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International audience; Non-stationarity potentially comes from many sources and they impact the analysis of a wide range of systems in various fields. There is a large set of statistical tests for checking specific departures from stationarity. This study uses Monte Carlo simulations over artificially generated time series data to assess the effectiveness of 16 statistical tests to detect the real state of a wide variety of time series (i.e., stationary or non-stationary) and to identify their source of non-stationarity, if applicable. Our results show that these tests have a low statistical power outside their scope of operation. Our results also corroborate with previous studies showing that there are effective individual statistical tests to detect stationary time series, but no effective individual tests for detecting non-stationary time series. For example, Dickey-Fuller (DF) family tests are effective in detecting stationary time series or non-stationarity time series with positive unit root, but fail to detect negative unit root as well as trend and break in the mean, variance, and autocorrelation. Stationarity and change point detection tests usually misclassify stationary time series as non-stationary. The Breusch-Pagan BG serial correlation test, the ARCH homoscedasticity test, and the structural change SC tests can help to identify the source of non-stationarity to some extent. This outcome reinforces the current practice of running several tests to determine the real state of a time series, thus highlighting the importance of the selection of complementary statistical tests to correctly identifying the source of non-stationarity.

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.

The basic methods of statistical data quality verification and source area calculation for turbulent fluxes are presented and discussed in the paper. The empirical base of analysis were results of three years (2013–2015) eddy-covariance measurements of energy balance and turbulent fluxes of greenhouse gases (water vapor, carbon dioxide and methane) conducted near to the Kopytkowo village in Biebrza National Park. We analyzed three stationary tests and tests for well-developed turbulence. It is shown that the automatic application of the tests can lead to the rejection of valid values as well as approval of unrealistic values. A particular care should be taken using tests for the condition of a welldeveloped turbulence. The methods of determining the source area of turbulent fluxes were discussed. It has been shown that different analytical algorithms lead to similar results and that in the case Kopytkowo the turbulent flux source area covers 100–150 thousand squared meters covered with typical for Biebrza wetlands vegetation. W pracy przedstawiono i przedyskutowano podstawowe metody statystycznej weryfikacji jakości danych strumieni turbulencyjnych oraz wyznaczania ich obszaru źródłowego. Bazę empiryczną analiz stanowiły wyniki trzyletnich (2013–2015) pomiarów bilansu cieplnego i strumieni gazów cieplarnianych (pary wodnej, dwutlenku węgla i metanu) prowadzone metodą kowariancji wirów w okolicy wsi Kopytkowo (Biebrzański Park Narodowy). Analizie poddano trzy testy stacjonarności oraz testy dobrze rozwiniętej turbulencji. Pokazano, że automatyczne stosowanie testów może prowadzić zarówno do odrzucenia poprawnych wartości jak i do przyjęcia wartości nierealnych. Szczególnie uważnie powinny być stosowane testy dotyczące warunku dobrze rozwiniętej turbulencji. Omówiono metody wyznaczania obszaru źródłowego strumieni turbulencyjnych. Pokazano, że różne algorytmy analityczne prowadzą do zbliżonych rezultatów oraz że w przypadku Kopytkowa obszar źródłowy obejmuje powierzchnię 100–150 tys. m2 pokrytą typową dla bagien biebrzańskich roślinnością. Praca wykonana w ramach projektu “Bilans absorpcji i emisji gazów cieplarnianych (metanu, dwutlenku węgla i pary wodnej) na obszarach bagiennych (studium Biebrzańskiego Parku Narodowego)”sfinansowanego ze środków Narodowego Centrum Nauki przyznanych na podstawie decyzji numer DECR2011/01/B/ST10/07550.

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior Turbulent flow high complexity makes it difficult to describe complex phenomena, such as the transport of vector and scalar quantities at the lower atmosphere, making the analysis of experimental data, such as time series, largely employed. The method mostly used by the micrometeorological community to quantify such turbulent transport is associated with the determination of the statistical covariance between two variables. It is known that the determination of statistical quantities for very long temporal windows leads to a large flux uncertainty. At the same time, the theory indicates that the association between fluxes and statistical covariance is only valid for temporally stationary series. The aim of the present study is to test the hypothesis that the estimate uncertainty is directly related to the series non-stationarity. To better understand this issue, we use a methodology based on a group of parametric and nonparametric statistical tests. The tests considered here are the T-test, F-test, median test, U-test and run test. Furthermore, the test results are compared with the outputs of two signal decomposition procedures: multiresolution analysis and empirical mode decomposition. The results suggest that the flux variability over large temporal scales characterizes the existence of temporal trends and low frequency components in the time series considered, so that it is more associated with an observational limitation of the analysis than with non-stationarity, as this concept should be the property of an ensemble, rather than of a single realization. Such limitation suggests the definition of a practical single order stationarity, associated with temporal trends and low frequency components whose energy is similar or larger to that of the turbulent fluctuations. For that reason, we affirm that the interactions test is, among all considered, the best suited for analyzing atmospheric data, because it is the most sensible to the existence of temporal trends. Furthermore, such test allows obtaining a temporal scale beyond which mesoscale events become important. A complexidade de escoamentos turbulentos causa dificuldade para a descrição de fenômenos complexos, como o transporte de grandezas vetoriais e escalares na baixa atmosfera, fazendo com que a análise de dados experimentais, principalmente séries temporais, seja amplamente utilizada. O método mais utilizado pela comunidade micrometeorológica para quantificar esse transporte pela turbulência está associado à determinação da covariância entre duas variáveis. Sabe-se que a determinação de quantidades estatísticas para janelas temporais muito longas resulta em uma grande incerteza nos valores dos fluxos obtidos através desse método. Ao mesmo tempo, a teoria indica que o procedimento de associar fluxos a covariâncias estatísticas só vale para séries temporalmente estacionárias. O objetivo deste trabalho é testar a hipótese de que a incerteza das estimativas esteja relacionada diretamente com a não-estacionariedade das séries temporais. Para entendermos melhor isso, usamos uma metodologia baseada em um conjunto de testes estatísticos paramétricos e não-paramétricos de hipótese nula. Os testes considerados são o teste-T, teste-F, teste da mediana, teste-U e o teste das interações. Os resultados dos testes são ainda comparados com os obtidos com dois métodos de decomposição de sinais: a análise de multiresolução e a Decomposição Empírica de Modos. Os resultados sugerem que a variabilidade dos fluxos nas grandes escalas temporais está associada diretamente com a presença de tendências e componentes de baixa frequência nas séries analisadas, e que este fato está mais ligado à limitação observacional em que a análise é realizada do que propriamente com a não-estacionariedade, já que esta última é uma propriedade de ensemble e não de apenas uma realização. Esta limitação sugere a definição de um conceito mais prático de estacionariedade de primeira ordem, que seja associado à presença de tendências ou componentes de baixa frequência com energias da ordem ou maiores que a energia das escalas turbulentas. Por esse motivo podemos afirmar que na análise de dados atmosféricos o teste das interações mostrou-se, entre todos os considerados, o mais sensível à presença de tendências, permitindo inclusive a obtenção de uma escala temporal na qual os eventos de meso/submesoescala ganham importância.

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 effectiveness 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.

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.

The purpose of this paper is to investigate the asymptotic null distribution of stationarity and nonstationarity tests when the distribution of the error term belongs to the normal domain of attraction of a stable law in any finite sample but the error term is an i.i.d. process with finite variance as \(T \uparrow \infty\). This local-to-finite variance setup is helpful to highlight the behavior of test statistics under the null hypothesis in the borderline or near borderline cases between finite and infinite variance and to assess the robustness of these test statistics to small departures from the standard finite variance context. From an empirical point of view, our analysis can be useful in settings where the (non)-existence of the (second) moments is not clear-cut, such as, for example, in the analysis of financial time series. A Monte Carlo simulation study is performed to improve our understanding of the practical implications of the limi theory we develop. The main purpose of the simulation experiment is to assess the size distortion of the unit root and stationarity tests under investigation.

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.

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.

In this paper, we study the asymptotic behaviour of several test statistics of the null hypothesis of stationarity under a sequence of local alternatives. The sequence of local alternatives is modelled as a nearly stationary process, i.e. a non-stationary process in any finite sample which converges to a stationary process as T ∞. From the asymptotic distributions, we find that the stationarity tests have non-trivial power under the above sequence of local alternatives. Our results complement those of Wright [Econometric Theory (1999) Vol. 15, pp. 704–709] who found that the Kwiatkowski, Phillips, Schmidt and Shin (KPSS) and the modified range statistics (MRS) tests have power equal to their size under a sequence of fractional alternatives. Finally, a simulation study investigates the power properties of the stationarity tests in finite samples.

We present some results regarding the periodogram analysis of nonstationary time series, allowing for the extension of spectral regression methods to cases in which the degree of integration d of a process is not in the stationary range. info:eu-repo/semantics/publishedVersion

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.