Long memory and nonlinear time series

Abstract

The last two decades have witnessed tremendous advances in econometric time-series research. The linear stationary framework of ARMA and VAR models driven by i.i.d. shocks, which was for many years the cornerstone of econometric modelling, has increasingly given way to methods that can deal with the manifestly nonstationary and nonlinear features of many economic and financial time series. Two types of model in particular have found their way into the mainstream of applied research, the unit-root/cointegration framework for nonstationary time series and the ARCH and related models of conditional heteroscedasticity. Recent research has been aimed at both extending our understanding of these well-established models, and widening the range of data features that can be handled. Long memory models generalize the unit root model of nonstationarity, and a range of new models of nonlinear dynamics allow for asymmetric responses, threshold behaviour and stochastically switching regimes. The concept of cointegration has been generalized to accommodate many of these novel features. The papers gathered in this special Annals issue were presented at a conference in Cardiff, UK on July 9 –11th 2000, called to bring together researchers with common interests in these topics. Thirty-six invited participants from six countries took part, and a total of 16 papers were delivered, of which 12 have been submitted and accepted, after revision, for publication in this issue. Eight of them take nonstationarity or long memory as a theme, and eight are concerned with nonlinearity. In other words, no fewer than four succeed in combining both concerns. This was not an outcome planned or anticipated by the conference organizers, but illustrates the extent to which time-series research represents a thoroughly unified and interconnected enterprise.