Cees Diks

A Note on the Hiemstra-Jones Test for Granger Non-causality

We address a consistency problem in the commonly used nonparametric test for Granger causality developed by Hiemstra and Jones (1994). We show that the relationship tested is not implied by the null hypothesis of Granger non-causality. Monte Carlo simulations using processes satisfying the null hypothesis show that, for a given nominal size, the actual rejection rate may tend to one as the sample size increases. Our results imply that evidence for nonlinear Granger causality reported in the applied empirical literature should be re-interpreted.

Reversibility as a criterion for discriminating time series

Abstract We propose a test for the hypothesis that a time series is reversible. If reversibility can be rejected all static transformations of linear Gaussian random processes can be excluded as a model for the time series.

Nonlinear time series analysis : methods and applications

Nonlinear dynamical systems stochastic time series a test for reversability detecting differences between reconstruction measures estimating invariants of noisy attractors the correlation integral of noisy attractors spiral wave tip dynamics spatio-temporal chaos - a solvable model.

Simulation study of direct causality measures in multivariate time series

Measures of the direction and strength of the interdependence among time series from multivariate systems are evaluated based on their statistical significance and discrimination ability. The best-known measures estimating direct causal effects, both linear and nonlinear, are considered, i.e., conditional Granger causality index (CGCI), partial Granger causality index (PGCI), partial directed coherence (PDC), partial transfer entropy (PTE), partial symbolic transfer entropy (PSTE) and partial mutual information on mixed embedding (PMIME). The performance of the multivariate coupling measures is assessed on stochastic and chaotic simulated uncoupled and coupled dynamical systems for different settings of embedding dimension and time series length. The CGCI, PGCI and PDC seem to outperform the other causality measures in the case of the linearly coupled systems, while the PGCI is the most effective one when latent and exogenous variables are present. The PMIME outweighs all others in the case of nonlinear simulation systems.

Time reversibility of intracranial human EEG recordings in mesial temporal lobe epilepsy

Abstract Intracranial electroencephalograms from patients suffering from mesial temporal lobe epilepsy were tested for time reversibility. If the recorded time series is irreversible, the input of the recording system cannot be a realisation of a linear Gaussian random process. We confirmed experimentally that the measurement equipment did not introduce irreversibility in the recorded output when the input was a realisation of a linear Gaussian random process. In general, the non-seizure recordings are reversible, whereas the seizure recordings are irreversible. These results suggest that time reversibility is a useful property for the characterisation of human intracranial EEG recordings in mesial temporal lobe epilepsy.

The nonlinear dynamic relationship of exchange rates: Parametric and nonparametric causality testing

The present study investigates the linear and nonlinear causal linkages among six currencies denoted relative to United States dollar (USD), namely Euro (EUR), Great Britain Pound (GBP), Japanese Yen (JPY), Swiss Frank (CHF), Australian Dollar (AUD) and Canadian Dollar (CAD). The data spans two periods between 3/20/1991 and 3/20/2007. We apply a new nonparametric test for Granger non-causality by Diks and Panchenko [Diks, C., Panchenko, V., 2005. A note on the Hiemstra-Jones test for Granger noncausality. Studies in Nonlinear Dynamics and Econometrics 9 (art. 4); Diks, C., Panchenko, V., 2006. A new statistic and practical guidelines for nonparametric Granger causality testing. Journal of Economic Dynamics & Control 30, 1647-1669] and the linear Granger test on the return time series. To detect strictly nonlinear causality, we examine the pairwise VAR-filtered residuals as well as in a six-variate formulation. We find remaining significant bi- and uni-directional causal nonlinear relationships in the series. Finally, we investigate causality after controlling for conditional heteroskedasticity using a GARCH-BEKK model. Whilst the nonparametric test statistics are smaller in some cases, significant nonlinear causal linkages persisted even after GARCH filtering during both periods. This indicates that currency returns may exhibit asymmetries and statistically significant higher-order moments.

Nonparametric Tests for Serial Independence Based on Quadratic Forms

Tests for serial independence and goodness-of-fit based on divergence notions between probability distributions, such as the Kullback-Leibler divergence or Hellinger distance, have recently received much interest in time series analysis. The aim of this paper is to introduce tests for serial independence using kernel-based quadratic forms. This separates the problem of consistently estimating the divergence measure from that of consistently estimating the underlying joint densities, the existence of which is no longer required. Exact level tests are obtained by implementing a Monte Carlo procedure using permutations of the original observations. The bandwidth selection problem is addressed by introducing a multiple bandwidth procedure based on a range of different bandwidth values. After numerically establishing that the tests perform well compared to existing nonparametric tests, applications to estimated time series residuals are considered. The approach is illustrated with an application to financial returns data.

Equivalence and Bifurcations of Finite Order Stochastic Processes

This article presents an equivalence notion of finite order stochastic processes. Local dependence measures are defined in terms of joint and marginal densities. The dependence measures are classified topologically using level sets. The corresponding bifurcation theory is illustrated with some simple examples.

Redundancies in the earth's climatological time series

We examine nonlinear coupling among a number of important climatological variables, d 13 C, d 18 O and insolation, using mutual information and redundancy. The coupling among these variables is found to vary over different climatological eras. The dependence between d 13 C and d 18 O is of particular strength in more recent samples. Tests for Granger causality suggest that d 18 O has an effect on d 13 C whereas the reverse is not the case. q 2000 Published by Elsevier Science B.V.

Spatio-temporal chaos: A solvable model

Abstract A solvable coupled map lattice model exhibiting spatio-temporal chaos is studied. Exact expressions are obtained for the spectra of Lyapunov exponents as a function of the model parameters. Although the model has spatio-temporal structure, the time series measured at a single lattice site are shown to consist of independent, identically distributed samples for several values of the model parameters. For these parameter values, the spatial series measured at a fixed time also consist of independent, identically distributed samples. In these cases, the information dimension density is 1, but the information entropy density depends on the model parameters. Thus, the model is an example where the information entropy density can be obtained neither from a time series measured at a single lattice site nor from a spatial series measured at a fixed time. We conclude that in studying only a time series or a spatial series without any knowledge of the system, one could be easily led into thinking that there is no spatio-temporal structure. For a full characterization of the system, structure in time and space will have to be considered simultaneously.