We present an econometric method for estimating the parameters of a diffusion model from discretely sampled data. The estimator is transparent, adaptive, and inherits the asymptotic properties of the generally unattainable maximum likelihood estimator. We use this method to estimate a new continuous-time model of the joint dynamics of interest rates in two countries and the exchange rate between the two currencies. The model allows financial markets to be incomplete and specifies the degree of incompleteness as a stochastic process. Our empirical results offer several new insights into the dynamics of exchange rates.

We propose a simple cross-sectional technique to extract daily factors from economic news released at different times and frequencies. Our approach can effectively handle the large number of different announcements that are relevant for tracking current economic conditions. We apply the technique to extract real-time measures of inflation, output, employment, and macroeconomic sentiment, as well as corresponding measures of disagreement among economists about these indices. We find that our procedure provides more timely and accurate forecasts of future changes in economic conditions than other real-time forecasting approaches.

We model the conditional mean and volatility of stock returns as a latent VAR process to study their contemporaneous and intertemporal relationships in a flexible statistical framework and without relying on exogenous predictors. We find a strong and robust negative correlation between the innovations to the conditional moments leading to pronounced countercyclical variation in the Sharpe ratio. We document significant lead-lag correlations between the moments that also appear related to business cycles. Finally, we show that although the conditional correlation between the mean and volatility is negative, the unconditional correlation is positive due to these lead-lag correlations.