Goodness-of-fit test for copulas

Copulas are often used in finance to characterize the dependence between assets. However, a choice of the functional form for the copula is an open question in the literature. This paper develops a goodness-of-fit test for copulas based on positive definite bilinear forms. The suggested test avoids the use of plug-in estimators that is the common practice in the literature. The test statistics can be consistently computed on the basis of V-estimators even in the case of large dimensions. The test is applied to a dataset of US large cap stocks to assess the performance of the Gaussian copula for the portfolios of assets of various dimension. The Gaussian copula appears to be inadequate to characterize the dependence between assets.

A new statistic and practical guidelines for nonparametric Granger causality testing

Upon illustrating how smoothing may cause over-rejection in nonparametric tests for Granger non-causality, we propose a new test statistic for which problems of this type can be avoided. We develop asymptotic theory for the new test statistic, and perform a simulation study to investigate the properties of the new test in comparison with its natural counterpart, the Hiemstra-Jones test. Our simulation results indicate that, if the bandwidth tends to zero at the appropriate rate as the sample size increases, the size of the new test remains close to nominal, while the power remains large. Transforming the time series to uniform marginals improves the behavior of both tests. In applications to Standard and Poor's index volumes and returns, the Hiemstra-Jones test suggests that volume Granger-causes returns. However, the evidence for this gets weaker if we carefully apply the recommendations suggested by our simulation study.

Rank-based entropy tests for serial independence

In nonparametric tests for serial independence the marginal distribution of the data acts as an infinite dimensional nuisance parameter. The decomposition of joint distributions in terms of a copula density and marginal densities shows that in general empirical marginals carry no information on dependence. It follows that the order of ranks is sufficient for inference, which motivates transforming the data to a pre-specified marginal distribution prior to testing. As a test statistic we use an estimator of the marginal redundancy, which has some desirable properties in the case of transforming to uniform marginals. We numerically study the finite sample properties of these tests when the data are transformed to uniform as well as normal marginals. The performance of the tests is compared with that of the BDS test as well as with a parametric rank-based test against ARCH alternatives.

Asset Prices, Traders' Behavior, and Market Design

The dynamics in a financial market with heterogeneous agents is analyzed under different market architectures. We start with a tractable behavioral model under Walrasian market clearing and simulate it under more realistic trading protocols. The key behavioral feature of the model is the switching of agents between simple forecasting rules on the basis of fitness measure. Analyzing the dynamics under order-driven protocols we show that behavioral and structural assumptions of the model are closely intertwined. High responsiveness of agents to a fitness measure causes excess volatility, however the frictions of the order-driven markets may stabilize the dynamics.

Nonparametric Tests for Serial Independence Based on Quadratic Forms

Tests for serial independence and goodness-of-fit based on divergence notions between probability distributions, such as the Kullback-Leibler divergence or Hellinger distance, have recently received much interest in time series analysis. The aim of this paper is to introduce tests for serial independence using kernel-based quadratic forms. This separates the problem of consistently estimating the divergence measure from that of consistently estimating the underlying joint densities, the existence of which is no longer required. Exact level tests are obtained by implementing a Monte Carlo procedure using permutations of the original observations. The bandwidth selection problem is addressed by introducing a multiple bandwidth procedure based on a range of different bandwidth values. After numerically establishing that the tests perform well compared to existing nonparametric tests, applications to estimated time series residuals are considered. The approach is illustrated with an application to financial returns data.

Infrared radiation and inversion population of CO2 laser levels in Venusian and Martian atmospheres

Formation mechanisms of nonequilibrium 10 micron CO2 molecule radiation and the possible existence of a natural laser effect in the upper atmospheres of Venus and Mars are theoretically studied. An analysis is made of the excitation process of CO2 molecule vibrational-band levels (with natural isotropic content) induced by direct solar radiation in bands 10.6, 9.4, 4.3, 2.7 and 2.0 microns. The model of partial vibrational-band temperatures was used in the case. The problem of IR radiation transfer in vibrational-rotational bands was solved in the radiation escape approximation