62 research outputs found
Exact optimal and adaptive inference in regression models under heteroskedasticity and non-normality of unknown forms
In this paper, we derive simple point-optimal sign-based tests in the context of linear and
nonlinear regression models with fixed regressors. These tests are exact, distribution-free, robust
against heteroskedasticity of unknown form, and they may be inverted to obtain confidence
regions for the vector of unknown parameters. Since the point-optimal sign tests depend on the
alternative hypothesis, we propose an adaptive approach based on split-sample techniques in
order to choose an alternative such that the power of point-optimal sign tests is close to the
power envelope. The simulation results show that when using approximately 10% of sample to
estimate the alternative and the rest to calculate the test statistic, the power of point-optimal sign
test is typically close to the power envelope. We present a Monte Carlo study to assess the
performance of the proposed âquasiâ-point-optimal sign test by comparing its size and power to
those of some common tests which are supposed to be robust against heteroskedasticity. The
results show that our procedures are superior
Exact optimal and adaptive inference in regression models under heteroskedasticity and non-normality of unknown forms
In this paper, we derive simple point-optimal sign-based tests in the context of linear and nonlinear regression models with fixed regressors. These tests are exact, distribution-free, robust against heteroskedasticity of unknown form, and they may be inverted to obtain confidence regions for the vector of unknown parameters. Since the point-optimal sign tests depend on the alternative hypothesis, we propose an adaptive approach based on split-sample techniques in order to choose an alternative such that the power of point-optimal sign tests is close to the power envelope. The simulation results show that when using approximately 10% of sample to estimate the alternative and the rest to calculate the test statistic, the power of point-optimal sign test is typically close to the power envelope. We present a Monte Carlo study to assess the performance of the proposed âquasiâ-point-optimal sign test by comparing its size and power to those of some common tests which are supposed to be robust against heteroskedasticity. The results show that our procedures are superior.Sign test, Point-optimal test, Nonlinear model, Heteroskedasticity, Exact inference, Distribution-free, Power envelope, Split-sample, Adaptive method, Projection
What Drives International Equity Correlations? Volatility or Market Direction?
We consider impulse response functions to study the impact of both return and volatility on correlation between international equity markets. Using data on US (as the reference country), Canada, UK and France equity indices, empirical evidence shows that without taking into account the effect of return, there is an (asymmetric) effect of volatility on correlation. The volatility seems to have an impact on correlation especially during downturn periods. However, once we introduce the effect of return, the impact of volatility on correlation disappears. These observations suggest that, the relation between volatility and correlation is an association rather than a causality. The strong increase in the correlation is driven by the past of the return and the market direction rather than the volatility
What Drives International Equity Correlations? Volatility or Market Direction?
We consider impulse response functions to study the impact of both return and volatility on correlation between international equity markets. Using data on US (as the reference country), Canada, UK and France equity indices, empirical evidence shows that without taking into account the effect of return, there is an (asymmetric) effect of volatility on correlation. The volatility seems to have an impact on correlation especially during downturn periods. However, once we introduce the effect of return, the impact of volatility on correlation disappears. These observations suggest that, the relation between volatility and correlation is an association rather than a causality. The strong increase in the correlation is driven by the past of the return and the market direction rather than the volatility.International equity markets, Asymmetric volatility, Asymmetric correlation, Vector autoregressive (VAR), DCC-GARCH, Generalized impulse response function, Granger causality
A Nonparametric Copula Based Test for Conditional Independence with Applications to Granger Causality
This paper proposes a new nonparametric test for conditional independence, which is based on the comparison of Bernstein copula densities using the Hellinger distance. The test is easy to implement because it does not involve a weighting function in the test statistic, and it can be applied in general settings since there is no restriction on the dimension of the data. In fact, to apply the test, only a bandwidth is needed for the nonparametric copula. We prove that the test statistic is asymptotically pivotal under the null hypothesis, establish local power properties, and motivate the validity of the bootstrap technique that we use in finite sample settings. A simulation study illustrates the good size and power properties of the test. We illustrate the empirical relevance of our test by focusing on Granger causality using financial time series data to test for nonlinear leverage versus volatility feedback effects and to test for causality between stock returns and trading volume. In a third application, we investigate Granger causality between macroeconomic variables. Le prĂ©sent document propose un nouveau test non paramĂ©trique dâindĂ©pendance conditionnelle, lequel est fondĂ© sur la comparaison des densitĂ©s de la copule de Bernstein suivant la distance de Hellinger. Le test est facile Ă rĂ©aliser, du fait quâil nâimplique pas de fonction de pondĂ©ration dans les variables utilisĂ©es et peut ĂȘtre appliquĂ© dans des conditions gĂ©nĂ©rales puisquâil nây a pas de restriction sur lâĂ©tendue des donnĂ©es. En fait, dans le cas de la copule non paramĂ©trique, lâapplication du test ne requiert quâune largeur de bande. Nous dĂ©montrons que les variables utilisĂ©es pour le test jouent asymptotiquement un rĂŽle crucial sous lâhypothĂšse nulle. Nous Ă©tablissons aussi les propriĂ©tĂ©s des pouvoirs locaux et justifions la validitĂ© de la technique bootstrap (technique dâauto-amorçage) que nous utilisons dans les contextes oĂč les Ă©chantillons sont de taille finie. Une Ă©tude par simulation illustre lâampleur adĂ©quate et la puissance du test. Nous dĂ©montrons la pertinence empirique de notre dĂ©marche en mettant lâaccent sur les liens de causalitĂ© de Granger et en recourant Ă des sĂ©ries temporelles de donnĂ©es financiĂšres pour vĂ©rifier lâeffet de levier non linĂ©aire, par opposition Ă lâeffet de rĂ©troaction de la volatilitĂ©, et la causalitĂ© entre le rendement des actions et le volume des transactions. Dans une troisiĂšme application, nous examinons les liens de causalitĂ© de Granger entre certaines variables macroĂ©conomiques.Nonparametric tests, conditional independence, Granger non-causality, Bernstein density copula, bootstrap, finance, volatility asymmetry, leverage effect, volatility feedback effect, macroeconomics, tests non paramĂ©triques, indĂ©pendance conditionnelle, non-causalitĂ© de Granger, copule de densitĂ© de Bernstein, bootstrap, finance, asymĂ©trie de la volatilitĂ©, effet de levier, effet de rĂ©troaction de la volatilitĂ©, macroĂ©conomie.
Asymptotic properties of the Bernstein density copula for dependent data
Copulas are extensively used for dependence modeling. In many cases the data does not reveal how the dependence can be modeled using a particular parametric copula. Nonparametric copulas do not share this problem since they are entirely data based. This paper proposes nonparametric estimation of the density copula for α-mixing data using Bernstein polynomials. We study the asymptotic properties of the Bernstein density copula, i.e., we provide the exact asymptotic bias and variance, we establish the uniform strong consistency and the asymptotic normality.nonparametric estimation, copula, Bernstein polynomial, α-mixing, asymptotic properties, boundary bias
Measuring causality between volatility and returns with high-frequency data
We use high-frequency data to study the dynamic relationship between volatility and equity
returns. We provide evidence on two alternative mechanisms of interaction between returns and
volatilities: the leverage effect and the volatility feedback effect. The leverage hypothesis asserts
that return shocks lead to changes in conditional volatility, while the volatility feedback effect
theory assumes that return shocks can be caused by changes in conditional volatility through a
time-varying risk premium. On observing that a central difference between these alternative
explanations lies in the direction of causality, we consider vector autoregressive models of
returns and realized volatility and we measure these effects along with the time lags involved
through short-run and long-run causality measures proposed in Dufour and Taamouti (2008), as
opposed to simple correlations. We analyze 5-minute observations on S&P 500 Index futures
contracts, the associated realized volatilities (before and after filtering jumps through the
bispectrum) and implied volatilities. Using only returns and realized volatility, we find a weak
dynamic leverage effect for the first four hours at the hourly frequency and a strong dynamic
leverage effect for the first three days at the daily frequency. The volatility feedback effect
appears to be negligible at all horizons. By contrast, when implied volatility is considered, a
volatility feedback becomes apparent, whereas the leverage effect is almost the same. We
interpret these results as evidence that implied volatility contains important information on
future volatility, through its nonlinear relation with option prices which are themselves forwardlooking.
In addition, we study the dynamic impact of news on returns and volatility, again
through causality measures. First, to detect possible dynamic asymmetry, we separate good
from bad return news and find a much stronger impact of bad return news (as opposed to good
return news) on volatility. Second, we introduce a concept of news based on the difference
between implied and realized volatilities (the variance risk premium) and we find that a positive
variance risk premium (an anticipated increase in variance) has more impact on returns than a
negative variance risk premium
Asymptotic properties of the Bernstein density copula for dependent data
Copulas are extensively used for dependence modeling. In many cases the data does
not reveal how the dependence can be modeled using a particular parametric copula.
Nonparametric copulas do not share this problem since they are entirely data based.
This paper proposes nonparametric estimation of the density copula for α-mixing data
using Bernstein polynomials. We study the asymptotic properties of the Bernstein
density copula, i.e., we provide the exact asymptotic bias and variance, we establish
the uniform strong consistency and the asymptotic normality
A nonparametric copula based test for conditional independence with applications to Granger causality
nonparametric tests, conditional independence, Granger non-causality, Bernstein density copula, bootstrap, finance, volatility asymmetry, leverage effect, volatility feedback effect, macroeconomics
Nonparametric tests for conditional independence using conditional distributions
Financial support from the Natural Sciences and Engineering Research
Council of Canada and from the Spanish Ministry of Education through grants SEJ 2007-63098 are also acknowledgedThe concept of causality is naturally defined in terms of conditional distribution, however almost all the empirical works focus on causality in mean. This paper aim to propose a nonparametric statistic to test the conditional independence and Granger non-causality between two variables conditionally on another one. The test statistic is based on the comparison of conditional distribution functions using an L2 metric. We use Nadaraya-Watson method to estimate the conditional distribution functions. We establish the asymptotic size and power properties of the test statistic and we motivate the validity of the local bootstrap. Further, we ran a simulation experiment to investigate the finite sample properties of the test and we illustrate its practical relevance by examining the Granger non-causality between S&P 500 Index returns and VIX volatility index. Contrary to the conventional t-test, which is based on a linear mean-regression model, we find that VIX index predicts excess returns both at short and long horizons
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