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 9th-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 sixteen papers were delivered, of which twelve 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 1

Modelling structural breaks, long memory and stock market volatility: an overview

“…Beran (1994a) is an excellent introduction to the topic. Baillie (1996), Doukhan, Oppenheim andTaqqu (2003), and Robinson (1994aRobinson ( , 2003 have provide comprehensive surveys on long memory processes and fractional integration while a recent annals Issue of this journal entitled Long Memory and Nonlinear Time Series, edited by Davidson and Terasvirta (2002), has dealt with non-stationarity, long memory and non-linearities in time series. The main aim of this section of the introduction is to integrate the literature reviews on long memory mentioned above with the most recent research on the subject, to provide an up-to-date overall picture of the studies on long memory processes and to put in the context the papers in this volume.…”

High and Low Prices and the Range in the European Stock Markets: A Long-Memory Approach

“…In addition, since fractional integration is closely related to non-linearities and structural breaks (e.g., Breidt et al, 1998;Diebold and Inoue, 2001;Davidson and Terasvirta, 2002;Granger and Hyung, 2004;Sibbertsen, 2004;Deo et al, 2006;Baillie and Morana, 2009;Lahiani and Scaillet, 2009;Choi et al, 2010;Hywang and Shin, 2018;etc. ), the method described in Gil-Alana ( 2008) and based on Bai and Perron (2003) for testing multiple breaks is also applied.…”

Persistence, Non-Linearities and Structural Breaks in European Stock Market Indices

“…Many studies have argued that fractional integration is very much related to nonlinearities (e.g. Diebold and Inoue, 2001;Davidson and Terasvirta, 2002;Deo et al, 2006) and therefore, in the present paper, we allow xt to be the errors in a non-linear regression model based on Chebyshev's polynomials in time. Specifically, the first model used is the following one:…”