This paper investigates the time series estimation of Cox, Ingersoll, and Ross's square root, mean-reverting specification for interest rate dynamics. For a priori resonable mean reversion, the stochastic behavior of interest rates is sufficiently close to a non-stationary process with a unit root so that least squares, the generalized method of moments, as well as maximum likelihood estimation provide upward biased estimates of the model's speed of adjustment coefficient. Corresponding bond yields, as a result, exhibit excessive mean reversion. In addition, estimates of the specification's long-term mean interest rate are seen to display erratic behavior when near a unit root. These conclusions are robust to assuming multiple state variable specifications, such as Brennan and Schwartz's two factor model of interest rate dynamics. We also document conditions under which this unit root problem can be alleviated when the cross-sectional restrictions of the Cox, Ingersoll, and Ross single factor term structure model are imposed.

Chan, Karolyi, Longstaff, and Sanders [1992] find no evidence that the October 1979 change in Federal Reserve operating policy resulted in a once-and-for-all deterministic break in the behavior of short term riskless interest rates. In contrast, we provide evidence of such a regime shift even after allowing the volatility of interest rate changes to depend on the level of interest rates. However, rather than modeling this regime-shift as a permanent event with no further shifts possible, it is more realistic to model the change in regimes itself as a random variable. Accordingly, we put forward a stochastic volatility interest rate model which generalizes previous specifications of interest rate dynamics and allowed testing for stochastic regime shifts. This Markov regime shifting model provides a more accurate description of the behavior of U.S. short term riskless interest rates. We also consider a specification that allows interest rate volatility to follow a diffusion proves and we provide a statistically efficient integration-based filtering procedure to estimate its parameters. Five U.S. short term riskless interest rate data, we cannot statistically distinguish between these alternative models. In either case, once the stochastic nature of interest rate volatility is taken in account, we find little or no evidence of a deterministic structural break in corresponding stochastic volatility interest rate dynamics around October 1979.

This paper examines the correlation across a number of international stock market indices. As correlation is not observable, we assume it to be a latent variable whose dynamics must be estimated using data on observables. To do so, we use ¯ltering methods to extract stochastic correlation from returns data. We ¯nd evidence that the estimated correlation structure is dynamically changing over time. We also investigate the link between stochastic correlation and volatility. In general, stochastic correlation tends to increase in response to higher volatility but the e®ect is by no means consistent. These results have important implications for portfolio theory as well as risk management.