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Instead of assuming the distribution of return series, Engle and Manganelli (2004) propose a new Value-at-Risk (VaR) modeling approach, Conditional Autoregressive Value-at-Risk (CAViaR), to directly compute the quantile of an individual asset's returns which performs better in many cases than those that invert a return distribution. In this paper we explore more flexible CAViaR models that allow VaR prediction to depend upon a richer information set involving returns on an index. Specifically, we formulate a time-varying CAViaR model whose parameters vary according to the evolution of the index. The empirical evidence reported in this paper suggests that our time-varying CAViaR models can do a better job for VaR prediction when there are spillover effects from one market or market segment to other markets or market segments.

We study how to measure and test for differences in dependence for small and large realizations of two variables of interest. We introduce a conditional version of Kendall's tau and provide formulas to evaluate it for any copula of interest. Two tests based on well known copulas are proposed to test the null hypothesis of symmetric dependence and these tests are shown to have higher power than competing tests proposed in the literature. Additionally, we suggest three examples of data generating processes that can lead to asymmetric dependence and study these both analytically and in a Monte Carlo framework. Finally, we illustrate the use of our tests on stock market returns and on quarterly U.S. GNP and unemployment data and we find evidence of asymmetries and nonlinearities.

This paper generalizes the Hyperbolic Asymmetric Power ARCH (HYAPARCH) model to allow for time varying skewness and kurtosis in the conditional distribution. This is done by modeling the conditional skewness and degrees of freedom of the skewed Student's t distribution of Lambert and Laurent (2001) as a function of the conditioning information. The proposed specification nests a large number of models in the literature and represents the first attempt to jointly model long memory in volatility and time variation in the third and fourth moments. The finite sample properties of MLE for this class of model are examined. The results indicate that the ARCH class of processes with time varying skewness can be reliably estimated with realistic sample sizes. Simulations and empirical evidence are unable to replicate the findings of Harvey and Siddique (1999), that accounting for time varying skewness reduces the persistence and asymmetry properties of the conditional variance. Simulations also suggest that time varying kurtosis estimation must be viewed with caution, because it can be difficult to identify in the presence of ARCH effects. Application of the HYAPARCH model with time varying skewness and degrees of freedom illustrates the usefulness of the proposed approach. Out of sample forecasts of the value at risk (VaR) however, generally support parsimonious models that assume conditional normality. When forecasting VaR, skewness and leptokurtosis in the unconditional return distribution is generally better captured via an asymmetric conditional variance model with Gaussian innovations.

We estimate the term premium in the term structure of risk-free interest rates using a Markov switching model with ARMA-GARCH errors. We find that the Markov switching term premium is closely related to the U.S. business cycle and plays a significant role in explaining changes in short-term interest rates. The result is not affected even when we consider other macro variables or excess return forecasting factors. In order to estimate the Markov switching model with the non-Markovian structure, we propose a new Bayesian approach by which we do not need to approximate the likelihood function and we generate the state variable using a Gibbs sampler.

In this paper we point out some features of the dynamical models describing the interaction of two similar agents competing in a market. Such models are fitted by a two-dimensional map symmetric with respect to the diagonal, i.e., such that M(x,y)=M(y,x). In particular we shall consider a model describing the strategic behavior of two firms that produce complementary goods and have adaptive expectations.The aim of the paper is the analysis of the trajectories generated by the iteration of M starting from different initial conditions. In particular we are interested in two different problems arising in such a situation. First, we analyze the conditions that allow an agent to reach a favourable position (in terms of its profit) in the long run. Second we investigate the mechanisms that lead the agents to behave in the same way in the long run (synchronization) and the phenomena associated with these particular situations, such as the on-off intermittency.