Bootstraping financial time series

It is well known that time series of returns are characterized by volatility clustering and excess kurtosis. Therefore, when modelling the dynamic behavior of returns, inference and prediction methods, based on independent and/or Gaussian observations may be inadequate. As bootstrap methods are not, in general, based on any particular assumption on the distribution of the data, they are well suited for the analysis of returns. This paper reviews the application of bootstrap procedures for inference and prediction of financial time series. In relation to inference, bootstrap techniques have been applied to obtain the sample distribution of statistics for testing, for example, autoregressive dynamics in the conditional mean and variance, unit roots in the mean, fractional integration in volatility and the predictive ability of technical trading rules. On the other hand, bootstrap procedures have been used to estimate the distribution of returns which is of interest, for example, for Value at Risk (VaR) models or for prediction purposes. Although the application of bootstrap techniques to the empirical analysis of financial time series is very broad, there are few analytical results on the statistical properties of these techniques when applied to heteroscedastic time series. Furthermore, there are quite a few papers where the bootstrap procedures used are not adequate.Publicad

The relationship between ARIMA-GARCH and unobserved component models with GARCH disturbances

The objective of this paper is to analyze the consequences of fitting ARIMA-GARCH models to series generated by conditionally heteroscedastic unobserved component models. Focusing on the local level model, we show that the heteroscedasticity is weaker in the ARIMA than in the local level disturbances. In certain cases, the IMA(1,1) model could even be wrongly seen as homoscedastic. Next, with regard to forecasting performance, we show that the prediction intervals based on the ARIMA model can be inappropriate as they incorporate the unit root while the intervals of the local level model can converge to the homoscedastic intervals when the heteroscedasticity appears only in the transitory noise. All the analytical results are illustrated with simulated and real time series

Direct versus iterated multiperiod Value-at-Risk forecasts

Since the late nineties, the Basel Accords require financial institutions to measure their financial risk by reporting daily predictions of Value at Risk (VaR) based on 10-day returns. However, a vast part of the related literature deals with VaR predictions based on one-period returns. Given its relevance for practitioners, in this paper, we survey the literature on available procedures to estimate VaR over an h-period. First, to convert 1 day into 10-day VaR, it is popular to use the square-root-of-time (SRoT) rule, which is only satisfied under very restrictive and unrealistic properties of returns. Alternatively, direct (based on h-period returns) and iterated (based on one-period returns) two-step procedures can be implemented to obtain 10-period VaR. We also illustrate and compare the performance of these procedures in the context of popular conditionally heteroscedastic models for returns using both simulated and real data. We show that, under realistic assumptions on the distribution of returns, multiperiod VaR predictions based on iterating an asymmetric GJR model with normal or bootstrapped errors are usually preferred. We also show that, in general, direct methods could be not only biased but also inefficient.Ministerio de Economía y Competitividad. Grant Number: PDI2019-108079GB-C21/AIE/10.13039/50110001103

El trabajo rítmico realizado a través de la música: Una herramienta para la rehabilitación de niños/niñas con dislalia funcional

En este trabajo se muestran los resultados obtenidos en dos variables: Adaptación a un ritmo externo y repetición de estructuras rítmicas, tras aplicar, como intervención indirecta, un programa de música específicamente diseñado para mejorar las bases funcionales del lenguaje oral, a un grupo experimental de sujetos con dislalia funcional. Dichos resultados se han extraído de una investigación más amplia, realizada según un diseño pre-test-rehabilitación-post-test, en la que durante cinco meses el grupo experimental recibió clases de música una vez por semana, además de la sesión de intervención directa con la logopeda. El grupo control no recibió clases de música y continuó con su tratamiento logopédico habitual. La investigación incidía en 7 variables de las que se han seleccionado las ya mencionadas por su relevancia en los problemas tratados. Los resultados sugieren que el trabajo rítmico realizado a través de la música ha contribuido a rehabilitar las dislalias funcionales que presentabanIn this work, it is shown the results obtained within two variables: Adaptation to an external rhythm and repetition of rhythmic structures, after implementing, as indirect intervention, a music programme specially designed to improve the functional basis of oral language, to an experimental group of subjects with functional difficulties of articulating the words. Those results have been extracted from a comprehensive research made according to a pre-test- rehabilitation- post-test design, in which for five months the experimental group received music lessons once a week, in addition to the direct intervention session with speech therapist. The control group doesn´t received music lessons and continued his usual speech therapy. The research touched on 7 variables; from those variables, we have selected the two mentioned above because they have a specific relevance on the dysfunctions treated. The results suggest that the rhythmic work through music has helped rehabilitate the difficulties presentin

Estimating non-stationary common factors : Implications for risk sharing

In this paper, we analyze and compare the finite sample properties of alternative factor extraction procedures in the context of non-stationary Dynamic Factor Models (DFMs). On top of considering procedures already available in the literature, we extend the hybrid method based on the combination of principal components and Kalman filter and smoothing algorithms to non-stationary models. We show that, unless the idiosyncratic noise is non-stationary, procedures based on extracting the factors using the nonstationary original series work better than those based on differenced variables. The results are illustrated in an empirical application fitting non-stationary DFM to aggregate GDP and consumption of the set of 21 OECD industrialized countries. The goal is to check international risk sharing is a short or long-run issue.Financial support is acknowledged from Projects ECO2015-70331-C2-1-R and ECO2015-70331-C2-2-R(MINECO/FEDER) by the Spanish Government

Bootstrap multi-step forecasts of non-Gaussian VAR models

In this paper, we establish the asymptotic validity and analyse the finite sample performance of a simple bootstrap procedure for constructing multi-step multivariate forecast densities in the context of non-Gaussian unrestricted VAR models. This bootstrap procedure avoids the backward representation, and, as a consequence, can be used to obtain multivariate forecast densities in, for example, VARMA or VAR-GARCH models. In the context of bivariate stationary VAR(p) models, we show that its finite sample properties are comparable to those of alternatives based on the backward representation. The bootstrap procedure is also implemented in a VAR-DCC model which lacks a backward representation. Finally, joint forecast densities of US quarterly inflation, unemployment and GDP growth are obtained. (C) 2014 International Institute of Forecasters. Published by Elsevier B.V. All rights reserved.The first two authors are grateful for financial support from projects ECO2009-08100 and ECO2012-32401 from the Spanish Government

Frontiers in VaR forecasting and backtesting

The interest in forecasting the Value at Risk (VaR) has been growing over the last two decades, due to the practical relevance of this risk measure for financial and insurance institutions. Furthermore, VaR forecasts are often used as a testing ground when fitting alternative models for representing the dynamic evolution of time series of financial returns. There are vast numbers of alternative methods for constructing and evaluating VaR forecasts. In this paper, we survey the new benchmarks proposed in the recent literature.Financial support from Project ECO2012-32401 by the Spanish Government is gratefully acknowledged by the second author. We are also grateful to the Editor Rob Hyndman for his support and to three anonymous reviewers for their detailed and constructive comments

Prediction regions for interval-valued time series

We approximate probabilistic forecasts for interval-valued time series by offering alternative approaches. After fitting a possibly non-Gaussian bivariate VAR model to the center/log-range system, we transform prediction regions (analytical and bootstrap) for this system into regions for center/range and upper/lower bounds systems. Monte Carlo simulations show that bootstrap methods are preferred according to several new metrics. For daily S&P500 low/high returns, we build joint conditional prediction regions of the return level and volatility. We illustrate the usefulness of obtaining bootstrap forecasts regions for low/high returns by developing a trading strategy and showing its profitability when compared to using point forecasts.Gloria González-Rivera acknowledges financial support from the 2015/2016 Chair of Excellence UC3M/Banco de Santander and the UC-Riverside Academic Senate grants. Esther Ruiz and Gloria González-Rivera are grateful to the Spanish Government contract grant ECO2015-70331-C2-2-R (MINECO/FEDER)

Growth in Stress

We propose a new global risk index, Growth-in-Stress (GiS), that measures the expected decrease in a country GDP growth as the global factors, which drive world growth, are subject to stressful conditions. Stress is measured as the 95% contours of the joint probability distribution of the factors. With GDP growth rates of a sample of 87 countries in the World Bank and International Monetary Fund databases and for the period 1985 to 2015, we extract three global factors: a first world growth factor driven mainly by all industrial and emerging countries; a second factor driven by “other developing” countries in Africa and America; and a third factor that is mostly related to East Asian economies. We find that the average GiS across industrialized, emerging and other developing countries has been going down from 1987. Post 2008 financial crisis, mainly from 2011 on, the world overall has fallen in a state-of-complacency with the average GiS falling quite dramatically to reach the lowest levels of risk (0-1% potential drop in growth) in 2015. However, the dispersion within groups is quite wide. It is the smallest among industrialized countries and the largest among emerging and other developing countries. We also measure the factor stress on different quantiles of the DGP growth distribution of each country. We calculate an Armageddon-type event as we seek to find the 5% GiS quantile under 95% extreme factor events and find that it can be as large as an annual 20% drop in growth.Financial Support from the Spanish Government contract grant ECO2015-70331-C2-2-R (MINECO/FEDER) is gratefully acknowledged. We are also grateful for very helpful comments to participants at Time Series Workshop meeting (2018, Zaragoza) and at Conference on Statistical Methods for Big Data (2018, Madrid). González-Rivera acknowledges the financial support of the UC-Riverside Academic Senate grants. Any remaining errors are obviously our responsibility

Identification of asymmetric conditional heteroscedasticity in the presence of outliers

The identification of asymmetric conditional heteroscedasticity is often based on samplecross-correlations between past and squared observations. In this paper we analyse theeffects of outliers on these cross-correlations and, consequently, on the identification ofasymmetric volatilities. We show that, as expected, one isolated big outlier biases thesample cross-correlations towards zero and hence could hide true leverage effect.Unlike, the presence of two or more big consecutive outliers could lead to detectingspurious asymmetries or asymmetries of the wrong sign. We also address the problemof robust estimation of the cross-correlations by extending some popular robustestimators of pairwise correlations and autocorrelations. Their finite sample resistanceagainst outliers is compared through Monte Carlo experiments. Situations with isolatedand patchy outliers of different sizes are examined. It is shown that a modified Ramsayweightedestimator of the cross-correlations outperforms other estimators in identifyingasymmetric conditionally heteroscedastic models. Finally, the results are illustrated withan empirical applicatio