Spatial ARMA Model Research Articles

Strictly stationary solutions of spatial ARMA equations

The generalization of the ARMA time series model to the multidimensional index set $$\mathbb {Z}^d$$ , $$d\ge 2$$ , is called spatial ARMA model. The purpose of the following is to specify necessary conditions and sufficient conditions for the existence of strictly stationary solutions of the ARMA equations when the driving noise is i.i.d. Two different classes of strictly stationary solutions are studied, solutions of causal and noncausal models. For the special case of a first-order model on $$\mathbb {Z}^2$$ conditions are obtained, which are simultaneously necessary and sufficient.

On stationarity and second-order properties of bilinear random fields

One-dimensional indexed bilinear (BL) models are widely used for modeling non Gaussian time series. Extending BL models to multidimensional indexed (spatial) SBL one, yields a novel class of models which are capable of taking into account the important characteristic of non Gaussianity and spatiality behavior. Our main contribution here is to extend various results on BL processes to SBL one. Our attention is thus focussed on the probabilistic structure of some SBLmodels. So, we establish necessary and sufficient conditions for the existence of regular stationary and ergodic solutions in term of their transfer functions. As a consequence, we observe that the second order structure is similar to a spatial ARMA model with some uncorrelated white noise. So, it is necessary to look into higher-order moments in order to distinguish between linear and nonlinear random fields. Our study may be applied to GARCH or ARMA random fields.

Spatial ARMA model for wind speed data

Spatial time series model for wind speed data is proposed. Based on few similar papers, first at each location univariate time series model, containing seasonal component and higher order autoregressive component is fitted. After eliminating time dependence in time series, empirical semivariogram based on time independent residuals is fitted and spatial weights for new location are calculated.

Spatial ARMA models and its applications to image filtering

The objective of this review paper is to summarize the main properties of the spatial ARMA models and describe some of the well-known methods used in image filtering based on estimation of spatial autoregressive models. A new proposal based on robust RA estimation is also presented. Previous studies have shown that under additive outliers the RA estimator is resistant to a small percentage of contamination and behaves better than the LS, M, and GM estimators. A discussion about how well these models fit to a digital image is presented. Some applications using real images are presented to illustrate how an image is filtered in practice.

Regional productivity and income convergence in the unified Germany, 1992–2000

Kosfeld R., Eckey H.-F. and Dreger C. (2006) Regional productivity and income convergence in the unified Germany, 1992–2000, Regional Studies 40, 755–767. This paper investigates regional convergence of labour productivity and income per capita in the period 1992–2000 for the unified Germany using spatial econometric techniques. Up to now only first-order spatial models have been employed in investigating convergence across regions and countries. An exploratory data analysis reveals, however, that the fundamental variables of the convergence equation exhibit a clear pattern of higher-order spatial dependencies. It is shown that higher-order spatial autocorrelation can be captured by the spatial ARMA model. In the spatial econometric analysis of German regional labour markets, new indicators of human capital and investment intensity are used that can resolve some ‘puzzles’ established in previous studies. Substantial differences in both β- and σ-convergence across West and East German regions are assessed. Kosfeld R., Eckey H.-F. et Dreger C. (2006) La productivité régionale et la convergence des revenus dans l'Allemagne unifiée, entre 1992 et 2000, Regional Studies 40, 755–767. A partir des techniques économétriques géographiques, cet article cherche à examiner la convergence régionale de la productivité du travail et du revenu par tête entre 1992 et l'an 2000 pour l'Allemagne unifiée. Jusqu'à présent, on n'a employé que des modèles géographiques du premier ordre pour examiner la convergence à travers les régions et les pays. Cependant, une analyse de données exploratoire laisse voir que les variables préalables de l'équation de convergence montrent une distribution des dépendances géographiques d'ordre supérieur assez évidente. On démontre que l'on peut capter l'autocorrélation géographique d'ordre supérieur en employant le modèle géographique ARMA. Dans l'analyse économétrique géographique des marchés du tavail régionaux allemands, on se sert des nouveaux indices du capital humain et du taux d'investissement qui peuvent résoudre des questions posées dans des études antérieures. On évalue d'importantes différences de la convergence β et σ à travers les régions de l'ouest et de l'est de l'Allemagne. Convergence régionale Théorie de croissance néoclassique Allemagne unifiée Modèle géographique ARMA Kosfeld R., Eckey H.-F. und Dreger C. (2006) Regionale Produktivität und Einkommenskonvergenz im wiedervereinigten Deutschland, 1992–2000, Regional Studies 40, 755–767. In dieser Arbeit wird die regionale Konvergenz der Arbeitsproduktivität und des Pro-Kopf-Einkommens im Zeitraum 1992–2000 für das vereinigte Deutschland auf der Basis von Modellen mit räumlicher Ökonometrietechniken untersucht. Bisher ist die Hypothese der Konvergenz von Regionen und Ländern allein unter Verwendung räumlicher Modelle erster Ordnung überprüft worden. Eine exploratorische Datenanalyse deckt jedoch auf, dass die fundamentalen Variablen der Konvergenzgleichung ein recht klares Muster räumlicher Abhängigkeiten höherer Ordnung aufweisen. Es lässt sich zeigen, dass die Autokorrelationen höherer Ordnung in einem räumlichen ARMA-Modell abgebildet werden können. In der räumlich-ökonometrischen Analyse deutscher Arbeitsmarktregionen machen wir von neuen Indikatoren des Humankapitals und der Investitionsintensität Gebrauch, die in der Lage sind, einige ‘Anomalien’ aufzulösen, die sich in vorangegangenen Studien ergeben haben. Substanzielle Unterschiede der β- und σ-Konvergenz zwischen den west- und ostdeutschen Regionen werden bewertet. Regionale Konvergenz Neoklassische Wachstumstheorie Vereinigtes Deutschland Räumliches ARMA-Modell Kosfeld R., Eckey H.-F. y Dreger C. (2006) Productividad regional y convergencia de ingresos en la Alemania unificada durante 1992–2000, 1992–2000, Regional Studies 40, 755–767. Mediante técnicas econométricas espaciales, en este artículo investigamos cuál fue la convergencia regional de la productividad laboral y la renta per cápita durante el periodo 1992–2000 para la Alemania unificada. Hasta ahora sólo se han empleado modelos espaciales de primer orden para investigar la convergencia en regiones y países. Sin embargo, un análisis preliminar de datos pone de manifiesto que las variables fundamentales de la ecuación de convergencia presentan un modelo claro de dependencias espaciales de orden superior. Se demuestra que puede captarse la autocorrelación espacial de orden superior mediante el modelo espacial ARMA. En los análisis econométricos espaciales de los mercados laborales regionales de Alemania utilizamos nuevos indicadores del capital humano y la intensidad de inversión porque son capaces de resolver algunos enigmas establecidos en estudios anteriores. Analizamos las considerables diferencias tanto en la convergencia β como σ en Alemania del este y el oeste. Convergencia regional Teoría neoclásica del crecimiento Alemania unificada Modelo espacial ARMA

Asymptotic Results for Spatial ARMA Models

Causal quadrantal-type spatial ARMA(p, q) models with independent and identically distributed innovations are considered. In order to select the orders (p, q) of these models and estimate their autoregressive parameters, estimators of the autoregressive coefficients, derived from the extended Yule–Walker equations are defined. Consistency and asymptotic normality are obtained for these estimators. Then, spatial ARMA model identification is considered and simulation study is given.