictive Control, to remove offset when there are unmodeled disturbances or plant/model mismatch. These integrating disturbances are usually modeled to enter either through the plant inputs or the plant outputs or partially through both. There is currently a lack of consensus in the literature...

Kalman filter based hybrid estimation algorithms have been used in many applications. However, performance analysis of these algorithms is difficult because many of these algorithms use a set of Kalman filters that are coupled with each other. We present an algorithm to compute the means and cross-covariances of the residuals of the set of coupling (or interacting) Kalman filters. Specifically,...

The modular variation of organismal form during evolution or development can be viewed as the result of dissociated local developmental processes. Whereas studies of modularity often are experimental, morphological integration is a more descriptive concept applying to groups of correlated phenotypic characters. Using simple path models, this paper shows that the classic underlying assumption of...

Population-wide oscillations are ubiquitously observed in mesoscopic signals of cortical activity. In these network states a global oscillatory cycle modulates the propensity of neurons to fire. Synchronous activation of neurons has been hypothesized to be a separate channel of signal processing information in the brain. A salient question is therefore if and how oscillations interact with spik...

Many economic variables are correlated over time. It is important to determine whether this observed correlation comes from time invariant unobserved heterogeneity among individuals or from temporal persistency of a shock. This paper examines how to estimate the auto-covariances and auto-correlations of individual dynamics separately from unobserved heterogeneity. When both cross-sectional and ...

Measuring natural selection has been a fundamental goal of evolutionary biology for more than a century, and techniques developed in the last 20 yr have provided relatively simple means for biologists to do so. Many of these techniques, however, share a common limitation: when applied to phenotypic data, environmentally induced covariances between traits and fitness can lead to biased estimates...