Simple, multi-step estimators are developed for the popular GARCH(1,1) model, where these estimators are either available entirely in closed form or dependent upon a preliminary estimate from, for example, quasi-maximum likelihood. Identification sources to asymmetry in the model's innovations,...

Linear GARCH(1,1) and threshold GARCH(1,1) processes are established as regularly varying, meaning their heavy tails are Pareto like, under conditions that allow the innovations from the, respective, processes to be skewed. Skewness is considered a stylized fact for many financial returns...

Strong consistency and weak distributional convergence to highly non-Gaussian limits are established for closed-form, two stage least squares (TSLS) estimators for a class of ARCH(p) models. Conditions for these results include (relatively) mild moment existence criteria that are supported...

While many studies find that the tail distribution of high frequency stock returns follow a power law, there are only a few explanations for this finding. This study presents evidence that time-varying volatility can account for the power law property of high frequency stock returns. The power...

We study the relationship between volatility and liquidity in the market for on-the-run Treasury securities using a novel framework for quantifying price impact. We show that at times of relatively low volatility, marginal trades that go with the flow of existing trades tend to have a smaller...

We estimate a reduced-form model of credit risk that incorporates stochastic volatility in default intensity via stochastic time-change. Our Bayesian MCMC estimation method overcomes nonlinearity in the measurement equation and state-dependent volatility in the state equation. We implement on...

This paper proposes a residual based cointegration test with improved power. Based on the idea of Hansen (1995) and Elliott & Jansson (2003) in the unit root testing case, stationary covariates are used to improve the power of the residual based Augmented Dickey Fuller (ADF) test. The asymptotic...

We derive the multivariate moment generating function (mgf) for the stationary distribution of a discrete sample path of n observations of a square-root diffusion (CIR) process, X(t). The form of the mgf establishes that the stationary joint distribution of (X(t(1)),...,X(t(n))) for any fixed...

This paper proposes a new model for high-dimensional distributions of asset returns that utilizes mixed frequency data and copulas. The dependence between returns is decomposed into linear and nonlinear components, enabling the use of high frequency data to accurately forecast linear dependence,...

Many important economic decisions are based on a parametric forecasting model that is known to be good but imperfect. We propose methods to improve out-of-sample forecasts from a misspecified model by estimating its parameters using a form of local M estimation (thereby nesting local OLS and...