Cointegration and Unit Roots. by Dolado, J, Jenkinson, T, SosvillaRivero, S

“…The analysis of cointegration develops out of the esxistence of unit roots and offers a generic route to test the validity of the equilibrium predictions of economic theories. …”

On the Interactions of Unit Roots and Exogeneity. by Hendry, D

“…The paper considers the impact on estimation and inference of interactions between the existence of unit roots in a data generation process and the presence or absence of weak and strong exogeneity of conditioning variables for the parameters of interest in individual cointegrated linear relationships. …”

Cointegration and Unit Roots: A Survey by Jenkinson, T, Dolado, J, Sosvilla-Rivero, S

“…The analysis of cointegration develops out of the existence of unit roots and offers a generic route to test the validity of the equilibrium predictions of economic theories. …”

An Empirical Study of Seasonal Unit Roots in Forecasting. by Clements, M, Hendry, D

“…It is shown that if there are shifts in the deterministic seasonal components then the imposition of unit roots can partially robustify sequences of rolling forecasts, yielding improved forecast accuracy. …”

The Asymptotic Distribution of Unit Root Tests of Unstable Autoregressive Processes. by Nielsen, B

“…Unit root testing has been developed through numerous papers since the work of Dickey and Fuller (1979). …”

Power of Tests for Unit Roots in the Presence of a Linear Trend. by Nielsen, B

“…Dickey and Fuller [Econometrica (1981) Vol. 49, pp. 1057-1072] suggested unit-root tests for an autoregressive model with a linear trend conditional on an initial observation. …”

Linear vs. Log-linear Unit-Root Specification: An Application of Mis-specification Encompassing. by Spanos, A, Hendry, D, Reade, J

“…The objective of this paper is to apply the mis-specification (M-S) encompassing perspective to the problem of choosing between linear and log--linear unit-root models. A simple M-S encompassing test, based on an auxiliary regression stemming from the conditional second moment, is proposed and its empirical size and power are investigated using Monte Carlo simulations. …”

Simulating Properties of the Likelihood Ratio Test for a Unit Root in an Explosive Second-Order Autoregression. by Nielsen, B, Reade, J

“…This paper provides a means of accurately simulating explosive autoregressive processes and uses this method to analyze the distribution of the likelihood ratio test statistic for an explosive second-order autoregressive process of a unit root. While the standard Dickey-Fuller distribution is known to apply in this case, simulations of statistics in the explosive region are beset by the magnitude of the numbers involved, which cause numerical inaccuracies. …”

Asymptotic theory for kernel estimators under moderate deviations from a unit root, with an application to the asymptotic size of nonparametric tests by Duffy, JA

“…We provide new asymptotic theory for kernel density estimators, when these are applied to autoregressive processes exhibiting moderate deviations from a unit root. This fills a gap in the existing literature, which has to date considered only nearly integrated and stationary autoregressive processes. …”

The local to unity dynamic Tobit model by Bykhovskaya, A, Duffy, J

“…We provide an application of our methods to testing for a unit root in the Swiss franc / euro exchange rate, during a period when this was subject to an occasionally binding lower bound.…”

Are Our FEERs Justified? by Barisone, G, Driver, R, Wren-Lewis, S

“…Even at an individual country level, the results provide support for the FEER, particularly in Canada, the UK and Germany. Panel unit root tests suggest that the real exchange rate and FEER cointegrate. …”

Likelihood analysis of a first order autoregressive model with exponential innovations by Nielsen, B, Shephard, N

“…We also show that, even if the process is stationary, the estimator is T-consistent, where T is the sample size. In the unit root case, the estimator is T2-consistent, while, in the explosive case, the estimator is ρT-consistent. …”

The empirical process of autoregressive residuals. by Engler, E, Nielsen, B

“…This contrasts the known result that in the unit root case without intercept the empirical process is asymptotically non-Gaussian. …”

Likelihood analysis of a first order autoregressive model with exponential innovations by Shephard, N, Nielsen, B

“…We also show that, even if the process is stationary, the estimator is T-consistent, where T is the sample size. In the unit root case, the estimator is T2-consistent, while, in the explosive case, the estimator is ρT-consistent. …”

Multi-step estimation for forecasting by Clements, M, Hendry, D

“…In a Monte Carlo forecasting study for integrated processes, estimating a unit root in the presence of a neglected negative moving-average error may favor dynamic estimation, though other solutions exist to that scenario. …”

Rationality and meromorphy of zeta functions by Lauder, A, Lauder, A

“…Second, the p-adic meromorphy of the unit root zeta function of a family of varieties over a finite field of characteristic p. …”

Consistent and conservative model selection with the adaptive Lasso in stationary and nonstationary autoregressions by Kock, A

“…In particular, this implies that it is able to discriminate between stationary and nonstationary autoregressions and it thereby constitutes an addition to the set of unit root tests. Next, and important in practice, we show that choosing the tuning parameter by Bayesian Information Criterion (BIC) results in consistent model selection. …”

Cointegration Tests in the Presence of Structural Breaks. by Campos, J, Ericsson, N, Hendry, D

“…Structural breaks in stationary time series can induce apparent unit roots in those series. Thus, using recently developed recursive Monte Carlo techniques, this paper investigates the properties of several cointegration tests when the marginal process of one of the variables in the cointegrating relationship is stationary with a structural break. …”

A joint Chow test for structural instability by Nielsen, B, Whitby, A

“…We use results on strong consistency of regression estimators to show that the 1-step test is appropriate for stationary, unit root or explosive processes modelled in the autoregressive distributed lags (ADL) framework. …”

Modelling income processes with lots of heterogeneity. by Browning, M, Ejrnæs, M, Alvarez, J

“…This is particularly important for unit root tests which are actually tests of a composite of two independent hypotheses. …”