Search

We study the convergence properties of inflation rates among the countries of the European Monetary Union over the period 1980–2013. Recently developed panel unit root/stationarity tests cannot reject the stationarity hypothesis. This implies that some countries have been in the process of converging absolutely or relatively. By using a clustering algorithm we statistically detect three absolute convergence clubs in the pre-euro period, which comprise early accession countries. In particular, Luxembourg clusters with Austria and Belgium, while a second sub-group includes Germany and France and the third The Netherlands and Finland. We also detect two separate clusters of early accession countries in the post-1997 period: a sub-group with Germany, Austria, Belgium and Luxembourg, and one with France and Finland. For the rest of the countries/cases we find evidence of divergent behavior. Robustness is checked by testing pairwise convergence in a Bayesian framework. The outcome broadly confirms our findings.

Control groups can sometimes provide counterfactual evidence for assessing the impact of an event or policy change on a target variable. Fitting a time series model to target and control series offers potential gains over a direct comparison between the target and a weighted average of the controls. More importantly it highlights the assumptions underlying methods such as difference in differences and synthetic control and in doing so suggests ways in which these assumptions may be tested. Our focus is on time series models that are both simple and transparent. Potential gains from fitting such models are analysed and their relative performance is investigated using examples taken from the literature, including the effect of the California smoking law of 1988 and German re-unification. At the same time, some of the draw-backs to current methodology become apparent. It is argued that a time series strategy for the selection of a valid set of controls is to be preferred to one based on data-driven regression methods.

In this paper we propose a test of the null hypothesis of time series linearity against a nonlinear alternative, when uncertainty exists as to whether or not the series contains a unit root. We provide a test statistic that has the same limiting null critical values regardless of whether the series under consideration is generated from a linear I(0) or linear I(1) process, and is consistent against nonlinearity of either form, being asymptotically equivalent to the efficient test in each case. Finite sample simulations show that the new procedure has better size control and offers substantial power gains over the recently proposed robust linearity test of Harvey and Leybourne (2007).

In this paper we propose a test of the null hypothesis of time series linearity against a nonlinear alternative, when uncertainty exists as to whether or not the series contains a unit root. We provide a test statistic that has the same limiting null critical values regardless of whether the series under consideration is generated from a linear I(0) or linear I(1) process, and is consistent against nonlinearity of either form, being asymptotically equivalent to the efficient test in each case. Finite sample simulations show that the new procedure has good size control and offers substantial power gains over the recently proposed robust linearity test of Harvey and Leybourne (2007).

Quantiles provide a comprehensive description of the properties of a variable and tracking changes in quantiles over time using signal extraction methods can be informative. It is shown here how stationarity tests can be generalized to test the null hypothesis that a particular quantile is constant over time by using weighted indicators. Corresponding tests based on expectiles are also proposed; these might be expected to be more powerful for distributions that are not heavy-tailed. Tests for changing dispersion and asymmetry may be based on contrasts between particular quantiles or expectiles. We report Monte Carlo experiments investigating the e¤ectiveness of the proposed tests and then move on to consider how to test for relative time invariance, based on residuals from fitting a time-varying level or trend. Empirical examples, using stock returns and U.S. inflation, provide an indication of the practical importance of the tests.

In this paper we develop a simple test procedure for a linear trend which does not require knowledge of the form of serial correlation in the data, is robust to strong serial correlation, and has a standard normal limiting null distribution under either I ( 0 ) or I ( 1 ) shocks. In contrast to other available robust linear trend tests, our proposed test achieves the Gaussian asymptotic local power envelope in both the I ( 0 ) and I ( 1 ) cases. For near- I ( 1 ) errors our proposed procedure is conservative and a modification for this situation is suggested. An estimator of the trend parameter, together with an associated confidence interval, which is asymptotically efficient, again regardless of whether the shocks are I ( 0 ) or I ( 1 ) , is also provided.

A time-varying quantile can be fitted to a sequence of observations by formulating a time series model for the corresponding population quantile and iteratively applying a suitably modified state space signal extraction algorithm. Quantiles estimated in this way provide information on various aspects of a time series, including dispersion, asymmetry and, for financial applications, value at risk. Tests for the constancy of quantiles, and associated contrasts, are constructed using indicator variables; these tests have a similar form to stationarity tests and, under the null hypothesis, their asymptotic distributions belong to the Cramér von Mises family. Estimates of the quantiles at the end of the series provide the basis for forecasting. As such they offer an alternative to conditional quantile autoregressions and, at the same time, give some insight into their structure and potential drawbacks.

International audience; The method of surrogate data, classically used for nonlinearity tests, amounts to the use of some constrained noise providing reference for statistical test. It is revisited here as a method for stationarization and this feature is put forward in the context of nonstationarity testing. The stationarization property of surrogates is first explored in a time-frequency perspective and used for devising a test of stationarity relative to an observation time. Then, more general forms of surrogates are developed, directly in time-frequency or mixed domains of representation (ambiguity and time-lag domains included) and it is shown how they allow for other tests of nonstationary features: detection of the existence of a transient in some noise; assessment of nonstationary cross-correlations.