Multivariate ARIMA Compositional Time Series Analysis

A compositional time series is obtained when a compositional data vector is observed atdifferent points in time. Inherently, then, a compositional time series is a multivariatetime series with important constraints on the variables observed at any instance in time.Although this type of data frequently occurs in situations of real practical interest, atrawl through the statistical literature reveals that research in the field is very much in itsinfancy and that many theoretical and empirical issues still remain to be addressed. Anyappropriate statistical methodology for the analysis of compositional time series musttake into account the constraints which are not allowed for by the usual statisticaltechniques available for analysing multivariate time series. One general approach toanalyzing compositional time series consists in the application of an initial transform tobreak the positive and unit sum constraints, followed by the analysis of the transformedtime series using multivariate ARIMA models. In this paper we discuss the use of theadditive log-ratio, centred log-ratio and isometric log-ratio transforms. We also presentresults from an empirical study designed to explore how the selection of the initialtransform affects subsequent multivariate ARIMA modelling as well as the quality ofthe forecasts

Compositional analysis of bivariate discrete probabilities

A joint distribution of two discrete random variables with finite support can be displayed as a two way table of probabilities adding to one. Assume that this table hasn rows and m columns and all probabilities are non-null. This kind of table can beseen as an element in the simplex of n · m parts. In this context, the marginals areidentified as compositional amalgams, conditionals (rows or columns) as subcompositions. Also, simplicial perturbation appears as Bayes theorem. However, the Euclideanelements of the Aitchison geometry of the simplex can also be translated into the tableof probabilities: subspaces, orthogonal projections, distances.Two important questions are addressed: a) given a table of probabilities, which isthe nearest independent table to the initial one? b) which is the largest orthogonalprojection of a row onto a column? or, equivalently, which is the information in arow explained by a column, thus explaining the interaction? To answer these questionsthree orthogonal decompositions are presented: (1) by columns and a row-wise geometric marginal, (2) by rows and a columnwise geometric marginal, (3) by independenttwo-way tables and fully dependent tables representing row-column interaction. Animportant result is that the nearest independent table is the product of the two (rowand column)-wise geometric marginal tables. A corollary is that, in an independenttable, the geometric marginals conform with the traditional (arithmetic) marginals.These decompositions can be compared with standard log-linear models.Key words: balance, compositional data, simplex, Aitchison geometry, composition,orthonormal basis, arithmetic and geometric marginals, amalgam, dependence measure,contingency table

Compositional data and Simpson's paradox

Simpson's paradox, also known as amalgamation or aggregation paradox, appears whendealing with proportions. Proportions are by construction parts of a whole, which canbe interpreted as compositions assuming they only carry relative information. TheAitchison inner product space structure of the simplex, the sample space of compositions, explains the appearance of the paradox, given that amalgamation is a nonlinearoperation within that structure. Here we propose to use balances, which are specificelements of this structure, to analyse situations where the paradox might appear. Withthe proposed approach we obtain that the centre of the tables analysed is a naturalway to compare them, which avoids by construction the possibility of a paradox.Key words: Aitchison geometry, geometric mean, orthogonal projection

A unified approach for representing rows and columns in contingency tables

By using suitable parameters, we present a uni¯ed aproach for describing four methods for representing categorical data in a contingency table. These methods include:correspondence analysis (CA), the alternative approach using Hellinger distance (HD),the log-ratio (LR) alternative, which is appropriate for compositional data, and theso-called non-symmetrical correspondence analysis (NSCA). We then make an appropriate comparison among these four methods and some illustrative examples are given.Some approaches based on cumulative frequencies are also linked and studied usingmatrices.Key words: Correspondence analysis, Hellinger distance, Non-symmetrical correspondence analysis, log-ratio analysis, Taguchi inertia

Intrinsic test of independence in contingency tables

A condition needed for testing nested hypotheses from a Bayesianviewpoint is that the prior for the alternative model concentratesmass around the small, or null, model. For testing independencein contingency tables, the intrinsic priors satisfy this requirement.Further, the degree of concentration of the priors is controlled bya discrete parameter m, the training sample size, which plays animportant role in the resulting answer regardless of the samplesize.In this paper we study robustness of the tests of independencein contingency tables with respect to the intrinsic priors withdifferent degree of concentration around the null, and comparewith other “robust” results by Good and Crook. Consistency ofthe intrinsic Bayesian tests is established.We also discuss conditioning issues and sampling schemes,and argue that conditioning should be on either one margin orthe table total, but not on both margins.Examples using real are simulated data are given

Compositional Time Series: An Application

The composition of the labour force is an important economic factor for a country.Often the changes in proportions of different groups are of interest.I this paper we study a monthly compositional time series from the Swedish LabourForce Survey from 1994 to 2005. Three models are studied: the ILR-transformed series,the ILR-transformation of the compositional differenced series of order 1, and the ILRtransformationof the compositional differenced series of order 12. For each of thethree models a VAR-model is fitted based on the data 1994-2003. We predict the timeseries 15 steps ahead and calculate 95 % prediction regions. The predictions of thethree models are compared with actual values using MAD and MSE and the predictionregions are compared graphically in a ternary time series plot.We conclude that the first, and simplest, model possesses the best predictive power ofthe three models

Calidad de vida relacionada con la salud y consumo de tabaco

La calidad de vida relacionada con la salud se ha descrito como un concepto multidimensional que incluye la identificación de síntomas, el estado funcional, la percepción de bienestar psicológico y la percepción general de salud. En el caso de la adicción al consumo de tabaco, la preocupación por la salud actual o futura es uno de los motivos más informados para dejar de fumar. En el presente estudio se analiza la relación entre la percepción de la calidad de vida relacionada con la salud y la etapa de cambio en el abandono del consumo de tabaco propuesta desde el modelo transteórico a fin de mejorar las estrategias de intervención comunitaria y clínica para la cesación tabáquica. Se ha administrado el cuestionario SF-36 a una muestra formada por 201 fumadores y exfumadores. Los datos obtenidos indican peor salud física percibida en las etapas de cambio más próximas al abandono de tabaco y una peor salud mental percibida en las etapas con tabaquismo activo. Se comparan los resultados con los observados en otras poblaciones y se discuten las implicaciones a nivel de tratamiento y prevención del tabaquismo

Compositional evolution with mass transfer in closed systems

Evolution of compositions in time, space, temperature or other covariates is frequentin practice. For instance, the radioactive decomposition of a sample changes its composition with time. Some of the involved isotopes decompose into other isotopes of thesample, thus producing a transfer of mass from some components to other ones, butpreserving the total mass present in the system. This evolution is traditionally modelledas a system of ordinary di erential equations of the mass of each component. However,this kind of evolution can be decomposed into a compositional change, expressed interms of simplicial derivatives, and a mass evolution (constant in this example). A rst result is that the simplicial system of di erential equations is non-linear, despiteof some subcompositions behaving linearly.The goal is to study the characteristics of such simplicial systems of di erential equa-tions such as linearity and stability. This is performed extracting the compositional differential equations from the mass equations. Then, simplicial derivatives are expressedin coordinates of the simplex, thus reducing the problem to the standard theory ofsystems of di erential equations, including stability. The characterisation of stabilityof these non-linear systems relays on the linearisation of the system of di erential equations at the stationary point, if any. The eigenvelues of the linearised matrix and theassociated behaviour of the orbits are the main tools. For a three component system,these orbits can be plotted both in coordinates of the simplex or in a ternary diagram.A characterisation of processes with transfer of mass in closed systems in terms of stability is thus concluded. Two examples are presented for illustration, one of them is aradioactive decay

A Log-linear model of grain size influence on the geochemistry of sediments

Sediment composition is mainly controlled by the nature of the source rock(s), and chemical (weathering) and physical processes (mechanical crushing, abrasion, hydrodynamic sorting) during alteration and transport. Although the factors controlling these processes are conceptually well understood, detailed quantification of compositional changes induced by a single process are rare, as are examples where the effects of several processes can be distinguished. The present study was designed to characterize the role of mechanical crushing and sorting in the absence of chemical weathering. Twenty sediment samples were taken from Alpine glaciers that erode almost pure granitoid lithologies. For each sample, 11 grain-size fractions from granules to clay (ø grades &-1 to &9) were separated, and each fraction was analysed for its chemical composition.The presence of clear steps in the box-plots of all parts (in adequate ilr and clr scales) against ø is assumed to be explained by typical crystal size ranges for the relevant mineral phases. These scatter plots and the biplot suggest a splitting of the full grain size range into three groups: coarser than ø=4 (comparatively rich in SiO2, Na2O, K2O, Al2O3, and dominated by “felsic” minerals like quartz and feldspar), finer than ø=8 (comparatively rich in TiO2, MnO, MgO, Fe2O3, mostly related to “mafic” sheet silicates like biotite and chlorite), and intermediate grains sizes (4≤ø &8; comparatively rich in P2O5 and CaO, related to apatite, some feldspar).To further test the absence of chemical weathering, the observed compositions were regressed against three explanatory variables: a trend on grain size in ø scale, a step function for ø≥4, and another for ø≥8. The original hypothesis was that the trend could be identified with weathering effects, whereas each step function would highlight those minerals with biggest characteristic size at its lower end. Results suggest that this assumption is reasonable for the step function, but that besides weathering some other factors (different mechanical behavior of minerals) have also an important contribution to the trend.Key words: sediment, geochemistry, grain size, regression, step function

Proposta de Centre d’ Educació Ambiental a la Vall del LLémana

L’ objectiu principal d’ aquesta proposta d’ educació ambiental és habilitar un espai físic que ja existeix, la rectoria de Cartellà, on els alumnes de primària i de secundària, i les famílies puguin participar d’ una sèrie d’ activitats encarades a l’ obtenció de nous valors relacionats amb el respecte cap a l’ entorn natural. El projecte s’ estructura bàsicament en dues parts: una primera on es situa i es descriu l’ espai on es destina la proposta i una segona on es tracten les actuacions específiques per tal d’ aconseguir que la gent es familiaritzi amb l’ entorn i aprengui a actuar de manera respectuosa amb el medi

Estudi històric i patològic del Mas Vell: rehabilitació del Mas Vell i transformació en centre d’esports d’aventura

L’objectiu que es va marcar abans de començar el projecte, era el de realitzar la rehabilitació del Mas Vell convertint-lo en un centre d’esports d’aventura. Per fer això creiem convenient que abans calia realitzar un estudi de les principals patologies que l’afectaven i de pas, datar la seva construcció i estudiar l’evolució i modificacions que ha patit al llarg dels anys. Per realitzar l’estudi patològic es crearien unes fitxes, localitzant, descrivint, explicant la causa de cada patologia en concret i donant la solució més adequada per reparar cada una d’elles. La rehabilitació del mas es faria pensant amb l’ús immediat que se li donarà, que serà un centre d’esports d’aventura. Les premisses que volíem seguir eren: no augmentar la volumetria que la masia tenia en el moment del seu abandonament, conservar l’aspecte rústic de l’edifici, tant en les parts que es conserven com en les que reconstruïm. Es pensava mantenir l’estructura de fusta de coberta i forjat que es trobés en bon estat. A la zona que estava en ruïnes es pensava construir les parets aterrades amb els mateixos materials originaris

L'Educació social com a DAM: Delegat d'Assitència al Menor

Descripció i anàlisi del sistema de funcionament de justícia juvenil en medi obert, i concretament la metodologia de treball dels DAM, per tal d’evidenciar les competències requerides a l’hora de desenvolupar l’exercici professional d’educador social com a DAM, tot exposant una anàlisi de la formació acadèmica impartida al llarg de la diplomatura d’Educació Social en relació a aquests requeriments

Creació d'un e-commerce

La finalitat d'aquest projecte és desenvolupar una aplicació de comerç electrònic per a la venda de productes en la xarxa. El projecte haurà de tenir dues parts ben diferenciades: el frontal -que serà visible per a qualsevol usuari de la xarxa- i la part d'administrador -nomès accessible per a l'administrador-. El projecte estarà desenvolupat amb eines J2EE, Ajax, jQuery i HTML5, oferint una total accessibilitat per als actuals navegadors.

Representaciones y significados acerca de la vejez institucionalizada

Este trabajo de investigación se enmarca en los estudios dedicados al conocimiento del significado que se le atribuye a la vejez en nuestra sociedad. El ámbito de interés se centra en la vida de las personas mayores dentro y fuera de las instituciones geriátricas con el objeto de comprender en qué medida estos factores pueden llegar a condicionar el imaginario acerca de la vejez. Más específicamente la idea central, que orienta la investigación y delimita claramente el tema de trabajo, se sintetiza en la siguiente pregunta clave: ¿cómo incide la institucionalización de los ancianos y las ancianas en la concepción y autopercepción de la vejez?

Constraint algorithm for k-presymplectic Hamiltonian systems. Application to singular field theories

The k-symplectic formulation of field theories is especially simple, since only tangent and cotangent bundles are needed in its description. Its defining elements show a close relationship with those in the symplectic formulation of mechanics. It will be shown that this relationship also stands in the presymplectic case. In a natural way,one can mimick the presymplectic constraint algorithm to obtain a constraint algorithmthat can be applied to k-presymplectic field theory, and more particularly to the Lagrangian and Hamiltonian formulations offield theories defined by a singular Lagrangian, as well as to the unified Lagrangian-Hamiltonian formalism (Skinner--Rusk formalism) for k-presymplectic field theory. Two examples of application of the algorithm are also analyzed.