On the record properties of integrated time series

This paper compares the statistical properties of the records from i.i.d. time series with those of time series containing a single unit root. It is shown that there are important differences in both the limiting distributions and the convergence rates of the associated record counting processes. Since the record properties of i.i.d. time series are shared by a large class of stationary time series, the reported differences underline the possibility of using record-based statistics for robust resting procedures of the unit root hypothesis

Cointegration tests based on record counting statistics

This paper presents of number of cointegration tests that exploit the statistical properties of the records from the original time series variables. We prove their consistency and obtain their asymptotic null distributions. Among the advantages of this novel methodology, the new tests are invariant with respect to the individual series' variances and also with respect to monotonic transformations applied to these series. In addition, these tests are robust against the presence of level breaks as long as the number of these breaks increases slowly enough with the sample size. Finally, an alternative scheme is proposed to deal with additive outliers, which prevent them from causing size distortions

Information-Theoretic Analysis of Serial Dependence and Cointegration

This paper is devoted to presenting wider characterizations of memory and cointegration in time series, in terms of information-theoretic statistics such as the entropy and the mutual information between pairs of variables. We suggest a nonparametric and nonlinear methodology for data analysis and for testing the hypotheses of long memory and the existence of a cointegrating relationship in a nonlinear context. This new framework represents a natural extension of the linear-memory concepts based on correlations. Finally, we show that our testing devices seem promising for exploratory analysis with nonlinearly cointegrated time series.Publicad

ON THE RECORD PROPERTIES OF INTEGRATED TIME SERIES

This paper compares the statistical properties of the records from i.i.d. time series with those of time series containing a single unit root. It is shown that there are important differences in both the limiting distributions and the convergence rates of the associated record counting processes. Since the record properties of i.i.d. time series are shared by a large class of stationary time series, the reported differences underline the possibility of using record-based statistics for robust resting procedures of the unit root hypothesis.

COINTEGRATION TESTS BASED ON RECORD COUNTING STATISTICS

This paper presents of number of cointegration tests that exploit the statistical properties of the records from the original time series variables. We prove their consistency and obtain their asymptotic null distributions. Among the advantages of this novel methodology, the new tests are invariant with respect to the individual series’ variances and also with respect to monotonic transformations applied to these series. In addition, these tests are robust against the presence of level breaks as long as the number of these breaks increases slowly enough with the sample size. Finally, an alternative scheme is proposed to deal with additive outliers, which prevent them from causing size distortions.

Information-Theoretic Analysis of Serial Dependence and Cointegration.

This paper is devoted to presenting wider characterizations of memory and cointegration in time series, in terms of information-theoretic statistics such as the entropy and the mutual information between pairs of variables. We suggest a nonparametric and nonlinear methodology for data analysis and for testing the hypotheses of long memory and the existence of a cointegrating relationship in a nonlinear context. This new framework represents a natural extension of the linear-memory concepts based on correlations. Finally, we show that our testing devices seem promising for exploratory analysis with nonlinearly cointegrated time series.

Range unit root tests

Since the seminal paper by Dickey and Fuller in 1979, unit-root tests have conditioned the standard approaches to analyse time series with strong serial dependence, the focus being placed in the detection of eventual unit roots in an autorregresive model fitted to the series. In this paper we propose a completely different method to test for the type of "long-wave" patterns observed not only in unit root time series but also in series following more complex data generating mechanism. To this end, our testing device analyses the trend exhibit by the data, without imposing any constraint on the generating mechanism. We call our device the Range Unit Root (RUR) Test since it is constructed from running ranges of the series. These statistics allow a more general characterization of a strong serial dependence in the mean behavior, thus endowing our test with a number of desirable properties. Among these properties are the invariance to nonlinear monotonic transformations of the series and the robustness to the presence of level shifts and additive outliers. In addition, the RUR test outperforms the power of standard unit root tests on near-unit-root stationary time series

Instrumental Variable Interpretation of Cointegration with Inference Results for Fractional Cointegration

In this paper we propose an alternative characterization of the central notion of cointegration, exploiting the relationship between the autocovariance and the cross-covariance functions of the series. This characterization leads us to propose a new estimator of the cointegrating parameter based on the instrumental variables (IV) methodology. The instrument is a delayed regressor obtained from the conditional bivariate system of nonstationary fractionally integrated processes with a weakly stationary error correction term. We prove the consistency of this estimator and derive its limiting distribution. We also show that, in the I(1) case, with a semiparametric correction simpler than the one required for the fully modified ordinary least squares (FM-OLS), our fully modified instrumental variables (FM-IV) estimator is median-unbiased, a mixture of normals, and asymptotically efficient. As a consequence, standard inference can be conducted with this new FM-IV estimator of the cointegrating parameter. We show by the use of Monte Carlo simulations that the small sample gains with the new IV estimator over OLS are remarkable.Publicad

A range unit root test

Since the seminal paper by Dickey and Fuller in 1979, unit-root tests have conditioned the standard approaches to analyse time series with strong serial dependence, the focus being placed in the detection of eventual unit roots in an autorregresive model fitted to the series. In this paper we propose a completely different method to test for the type of long-wave patterns observed not only in unit root time series but also in series following more complex data generating mechanisms. To this end, our testing device analyses the trend exhibit by the data, without imposing any constraint on the generating mechanism. We call our device the Range Unit Root (RUR) Test since it is constructed from running ranges of the series. These statistics allow a more general characterization of a strong serial dependence in the mean behavior, thus endowing our test with a number of desirable properties, among which its error-model-free asymptotic distribution, the invariance to nonlinear monotonic transformations of the series and the robustness to the presence of level shifts and additive outliers. In addition, the RUR test outperforms the power of standard unit root tests on near-unit-root stationary time series and is asymptotically immune to noise