In the class of univariate conditional volatility models, the three most popular are the generalized autoregressive conditional heteroskedasticity (GARCH) model of Engle (1982) and Bollerslev (1986), the GJR (or threshold GARCH) model of Glosten, Jagannathan and Runkle (1992), and the...

An early development in testing for causality (technically, Granger non-causality) in the conditional variance (or volatility) associated with financial returns, was the portmanteau statistic for non-causality in variance of Cheng and Ng (1996). A subsequent development was the Lagrange...

This paper derives the statistical properties of a two-step approach to estimating multivariate rotated GARCH-BEKK (RBEKK) models. From the definition of RBEKK, the unconditional covariance matrix is estimated in the first step to rotate the observed variables in order to have the identity...

We propose a nonparametric Bayesian approach for conducting inference on probabilistic surveys. We use this approach to study whether U.S. Survey of Professional Forecasters density projections for output growth and inflation are consistent with the noisy rational expectations hypothesis. We...

In this paper we expand the literature of risk neutral density estimation across maturities from implied volatility curves, usually estimated and interpolated through cubic smoothing splines. The risk neutral densities are computed through the second derivative as in Panigirtzoglou and...

This article discusses Windle and Carvalho's (2014) state-space model for observations and latent variables in the space of positive symmetric matrices. The present discussion focuses on the model specification and on the contribution to the positive-value time series literature. I apply the...