Our subject is estimation and inference concerning long-run economic equilibria in models with stochastic trends. An asymptotic theory is provided to analyze a menu of currently existing estimators of cointegrated systems. We study in detail the single-equation ECM (SEECM) approach of Hendry. Our theoretical results lead to prescriptions for empirical work, such as specifying SEECM's nonlinearly and including lagged equilibrium relationships rather than lagged differences of the dependent variable as covariates. Simulations support these prescriptions, and point to problems of overfitting not encountered in the semi parametric approach of Phillips and Hansen (1990).

Correlations are crucial for pricing and hedging derivatives whose payoff depends on more than one asset. Typically, correlations computed separately for ordinary and stressful market conditions differ considerably, a pattern widely termed "correlation breakdown." As a result, risk managers worry that their hedges will be useless when they are most needed, namely during "stressful" market situations. We show that such worries may not be justified since "correlation breakdowns" can easily be generated by data whose distribution is stationary and, in particular, whose correlation coefficient is constant. We make this point analytically, by way of several numerical examples, and via an empirical illustration. But, risk managers should not necessarily relax. Although "correlation breakdown" can be an artifact of poor data analysis, other evidence suggests that correlations do in fact change over time.

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Financial market observers have noted that during periods of high market volatility, correlations between asset prices can differ substantially from those seen in quieter markets. For example, correlations among yield spreads were substantially higher during the fall of 1998 than in earlier or later periods. Such differences in correlations have been attributed either to structural breaks in the underlying distribution of returns or to "contagion" across markets that occurs only during periods of market turbulence. However, we argue that the differences may reflect nothing more than time-varying sampling volatility. As noted by Boyer, Gibson, and Loretan (1999), increases in the volatility of returns are generally accompanied by an increase in sampling correlations even when the true correlations are constant. We show that this result is not just of theoretical interest: When we consider quarterly measures of volatility and correlation for three pairs of asset returns, we find that the theoretical relationship can explain much of the movement in correlations over time. We then examine the implications of this link between measures of volatility and correlation for risk management, bank supervision, and monetary policy making.