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To link to full-text access for this article, visit this link: http://dx.doi.org/10.1016/j.jeconom.2005.06.012 Byline: James Davidson Abstract: This paper considers alternative methods of testing cointegration in fractionally integrated processes, using the bootstrap. The investigation focuses on (a) choice of statistic, (b) use of bias correction techniques, and (c) designing the simulation of the null hypothesis. Three residual-based tests are considered, two of the null hypothesis of non-cointegration, the third of the null hypothesis that cointegration exists. The tests are compared in Monte Carlo experiments to throw light on the relative roles of issues (a)-(c) in test performance. Author Affiliation: School of Business and Economics, University of Exeter, Exeter EX4 4PU, UK Article Note: (footnote) [star] Research supported by the ESRC under award L138251025.

This paper analyses a class of nonlinear time series models exhibiting long memory. These processes exhibit short memory fluctuations around a local mean (regime) which switches randomly such that the durations of the regimes follow a power law. We show that if a large number of independent copies of such a process are aggregated, the resulting processes are Gaussian, have a linear representation, and converge after normalisation to fractional Brownian motion. Alternatively, an aggregation scheme with Gaussian common components can yield the same result. However, a non-aggregated regime process is shown to converge to a Levy motion with infinite variance, suitably normalised, emphasising the fact that time aggregation alone fails to yield a FCLT. Two cases arise, a stationary case in which the partial sums of the process converge, and a nonstationary case in which the process itself converges, the Hurst coefficient falling in the ranges (1/2 1) and (0, 1/2), respectively. We comment on the relevance of our results to the interpretation of the long memory phenomenon, and also report some simulations aimed to throw light on the problem of discriminating between the models in practice. JEL classification: C22 Keywords: Long memory; Regime-switching; Aggregation; Levy motion

The paper proposes a framework for modelling cointegration in fractionally integrated processes, and considers methods for testing the existence of cointegrating relationships using the parametric bootstrap. In these procedures, ARFIMA models are fitted to the data, and the estimates used to simulate the null hypothesis of non-cointegration in a vector autoregressive modelling framework. The simulations are used to estimate p-values for alternative regression-based test statistics, including the F goodness-of-fit statistic, the Durbin-Watson statistic and estimates of the residual d. The bootstrap distributions are economical to compute, being conditioned on the actual sample values of all but the dependent variable in the regression. The procedures are easily adapted to test stronger null hypotheses, such as statistical independence. The tests are not in general asymptotically pivotal, but implemented by the bootstrap, are shown to be consistent against alternatives with both stationary and nonstationary cointegrating residuals. As an example, the tests are applied to the series for UK consumption and disposable income. The power properties of the tests are studied by simulations of artificial cointegrating relationships based on the sample data. The F test performs better in these experiments than the residual-based tests, although the Durbin-Watson in turn dominates the test based on the residual d. JEL classification: C32; C15 Keywords: Bootstrap; Fractional integration; Cointegration

This paper considers methods of deriving sufficient conditions for the central limit theorem and functional central limit theorem to hold in a broad class of time series processes, including nonlinear processes and semiparametric linear processes. The common thread linking these results is the concept of near-epoch dependence on a mixing process, since powerful limit results are available under this limited-dependence property. The particular case of near-epoch dependence on an independent process provides a convenient framework for dealing with a range of nonlinear cases, including the bilinear, GARCH, and threshold autoregressive models. It is shown in particular that even SETAR processes with a unit root regime have short memory, under the right conditions. A simulation approach is also demonstrated, applicable to cases that are analytically intractable. A new FCLT is given for semiparametric linear processes, where the forcing processes are of the NED-on-mixing type, under conditions that are evidently close to necessary. JEL classification: C10; C22 Keywords: Near-epoch dependence; FCLT; Nonlinear; Bilinear; GARCH; TAR

This paper presents and applies some results on the interpretation of cointegrating regressions. The key concept is the irreducible cointegrating (IC) relation, one from which no variable can be omitted without loss of the cointegration property. Extending earlier results, it is shown that under certain circumstances, IC relations are identified structural forms. It is possible, at least in principle, to learn about the structure of simultaneous long-run relations directly from cointegration analyses, in contrast with the well-known fact that no such knowledge can be obtained from the correlations between stationary variables. IC relations can also be estimated by asymptotically mixed Gaussian and median unbiased estimators, permitting standard inference. MINIMAL, an algorithm for extracting the IC subsets of a data set, is applied to variety of artificial and actual data. Keywords: Structural; Identification; Cointegration; Irreducible cointegrating vector