Autocontour-based evaluation of multivariate predictive densities

González‐Rivera, Gloria; Yoldaş, Emre

doi:10.1016/j.ijforecast.2011.06.001

Cited by 13 publications

(3 citation statements)

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“…Alternatively, Hong and Li (2005) propose a nonparametric-kernel-based test with power against violations of both independence and density functional form, but it depends on the choice of a bandwidth, which could be problematic to choose in an empirical context. Instead of testing for independence and uniformity of PITs, González-Rivera et al (2011) and González-Rivera and Yoldas (2012) propose autocontour (ACR) tests to evaluate the adequacy of the conditional density model based on the generalized errors of the model. They propose the "autocontour" device as a graphical tool that can be very helpful for guiding the modelling.…”

Section: Introductionmentioning

confidence: 99%

A bootstrap approach for generalized Autocontour testing Implications for VIX forecast densities

Mazzeu

González‐Rivera

Ruiz

et al. 2020

Econometric Reviews

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We propose an extension of the Generalized Autocontour (G-ACR) tests for dynamic specification of in-sample conditional densities and for evaluation of out-of-sample forecast densities. The new tests are based on probability integral transforms (PITs) computed from bootstrap conditional densities that incorporate parameter uncertainty. Then, the parametric specification of the conditional moments * Financial support from the Spanish Ministry of Education and Science, research project ECO2015-70331-C2-2-R (MINECO/FEDER) is acknowledged by the four authors. The fourth author also acknowledges research project ECO2012-3240 and FCT grant UID/GES/00315/2013. Gloria González-Rivera wishes to thank the Department of Statistics at UC3M for their hospitality and the financial support of the 2015 Chair of Excellence UC3M/Banco de Santander, and the UCR Academic Senate grant. We are grateful to the participants at the New Developments in Econometrics and Time Series Workshop, Madrid, October 2016, and at the IMF/IIF Workshop on Forecasting Issues on Developing Economies, Washington DC, April 2017, and to seminar participants at the Management School of the University of Liverpool, for their very useful comments. We are also thankful to J. Mencía and E. Sentana for their help with the codes to estimate the MEM model. 1can be tested without relying on any parametric error distribution yet exploiting distributional properties of the variable of interest. We show that the finite sample distribution 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 that provide information about the potential sources of misspecification. We apply the BG-ACR tests to the Heterogeneous Autoregressive (HAR) model and the Multiplicative Error Model (MEM) of the U.S. volatility index VIX. We find strong evidence against the parametric assumptions of the conditional densities, i.e. normality in the HAR model and semi non-parametric Gamma (GSNP) in the MEM. In both cases, the true conditional density seems to be more skewed to the right and more peaked than either normal or GSNP densities, with location, variance and skewness changing over time. The preferred specification is the heteroscedastic HAR model with bootstrap conditional densities of the log-VIX. Supplementary materials for this article are available online.

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Section: Introductionmentioning

confidence: 99%

A bootstrap approach for generalized Autocontour testing Implications for VIX forecast densities

Mazzeu

González‐Rivera

Ruiz

et al. 2020

Econometric Reviews

Self Cite

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“…There is a rather extensive literature on the evaluation of point multivariate forecasts; see, for example, Komunjer and Owyang (). Also, recently, several authors have proposed different evaluation criteria for multivariate forecast densities; see Diebold, Han, and Tay (), Clements and Smith (), Gneiting et al (), González‐Rivera and Yoldas (), and González‐Rivera and Sun (). However, the literature on evaluating multivariate prediction regions is rather thin.…”

Section: Introductionmentioning

confidence: 99%

Prediction regions for interval‐valued time series

González‐Rivera

Luo

Ruiz

2020

J of Applied Econometrics

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We approximate probabilistic forecasts for interval-valued time series by offering alternative approaches. After fitting a possibly non-Gaussian bivariate vector autoregression (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&P 500 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.

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“…Many tasks, such as the computation of Value-at-Risk measures for portfolios containing multiple assets or the planning of production for a firm that serves many markets from one central production facility, require the construction and evaluation of multivariate density forecasts. Beginning with Smith (1985) and Diebold et al (1999), the literature has proposed several approaches for testing whether a sequence of multivariate density forecasts coincides with the corresponding true densities (e. g., Smith, 2000, 2002;Corradi and Swanson, 2006a;Bai and Chen, 2008;González-Rivera and Yoldas, 2012;Ko and Park, 2013a;Ziegel and Gneiting, 2014).…”

Section: Introductionmentioning

confidence: 99%