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A flexible multivariate model of a time-varying joint distribution of asset returns is developed which allows for regime switching and a joint skew-normal distribution. A suite of tests for linear and nonlinear financial market contagion is developed within the framework. The model is illustrated through an application to contagion between US and European equity markets during the Global Financial Crisis. The results show that correlation contagion dominates coskewness contagion, but that coskewness contagion is significant for Greece. A flight to safety to the US is also evident in the significance of breaks in the skewness parameter in the crisis regime. Comparison to the Asian crisis shows that similar patterns emerge, with a flight to safety to Japan, and Malaysia affected by coskewnes contagion with Hong Kong.

A new test for financial market contagion based on changes in extremal dependence defined as co-kurtosis and co-volatility is developed to identify the propagation mechanism of shocks across international financial markets. The proposed approach captures changes in various aspects of the asset return relationships such as crossmarket mean and skewness (co-kurtosis) as well as cross-market volatilities (covolatility). Monte Carlo experiments show that the tests perform well except for when crisis periods are short in duration. Small crisis sample critical values are calculated for use in this case. In an empirical application involving the global financial crisis of 2008-09, the results show that significant contagion effects are widespread from the US banking sector to global equity markets and banking sectors through either the cokurtosis or the co-volatility channels, reinforcing that higher order moments matter during crises.

Financial time series often exhibit properties that depart from the usual assumptions of serial independence and normality. These include volatility clustering, heavy-tailedness and serial dependence. A voluminous literature on different approaches for modeling these empirical regularities has emerged in the last decade. In this paper we review the estimation of a variety of highly flexible stochastic volatility models, and introduce some efficient algorithms based on recent advances in state space simulation techniques. These estimation methods are illustrated via empirical examples involving precious metal and foreign exchange returns. The corresponding Matlab code is also provided.