Hausman (1978) developed a widely-used model specification test that has passed the test of time. In this paper, we show that the asymptotic variance of the difference of the two estimators can be a singular matrix. Three illustrative examples are used, namely an exogeneity test for the linear...

This paper investigates some structural properties of a family of GARCH processes. A simple sufficient condition for the existence of the αδ-order stationary solution of the processes is derived, where α ∈ (0, 1] and δ 0. The solution is strictly stationary and ergodic, and the causal...

In this paper we examine the asymptotic properties of the estimator of the long-run coefficient (LRC) in a dynamic regression model with integrated regressors and serially correlated errors. We show that the OLS estimators of the regression coefficients are inconsistent but the OLS-based...

Nonlinear time series models, especially those with regime-switching and/or conditionally heteroskedastic errors, have become increasingly popular in the economics and finance literature. However, much of the research has concentrated on the empirical applications of various models, with little...

In this paper we advance the idea that optimal risk management under the Basel II Accord will typically require the use of a combination of different models of risk. This idea is illustrated by analyzing the best empirical models of risk for five stock indexes before, during, and after the...

Many macroeconomic forecasts and forecast updates like those from IMF and OECD typically involve both a model component, which is replicable, as well as intuition, which is non-replicable. Intuition is expert knowledge possessed by a forecaster. If forecast updates are progressive, forecast...