Local to unity limit theory is used in applications to construct confidence intervals (CIs) for autoregressive roots through inversion of a unit root test (Stock (1991)). Such CIs are asymptotically valid when the true model has an autoregressive root that is local to unity (ρ = 1 + c/n), but...

We propose a functional estimation procedure for homogeneous stochastic differential equations based on a discrete sample of observations and with minimal requirements on the data generating process. We show how to identify the drift and diffusion function in situations where one or the other...

Some new tools for analyzing spurious regressions are presented. The theory utilizes the general representation of a stochastic process in terms of an orthonormal system and provides an extension of the Weierstrass theorem to include the approximation of continuous functions and stochastic...

This paper develops a regression limit theory for nonstationary panel data with large numbers of cross section and time series observations. The limit theory allows for both sequential limits and joins limits, and the relationship between these multidimensional limits is explored. The panel...

Band spectral regression with both deterministic and stochastic trends is considered. It is shown that trend removal by regression in the time domain prior to band spectral regression can lead to biased and inconsistent estimates in models with frequency dependent coefficients. Both...

This paper considers studentized tests in time series regressions with nonparametrically autocorrelated errors. The studentization is based on robust standard errors with truncation lag M=bT for some constant b is an element of (0, 1] and sample size T. It is shown that the nonstandard fixed-b...

This paper investigates a generalized method of moments (GMM) approach to the estimation of autoregressive roots near unity with panel data and incidental deterministic trends. Such models arise in empirical econometric studies of firm size and in dynamic panel data modeling with weak...

This paper characterizes empirically achievable limits for time series econometric modeling and forecasting. The approach involves the concept of minimal information loss in time series regression and the paper shows how to derive bounds that delimit the proximity of empirical measures to the...