Comparing Density Forecasts in a Risk Management Context
International Journal of Forecasting , Volume 36, Issue 2, April–June 2020, Pages 531-551
We compare multivariate and univariate approaches to assessing the accuracy of competing density forecasts of a portfolio return in the downside part of the support. We argue that the common practice of performing multivariate forecast comparisons can be problematic in the context of assessing portfolio risk, since better multivariate forecasts do not necessarily correspond to better aggregate portfolio return forecasts. This is illustrated by examples that involve (skew) elliptical distributions and an application to daily returns of a number of US stock prices. In addition, time-varying test statistics and Value-at-Risk forecasts provide empirical evidence of regime changes over the last decades.
We compare multivariate and univariate approaches to assessing the accuracy of competing density forecasts of a portfolio return in the downside part of the support. We argue that the common practice of performing multivariate forecast comparisons can be problematic in the context of assessing portfolio risk, since better multivariate forecasts do not necessarily correspond to better aggregate portfolio return forecasts. This is illustrated by examples that involve (skew) elliptical distributions and an application to daily returns of a number of US stock prices. In addition, time-varying test statistics and Value-at-Risk forecasts provide empirical evidence of regime changes over the last decades.
Transfer Entropy for Nonparametric Granger Causality Detection: An Evaluation of Different Resampling Methods
Entropy, Entropic Applications in Economics and Finance, 2017, 19(7), 372
The information-theoretical concept transfer entropy is an ideal measure for detecting conditional independence, or Granger causality in a time series setting. The recent literature indeed witnesses an increased interest in applications of entropy-based tests in this direction. However, those tests are typically based on nonparametric entropy estimates for which the development of formal asymptotic theory turns out to be challenging. In this paper, we provide numerical comparisons for simulation-based tests to gain some insights into the statistical behavior of nonparametric transfer entropy-based tests. In particular, surrogate algorithms and smoothed bootstrap procedures are described and compared. We conclude this paper with a financial application to the detection of spillover effects in the global equity market.
The information-theoretical concept transfer entropy is an ideal measure for detecting conditional independence, or Granger causality in a time series setting. The recent literature indeed witnesses an increased interest in applications of entropy-based tests in this direction. However, those tests are typically based on nonparametric entropy estimates for which the development of formal asymptotic theory turns out to be challenging. In this paper, we provide numerical comparisons for simulation-based tests to gain some insights into the statistical behavior of nonparametric transfer entropy-based tests. In particular, surrogate algorithms and smoothed bootstrap procedures are described and compared. We conclude this paper with a financial application to the detection of spillover effects in the global equity market.
Detecting Granger Causality with a Nonparametric Information-based Statistic
CeNDEF Working paper 17-03 University of Amsterdam
Testing causal effects has attracted much attention in the domains of many disciplines since Granger’s pioneering work. The recent literature shows an increasing interest in testing for Granger non-causality in a general sense by nonparametric evaluation of conditional dependence. This paper introduces a novel nonparametric test based on the first order Taylor expansion of an information theoretic measure: transfer entropy. The new test statistic is shown to have an information-based interpretation for Granger non-causality. The proposed test avoids the lack of power problem in the frequently-used test proposed by Diks and Panchenko (2006), which is not a consistent test under some alternatives. Attributed to the U-statistic representation, the asymptotic normality of our test statistic is achieved when all densities are estimated with appropriate sample-size dependent bandwidth. Simulation result confirms the usefulness of this test. Finally two applications to financial data of daily and intraday frequency conclude this paper.
Testing causal effects has attracted much attention in the domains of many disciplines since Granger’s pioneering work. The recent literature shows an increasing interest in testing for Granger non-causality in a general sense by nonparametric evaluation of conditional dependence. This paper introduces a novel nonparametric test based on the first order Taylor expansion of an information theoretic measure: transfer entropy. The new test statistic is shown to have an information-based interpretation for Granger non-causality. The proposed test avoids the lack of power problem in the frequently-used test proposed by Diks and Panchenko (2006), which is not a consistent test under some alternatives. Attributed to the U-statistic representation, the asymptotic normality of our test statistic is achieved when all densities are estimated with appropriate sample-size dependent bandwidth. Simulation result confirms the usefulness of this test. Finally two applications to financial data of daily and intraday frequency conclude this paper.