In regressions involving integrable functions we examine the limit properties of IV estimators that utilise integrable transformations of lagged regressors as instruments. The regressors can be either I(0) or nearly integrated (NI) processes. We show that this kind of nonlinearity in the...

Comparisons between European and North American sports leagues have occurred over the years. In this paper, we attempt to bring these comparisons down to the essential elements -what has come to be called Rottenberg's (1956) invariance principle and theoretical insights into attempts to alter...

This paper studies the asymptotic validity of sieve bootstrap for nonstationary panel factor series. Two main results are shown. Firstly, a bootstrap Invariance Principle is derived pointwise in i, obtaining an upper bound for the order of truncation of the AR polynomial that depends on n and...

We consider the maximum process of a random walk with additive independent noise in the form of maxi=1,…,n(Si+Yi). The random walk may have dependent increments, but its sample path is assumed to converge weakly to a fractional Brownian motion. When the largest noise has the same order as the...

We establish an invariance principle for a general class of stationary random fields indexed by Zd, under Hannan’s condition generalized to Zd. To do so we first establish a uniform integrability result for stationary orthomartingales, and second we establish a coboundary decomposition for...

Let X,X1,X2,… be independent and identically distributed Rd-valued random vectors and assume X belongs to the generalized domain of attraction of some operator semistable law without normal component. Then without changing its distribution, one can redefine the sequence on a new probability...

In 1983, N. Herrndorf proved that for a ϕ-mixing sequence satisfying the central limit theorem and lim infn→∞σn2/n0, the weak invariance principle takes place. The question whether for strictly stationary sequences with finite second moments and a weaker type (α, β, ρ) of mixing the...

Large sample properties are studied for a first-order autoregression (AR(1)) with a root greater than unity. It is shown that, contrary to the AR coefficient, the least-squares (LS) estimator of the intercept and its t-statistic are asymptotically normal without requiring the Gaussian error...

Weak convergence of partial sums and multilinear forms in independent random variables and linear processes to stochastic integrals now plays a major role in nonstationary time series and has been central to the development of unit root econometrics. The present paper develops a new and...