Long memory in time series of economic growth and convergence

One of the most hotly debated topics in macroeconomics in recent years has been the nature of fluctuations in the growth process of aggregate output in the longer term. Traditionally, economists have conceived of the growth process as consisting of a deterministic trend (such as exponential growth) on which is superimposed either deterministic cyclical fluctuations (a decidedly minority view in the meantime) or a stable, mean-reverting stochastic process of ARMA type. Since Nelson and Plosser (1982) this view has been challenged by purported evidence of a unit root in univariate time series such as GDP, i.e., essentially a random walk component, which puts into question the notion of any underlying deterministic trend. However, this knife-edge distinction between a unit root and a near unit root but stable process has proven difficult to maintain empirically, especially since the main test employed, the Dickey-Fuller test, has been shown to have limited power against a range of alternative hypotheses.