ARMA modeling of time series based on rational approximation of spectral density function

This study is concerned with Autoregressive Moving Average (ARMA) models of time series. ARMA models form a subclass of the class of general linear models which represents stationary time series, a phenomenon encountered most often in practice by engineers, scientists and economists. It is always desirable to employ models which use parameters parsimoniously. Parsimony will be achieved by ARMA models because it has only finite number of parameters. Even though the discussion is primarily concerned with stationary time series, later we will take up the case of homogeneous non stationary time series which can be transformed to stationary time series. Time series models, obtained with the help of the present and past data is used for forecasting future values. Physical science as well as social science take benefits of forecasting models. The role of forecasting cuts across all fields of management-—finance, marketing, production, business economics, as also in signal process, communication engineering, chemical processes, electronics etc. This high applicability of time series is the motivation to this study.

Análisis diacrónico de la producción española de tesis doctorales en educación matemática mediante la metodología ARIMA (Auto-Regressive Integrated Moving Average) en datos de diseños longitudinales.

Se analiza la manera en que se realizan las tesis doctorales en educación matemática en España. Se utiliza la metodología ARIMA (Auto-Regressive Integrated Moving Average) para realizar el análisis de manera diacrónica sobre datos longitudinales. Se hace incapié en la importancia de la metodología usada y sus ventajas frente a las metodologías tradicionalmente usadas en análisis diacrónicos. Se exponen las cuatro fases de la metodología ARIMA, correspondientes a la identificación del proceso, la estimación de cambio en el proceso, la validación del mismo y la predicción de sus consecuencias.

Precision of yule-walker methods for the arma spectral model

In this work a new method is proposed of separated estimation for the ARMA spectral model based on the modified Yule-Walker equations and on the least squares method. The proposal of the new method consists of performing an AR filtering in the random process generated obtaining a new random estimate, which will reestimate the ARMA model parameters, given a better spectrum estimate. Some numerical examples will be presented in order to ilustrate the performance of the method proposed, which is evaluated by the relative error and the average variation coefficient.

Preprocessing data for short-term load forecasting with a general regression neural network and a moving average filter

This paper proposes a filter based on a general regression neural network and a moving average filter, for preprocessing half-hourly load data for short-term multinodal load forecasting, discussed in another paper. Tests made with half-hourly load data from nine New Zealand electrical substations demonstrate that this filter is able to handle noise, missing data and abnormal data. © 2011 IEEE.

Some misspecfication problems in long-memory time series models

Doctor of Philosophy in Mathematics

Análise dinâmica de mercados financeiros

Na sociedade actual, é cada vez mais difícil desassociar o ambiente financeiro do ambiente social, tendo o primeiro influência directa ou indirecta em praticamente todos os aspectos da sociedade. A esta influência está associada a vasta quantidade de informação e serviços financeiros que possibilitam uma melhor compreensão do ambiente socioeconómico actual, permitindo também o estudo das evoluções e das dinâmicas dos mercados financeiros. Este trabalho refere-se ao estudo e comparação de algumas ferramentas disponíveis para a análise dinâmica e tentativa de previsão de alguns índices de bolsa escolhidos. Tais métodos a estudar são modelos clássicos como o Autoregressivo, Média Móvel e o Modelo Misto apresentado por Box e Jenkins. São também propostos dois métodos que tentam distanciar-se dos métodos tradicionais por apenas considerarem para a sua previsão os momentos semelhantes ao momento actual que se tenta prever, ao invés de considerar todo o espectro dos dados disponíveis, tal como os métodos clássicos referidos anteriormente.

Principal components and generalized linear modeling in the correlation between hospital admissions and air pollution

OBJECTIVE To analyze the association between concentrations of air pollutants and admissions for respiratory causes in children. METHODS Ecological time series study. Daily figures for hospital admissions of children aged < 6, and daily concentrations of air pollutants (PM10, SO2, NO2, O3 and CO) were analyzed in the Região da Grande Vitória, ES, Southeastern Brazil, from January 2005 to December 2010. For statistical analysis, two techniques were combined: Poisson regression with generalized additive models and principal model component analysis. Those analysis techniques complemented each other and provided more significant estimates in the estimation of relative risk. The models were adjusted for temporal trend, seasonality, day of the week, meteorological factors and autocorrelation. In the final adjustment of the model, it was necessary to include models of the Autoregressive Moving Average Models (p, q) type in the residuals in order to eliminate the autocorrelation structures present in the components. RESULTS For every 10:49 μg/m3 increase (interquartile range) in levels of the pollutant PM10 there was a 3.0% increase in the relative risk estimated using the generalized additive model analysis of main components-seasonal autoregressive – while in the usual generalized additive model, the estimate was 2.0%. CONCLUSIONS Compared to the usual generalized additive model, in general, the proposed aspect of generalized additive model − principal component analysis, showed better results in estimating relative risk and quality of fit.

Improving accuracy for OTD based 3G geolocation in real urban/suburban environments

This paper presents the recent research results about the development of a Observed Time Difference (OTD) based geolocation algorithm based on network trace data, for a real Universal Mobile Telecommunication System (UMTS) Network. The initial results have been published in [1], the current paper focus on increasing the sample convergence rate, and introducing a new filtering approach based on a moving average spatial filter, to increase accuracy. Field tests have been carried out for two radio environments (urban and suburban) in the Lisbon area, Portugal. The new enhancements produced a geopositioning success rate of 47% and 31%, and a median accuracy of 151 m and 337 m, for the urban and suburban environments, respectively. The implemented filter produced a 16% and 20% increase on accuracy, when compared with the geopositioned raw data. The obtained results are rather promising in accuracy and geolocation success rate. OTD positioning smoothed by moving average spatial filtering reveals a strong approach for positioning trace extracted events, vital for boosting Self-Organizing Networks (SON) over a 3G network.

Technology shocks and aggregate fluctuations in an estimated hybrid RBC model

This paper contributes to the on-going empirical debate regarding the role of the RBC model and in particular of technology shocks in explaining aggregate fluctuations. To this end we estimate the model’s posterior density using Markov-Chain Monte-Carlo (MCMC) methods. Within this framework we extend Ireland’s (2001, 2004) hybrid estimation approach to allow for a vector autoregressive moving average (VARMA) process to describe the movements and co-movements of the model’s errors not explained by the basic RBC model. The results of marginal likelihood ratio tests reveal that the more general model of the errors significantly improves the model’s fit relative to the VAR and AR alternatives. Moreover, despite setting the RBC model a more difficult task under the VARMA specification, our analysis, based on forecast error and spectral decompositions, suggests that the RBC model is still capable of explaining a significant fraction of the observed variation in macroeconomic aggregates in the post-war U.S. economy.

Large Bayesian VARMAs

Vector Autoregressive Moving Average (VARMA) models have many theoretical properties which should make them popular among empirical macroeconomists. However, they are rarely used in practice due to over-parameterization concerns, difficulties in ensuring identification and computational challenges. With the growing interest in multivariate time series models of high dimension, these problems with VARMAs become even more acute, accounting for the dominance of VARs in this field. In this paper, we develop a Bayesian approach for inference in VARMAs which surmounts these problems. It jointly ensures identification and parsimony in the context of an efficient Markov chain Monte Carlo (MCMC) algorithm. We use this approach in a macroeconomic application involving up to twelve dependent variables. We find our algorithm to work successfully and provide insights beyond those provided by VARs.