We develop a jackknife estimator for the conditional variance of a minimum-tracking- error-variance portfolio constructed using estimated covariances. We empirically evaluate the performance of our estimator using an optimal portfolio of 200 stocks that has the lowest tracking error with respect...

In this paper, we develop the theoretical and empirical properties of a new class of multi-variate GARCH models capable of estimating large time-varying covariance matrices, Dynamic Conditional Correlation Multivariate GARCH. We show that the problem of multivariate conditional variance...

We investigate the potential for Large Language Models (LLMs) to enhance scientific practice within experimentation by identifying key areas, directions, and implications. First, we discuss how these models can improve experimental design, including improving the elicitation wording, coding...

Volatility has been one of the most active and successful areas of research in time series econometrics and economic forecasting in recent decades. This chapter provides a selective survey of the most important theoretical developments and empirical insights to emerge from this burgeoning...

What do academics have to offer market risk management practitioners in financial institutions? Current industry practice largely follows one of two extremely restrictive approaches: historical simulation or RiskMetrics. In contrast, we favor flexible methods based on recent developments in...

Most affine models of the term structure with stochastic volatility (SV) predict that the variance of the short rate is simultaneously a linear combination of yields and the quadratic variation of the spot rate. However, we find empirically that the A1(3) SV model generates a time series for the...

I review and interpret two of Robert Engle's most important contributions: the theory and application of cointegration, and the theory and application of dynamic volatility models. I treat the latter much more extensively, de-emphasizing technical aspects and focusing instead on the intuition,...

Movements in the prices of different assets are likely to directly influence one another. This paper develops a model that identifies the contemporaneous interactions between asset prices in U.S. financial markets by relying on the heteroskedasticity in their movements. In particular, we...

We propose testing asset-pricing models using multi-horizon returns (MHR). A correctly specified stochastic discount factor prices the cross-section of returns at all horizons. We show that MHR are informative about the model's conditional implications. Different from typical conditioning...

Although ARCH-related models have proven quite popular in finance, they are less frequently used in macroeconomic applications. In part this may be because macroeconomists are usually more concerned about characterizing the conditional mean rather than the conditional variance of a time series....