Análisis de series temporales : modelos ARIMA

Este documento es de utilidad como material docente a cualquier estudiante o persona interesada que quiera introducirse en el estudio del análisis de series temporales. Puede ser utilizado como libro de texto en algunas de las asignaturas que se imparten en la licenciatura en Economía y en la licenciatura en Administración de Empresas. Los modelos de series temporales ARIMA constituyen el núcleo del contenido de este documento. Estos modelos se basan en la teoría de los procesos estocásticos que se desarrolla en el capítulo 2. Los modelos ARMA estacionarios se explican con detalle en el capítulo 3 y los modelos ARIMA no estacionarios en el capítulo 4. La metodología de modelización ARIMA con las fases de identificación, estimación y contraste de diagnósticos se explica detalladamente en el capítulo 5 y el capítulo 6 se dedica a la predicción. El capítulo 7 trata sobre la especificación de los modelos de series temporales adecuados a los datos estacionales. Por último, el capítulo 8 reúne una colección de ejercicios para el trabajo propio del lector.

Removing observational noise from fisheries-independent time series data using ARIMA models

Abundance indices derived from fishery-independent surveys typically exhibit much higher interannual variability than is consistent with the within-survey variance or the life history of a species. This extra variability is essentially observation noise (i.e. measurement error); it probably reflects environmentally driven factors that affect catchability over time. Unfortunately, high observation noise reduces the ability to detect important changes in the underlying population abundance. In our study, a noise-reduction technique for uncorrelated observation noise that is based on autoregressive integrated moving average (ARIMA) time series modeling is investigated. The approach is applied to 18 time series of finfish abundance, which were derived from trawl survey data from the U.S. northeast continental shelf. Although the a priori assumption of a random-walk-plus-uncorrelated-noise model generally yielded a smoothed result that is pleasing to the eye, we recommend that the most appropriate ARIMA model be identified for the observed time series if the smoothed time series will be used for further analysis of the population dynamics of a species.

Price forecasting in the day-ahead Iberian electricity market using a conjectural variations Arima model

Price forecast is a matter of concern for all participants in electricity markets, from suppliers to consumers through policy makers, which are interested in the accurate forecast of day-ahead electricity prices either for better decisions making or for an improved evaluation of the effectiveness of market rules and structure. This paper describes a methodology to forecast market prices in an electricity market using an ARIMA model applied to the conjectural variations of the firms acting in an electricity market. This methodology is applied to the Iberian electricity market to forecast market prices in the 24 hours of a working day. The methodology was then compared with two other methodologies, one called naive and the other a direct forecast of market prices using also an ARIMA model. Results show that the conjectural variations price forecast performs better than the naive and that it performs slightly better than the direct price forecast.

Performance of state space and ARIMA models for consumer retail sales forecasting

Forecasting future sales is one of the most important issues that is beyond all strategic and planning decisions in effective operations of retail businesses. For profitable retail businesses, accurate demand forecasting is crucial in organizing and planning production, purchasing, transportation and labor force. Retail sales series belong to a special type of time series that typically contain trend and seasonal patterns, presenting challenges in developing effective forecasting models. This work compares the forecasting performance of state space models and ARIMA models. The forecasting performance is demonstrated through a case study of retail sales of five different categories of women footwear: Boots, Booties, Flats, Sandals and Shoes. On both methodologies the model with the minimum value of Akaike's Information Criteria for the in-sample period was selected from all admissible models for further evaluation in the out-of-sample. Both one-step and multiple-step forecasts were produced. The results show that when an automatic algorithm the overall out-of-sample forecasting performance of state space and ARIMA models evaluated via RMSE, MAE and MAPE is quite similar on both one-step and multi-step forecasts. We also conclude that state space and ARIMA produce coverage probabilities that are close to the nominal rates for both one-step and multi-step forecasts.

Causalités à court et à long terme dans les modèles VAR et ARIMA multivariés.

La causalité au sens de Granger est habituellement définie par la prévisibilité d'un vecteur de variables par un autre une période à l'avance. Récemment, Lutkepohl (1990) a proposé de définir la non-causalité entre deux variables (ou vecteurs) par la non-prévisibilité à tous les délais dans le futur. Lorsqu'on considère plus de deux vecteurs (ie. lorsque l'ensemble d'information contient les variables auxiliaires), ces deux notions ne sont pas équivalentes. Dans ce texte, nous généralisons d'abord les notions antérieures de causalités en considérant la causalité à un horizon donné h arbitraire, fini ou infini. Ensuite, nous dérivons des conditions nécessaires et suffisantes de non-causalité entre deux vecteurs de variables (à l'intérieur d'un plus grand vecteur) jusqu'à un horizon donné h. Les modèles considérés incluent les autoregressions vectorielles, possiblement d'ordre infini, et les modèles ARIMA multivariés. En particulier, nous donnons des conditions de séparabilité et de rang pour la non-causalité jusqu'à un horizon h, lesquelles sont relativement simples à vérifier.

From Market Concentration to Market Diversification: WTO and the Marine Products Exports from Kerala- Using ARIMA

Marine product export does something pivotal in the fish export economy of Kerala. The post WTO period has witnessed a strengthening of food safety and quality standards applied on food products in the developed countries. In the case of the primary importers, like the EU, the US and Japan, market actions will have far reaching reverberations and implications for the marine product exports from developing nations. The article focuses on Kerala’s marine product exports that had been targeting the markets of the EU, the US and Japan, and the concomitant shift in markets owing to the stringent stipulations under the WTO regime. Despite the overwhelming importance of the EU in the marine product exports of the state, the pronounced influence of irregular components on the quantity and value of marine product exports to the EU in the post WTO period raises concern. However, the tendencies of market diversification validated by the forecast generated for the emerging markets of the SEA, the MEA and others, to an extent, allay the pressures on the marine product export sector of the state which had hitherto relied heavily on the markets of the EU, the US and Japan

Multivariate ARIMA Compositional Time Series Analysis

A compositional time series is obtained when a compositional data vector is observed at different points in time. Inherently, then, a compositional time series is a multivariate time 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, a trawl through the statistical literature reveals that research in the field is very much in its infancy and that many theoretical and empirical issues still remain to be addressed. Any appropriate statistical methodology for the analysis of compositional time series must take into account the constraints which are not allowed for by the usual statistical techniques available for analysing multivariate time series. One general approach to analyzing compositional time series consists in the application of an initial transform to break the positive and unit sum constraints, followed by the analysis of the transformed time series using multivariate ARIMA models. In this paper we discuss the use of the additive log-ratio, centred log-ratio and isometric log-ratio transforms. We also present results from an empirical study designed to explore how the selection of the initial transform affects subsequent multivariate ARIMA modelling as well as the quality of the forecasts

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.

Gestión del riesgo de liquidez en una institución financiera utilizando un modelo híbrido entre la metodología ARIMA y Redes Neuronales Artificiales

En las instituciones financieras, una deficiente gestión del riesgo de liquidez puede ocasionar pérdidas financieras, ya sea por: intereses excesivos de créditos con otras instituciones, venta de activos con precios inferiores al valor del mercado, pérdida de oportunidades de negocios, pérdida de confianza con el depositante e incluso hasta la quiebra de la entidad. Es por esta razón, que el monitoreo de la liquidez se vuelve indispensable para el correcto funcionamiento de un banco, y se motiva al desarrollo de nuevas metodologías para su cuantificación. Si bien la gestión del riesgo de liquidez depende de cada institución bancaria y de su estructura en activos y pasivos, esta investigación se concentra en el análisis de la disminución del pasivo (depósitos) y/o el incremento del activo (cartera) y su afectación a los niveles de liquidez. Con este antecedente, para determinar la posición futura de liquidez de la institución investigada, se analiza las necesidades de fondos (obtenidas con la proyección de los depósitos) y la fuente de recursos (proyección de la cartera de créditos), permitiendo determinar superávits o déficits futuros de liquidez. En realidad el planteamiento es un monitoreo de la liquidez con un vista hacia el futuro, facilitando la toma de decisiones para mantener y controlar el nivel de liquidez requerido por la institución. Para cumplir con el objetivo de predicción, se pone a prueba una metodología alternativa para la proyección de series temporales, la cual combina los resultados de los modelos ARIMA y Redes Neuronales Artificiales. Con el modelo ARIMA se estima la relación lineal entre los rezagos propios de la serie, mientras que con las Redes Neuronales Artificiales se estima el componente no lineal que la estimación ARIMA no pudo captar. Los resultados son comparados con los obtenidos por las dos metodologías por separado. Se concluye que el modelo híbrido propuesto tiene mayor exactitud al estimar ambas series temporales.

The influence of ARIMA-GARCH parameters in feed forward neural networks prediction

The objective of this article is to find out the influence of the parameters of the ARIMA-GARCH models in the prediction of artificial neural networks (ANN) of the feed forward type, trained with the Levenberg-Marquardt algorithm, through Monte Carlo simulations. The paper presents a study of the relationship between ANN performance and ARIMA-GARCH model parameters, i.e. the fact that depending on the stationarity and other parameters of the time series, the ANN structure should be selected differently. Neural networks have been widely used to predict time series and their capacity for dealing with non-linearities is a normally outstanding advantage. However, the values of the parameters of the models of generalized autoregressive conditional heteroscedasticity have an influence on ANN prediction performance. The combination of the values of the GARCH parameters with the ARIMA autoregressive terms also implies in ANN performance variation. Combining the parameters of the ARIMA-GARCH models and changing the ANN`s topologies, we used the Theil inequality coefficient to measure the prediction of the feed forward ANN.

Padrão sazonal da produção industrial, exportações e importações: uma aplicação do X-12 ARIMA

Este trabalho tem por objetivo identificar os coeficientes sazonais de algumas variáveis econômicas (produção industrial, exportações e importações), isentos das mudanças estruturais registradas na economia. O estudo verifica se os planos de estabilização implementados pelo governo nos últimos quinze anos afetaram o padrão sazonal daquelas séries. Para tanto aplica-se o X-12-ARIMA, o novo método de dessazonalização de séries desenvolvido pelo U.S. Bureau of the Census. O uso desse método torna-se necessário, porque os demais métodos conhecidos impedem testar nossa hipótese, ao não permitirem o emprego de intervenções, não obtendo assim os melhores estimadores para os coeficientes sazonais. O estudo cobre o período que vai de 1980 a 1997 e os resultados confirmam a nossa hipótese de mudança no padrão sazonal no período. As nossas variáveis econômicas foram - de um ou de outro modo - atingidas pelos planos de estabilização implementados nos últimos quinze anos.

Elementos teóricos del ajuste estacional de series económicas utilizando X-12-ARIMA y TRAMO-SEATS

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Estudios de series temporales demográficas mediante modelos ARIMA de Box-Jenkins: una aplicación a series de la ciudad de Rosario, Argentina

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Previsão da velocidade dos ventos por redes neurais artificiais e arima de box & jenkins

Pós-graduação em Engenharia Elétrica - FEIS