Model uncertainty and the forecast accuracy of ARMA models: A survey

The objective of this paper is to analyze the effects of uncertainty on density forecasts of linear univariate ARMA models. We consider three specific sources of uncertainty: parameter estimation, error distribution and lag order. For moderate sample sizes, as those usually encountered in practice, the most important source of uncertainty is the error distribution. We consider alternative procedures proposed to deal with each of these sources of uncertainty and compare their finite properties by Monte Carlo experiments. In particular, we analyze asymptotic, Bayesian and bootstrap procedures, including some very recent procedures which have not been previously compared in the literature.We thank the Spanish Ministry of Education and Science, research project ECO2012-32401, for the financial suppor

Copulas, Chaotic Processes and Time Series: a Survey

In this work we summarize some of recent and classical results on the role played by copulas in the analysis of chaotic processes and univariate time series. We review some aspects of the copulas related to chaotic process, its properties and applications. We also present a review on classical and modern approaches to understand the relationship among random variables in Markov processes as well as short and long memory time series as well as ergodic properties of copula-based Markov processes

Topics in density forecast in stationary parametric univariate time series models

In this thesis we study the computation and evaluation of density forecasts under model uncertainty in time series univariate models. First, we analyze the effects of uncertainty on density forecasts of linear univariate ARMA models. We consider three specific sources of uncertainty: parameter estimation, error distribution and lag order. For moderate sample sizes, as those usually encountered in practice, the most important source of uncertainty is the error distribution. We consider alternative procedures proposed to deal with each of these sources of uncertainty and compare their finite sample properties by Monte Carlo experiments. In particular, we analyze asymptotic, Bayesian and bootstrap procedures, including some very recent procedures which have not been previously compared in the literature. Second, we propose an extension of the Generalized Autocontour (G-ACR) tests of González-Rivera and Sun (2015) for one-step-ahead dynamic specifications of conditional densities in-sample and of forecast densities out-of-sample. The new tests are based on probability integral transforms (PITs) computed from bootstrap conditional densities that incorporate the parameter uncertainty without assuming any particular forecast error density. Consequently, the parametric specification of the conditional moments can be tested without relying on any particular error distribution. We show that the asymptotic distributions of the bootstrapped G-ACR (BG-ACR) tests are well approximated using standard asymptotic distributions. Furthermore, the proposed tests are easy to implement and are accompanied by graphical tools which provide suggestions about the potential misspecification. The results are illustrated by testing the dynamic specification of the Heterogenous autoregressive (HAR) model when fitted to the popular U.S. volatility index VIX.En esta tesis estudiamos la construcción y evaluación de densidades de previsión bajo incertidumbre de modelo en modelos de series temporales univariantes. Primero, analizamos los efectos de la incertidumbre en las densidades de previsión de modelos ARMA univariantes lineales. Consideramos tres fuentes específicas de incertidumbre: estimación de los parámetros, distribución de los errores y la orden del desfase. Para muestras de tamaño moderado, como aquellas que se encuentran normalmente en la práctica, la fuente más importante de incertidumbre es la de la distribución de los errores. Consideramos procedimientos alternativos propuestos para tratar cada una de esas fuentes de incertidumbre y comparamos sus propiedades para muestras finitas por medio de experimentos de Monte Carlo. En particular, analizamos procedimientos asintóticos, Bayesianos y de bootstrap, incluyendo algunos procedimientos muy recientes los cuales no han sido previamente comparados en la literatura. Segundo, proponemos una extensión del test Generalized Autocontour (G-ARC) de González-Rivera and Sun (2015) para las especificaciones dinámicas de un-paso-adelante de densidades condicionadas in-sample y densidades de predicción out-of-sample. Los nuevos tests están basados en la transformación de probabilidad integral (PITs) calculados por medio de densidades condicionadas de boostrap que incorporan la incertidumbre de parámetros sin asumir ninguna densidad particular del error de predicción. Como consecuencia, la especificación paramétrica de los momentos condicionados puede ser testeada sin basarse en ninguna distribución particular del error. Demostramos que las distribuciones de los tests de boostrap G-ARC (BG-ACR) están bien aproximadas cuando usando distribuciones asintóticas estándar. Además, los tests propuestos son fáciles de implementar y están acompañados por herramientas gráficas, las cuáles proveen recomendaciones sobre la posible mala especificación del modelo. Los resultados son ilustrados testeando la especificación dinámica del modelo autorregresivo hetereogéneo (HAR) cuando se ajusta al popular índice de volatilidad norteamericano VIX.Programa Oficial de Doctorado en Economía de la Empresa y Métodos CuantitativosPresidente: Antoni Espasa Terrades; Secretario: Eva Senra Días; Vocal: Ángeles Carnero Fernánde