This article provides a methodological and empirical approach for assessing price level convergence and its relation to purchasing power parity (PPP) using annual price data for seventeen U.S. cities during the period 1918 to 2005. We suggest a new panel data procedure that can handle a wide...

Asymptotic properties of the quasi-maximum likelihood estimator (QMLE) for non-linear ARCH(q) models -- including for example Asymmetric Power ARCH and log-ARCH -- are derived. Strong consistency is established under the assumptions that the ARCH process is geometrically ergodic, the conditional...

This paper expounds some of the results of Fourier theory that are essential to the statistical analysis of time series. It employs the algebra of circulant matrices to expose the structure of the discrete Fourier transform and to elucidate the filtering operations that may be applied to finite...

We consider forecasting and prequential (predictive sequential) validation of meta-elliptical distributions with time varying parameters. Using the weak prequential principle of Dawid, we conduct model validation avoiding nuisance parameter problems. Results rely on the structure of...

The asymptotic null distribution of the nonlinear IV panel unit root test due to Chang (2002, Journal of Econometrics 110, 261-292) is examined under the assumption of an invertible general linear process with a weak summability condition. An autoregressive approximation of order p, with p...

Practitioners often have at their disposal a large number of instruments that are weakly exogenous for the parameter of interest. However, not every instrument has the same predictive power for the endogenous variable, and using too many instruments can induce bias. We consider two ways of...