On the resultant property of the Fisher information matrix of a vector ARMA process

A matrix is called a multiple resultant matrix associated to two matrix polynomials when it becomes singular if and only if the two matrix polynomials have at least one common eigenvalue. In this paper a new multiple resultant matrix is introduced. It concerns the Fisher information matrix (FIM) of a stationary vector autoregressive and moving average time series process (VARMA). The two matrix polynomials are the autoregressive and the moving average matrix polynomials of the VARMA process. In order to show that the FIM is a multiple resultant matrix two new representations of the FIM are derived. To construct such representations appropriate matrix differential rules are applied. The newly obtained representations are expressed in terms of the multiple Sylvester matrix and the tensor Sylvester matrix. The representation of the FIM expressed by the tensor Sylvester matrix is used to prove that the FIM becomes singular if and only if the autoregressive and moving average matrix polynomials have at least one common eigenvalue. It then follows that the FIM and the tensor Sylvester matrix have equivalent singularity conditions. In a simple numerical example it is shown however that the FIM fails to detect common eigenvalues due to some kind of numerical instability. Whereas the tensor Sylvester matrix reveals it clearly, proving the usefulness of the results derived in this paper. © 2005 Elsevier Inc. All rights reserved.SCOPUS: ar.jinfo:eu-repo/semantics/publishe

Corrections to "Construction of the exact Fisher information matrix of Gaussian time series models by means of matrix differential rules"

This note contains some corrections and amplifications that were deduced from the implementation and testing of the method

ARIMA Models with Time-Dependent Coefficients: Official Statistics Examples

About 25 years ago, effective methods for dealing with time series models that vary with time appeared in the statistical literature. Except in a few cases, they have never been used for economic statistics. In this chapter, we consider autoregressive integrated moving average (ARIMA) models with time-dependent coefficients (tdARIMA) applied to monthly industrial production series. We start with a small-size study with time-dependent integrated autoregressive (tdARI) models on Belgian series compared to standard ARI models with constant coefficients. Then, a second, bigger, illustration is given on 293 U.S. industrial production time series with tdARIMA models. We employ the software package Tramo to obtain linearized series and model specifications and build both the ARIMA models with constant coefficients (cARIMA) and the tdARIMA models, using specialized software. In these tdARIMA models, we use the simplest specification for each coefficient: a simple regression with respect to time. Surprisingly, for a large part of the series, there are statistically significant slopes, indicating that the tdARIMA models fit better the series than the cARIMA models

Notes historiques sur la paroisse Saint-Lambert de Voroux-Goreux rédigées à l'occasion du Centenaire de l'érection de son église en succursale épiscopale 1887-1987

Histoire du village de Voroux-Goreux en Hesbaye liégeoise et de sa paroisse Saint-Lambert et Saint-Huber

Sex steroid dynamics during embryogenesis and sexual differentiation in Eurasian perch, Perca fluviatilis

It is widely accepted that sex steroid hormones play an important and a specific role during the process of sex differentiation in fish. In order to describe the role of the three main sex steroid hormones (testosterone--T, 17beta-estradiol--E2 and 11keto-testosterone--11KT) during embryogenesis and sex differentiation in Eurasian perch, Perca fluviatilis, eggs, larvae and juveniles originating from two mixed-sex and two all-female progenies were regularly sampled from fertilization to hatching (D0) and from hatching to day 70 post-hatching (D70). Just after spawning, a significant amount of sex steroids [T (1634.2pgg(-1)), E2 (554.4pgg(-1)) and 11KT (1513.2pgg(-1))] was measured in non-fertilised eggs suggesting a maternal transmission of these steroids. From D2 to D70 post-hatching, E2 levels were significantly higher in mixed-sex progenies (median: 725.7pgg(-1)) than in all-female progenies (156.2pgg(-1)) and significantly increased after the onset of the histological differentiation of the gonad in both progenies (D35). Levels of 11KT were significantly higher in mixed-sex (median: 431.5pgg(-1)) than in all-female progenies (below the limit of assay detection) and significantly increased at D35 in all-female progenies (median value: 343.2pgg(-1)). Mean 11KT to E2 ratio was six-fold higher in mixed-sex progenies (1.35) than in all-female progenies (0.24). The data suggest that the 11-oxygenated androgen (11KT) plays a major role in the male differentiation process, and that sex differentiation in Eurasian perch is probably determined by the 11KT to E2 ratio

Prediction of stock price developments using the Box-Jenkins method

Stock prices develop in a non-linear way. Naturally, the stock price prediction is one of the most important issues at stock markets. Therefore, a variety of methods and technologies is devoted to the prediction of these prices. The present article predicts the future development of the stock price of ČEZ, a. s., on the Prague Stock Exchange using the ARIMA method - the Box-Jenkins method. The analysis employs the final price of the last trading day in a given month, from February 2012 to September 2017. The data come from the Prague Stock Exchange database. Statistica software is used for processing the data, namely advanced time series prediction methods, the ARIMA tool, and autocorrelation functions. First, the current stock development of ČEZ, a.s., was graphically evaluated, and this was followed by a stock price prediction for the next 60 days in which the shares would be traded. Lastly, the prediction residues were analysed. It was confirmed that the calculation was done correctly, but with little accuracy. The conclusion is an assertion that the Box-Jenkins method is not a suitable tool for prediction

Notes historiques sur la paroisse Saint-Lambert de Voroux-Goreux. Deuxième édition augmentée

Contribution à la connaissance et à la conservation du patrimoine matériel et immatériel voroutois

Cambrai – Château de Selles

Le château de Selles se situe à Cambrai, dans le département du Nord. Classé au titre des Monuments historiques depuis le 21 septembre 1981, il est partiellement conservé sous la terrasse d’un bastion moderne qui porte aujourd’hui le Palais de Justice, à l’angle du boulevard Dupleix et de la rue du Château de Selles. Ce programme de recherche, initié dès 2011, dans un souci de sauvegarde par l’image des manifestations graphiques en voie de disparition, a pour objectif l’inventaire et l’étude ..