Abdessamad Saidi

Robust Optimal Tests for Causality in Multivariate Time Series

Here, we derive optimal rank-based tests for noncausality in the sense of Granger between two multivariate time series. Assuming that the global process admits a joint stationary vector autoregressive (VAR) representation with an elliptically symmetric innovation density, both no feedback and one direction causality hypotheses are tested. Using the characterization of noncausality in the VAR context, the local asymptotic normality (LAN) theory described in Le Cam (1986, Asymptotic Methods in Statistical Decision Theory ) allows for constructing locally and asymptotically optimal tests for the null hypothesis of noncausality in one or both directions. These tests are based on multivariate residual ranks and signs (Hallin and Paindaveine, 2004a, Annals of Statistics 32, 2642–2678) and are shown to be asymptotically distribution free under elliptically symmetric innovation densities and invariant with respect to some affine transformations. Local powers and asymptotic relative efficiencies are also derived. The level, power, and robustness (to outliers) of the resulting tests are studied by simulation and are compared to those of the Wald test. Finally, the new tests are applied to Canadian money and income data.

Aggregation and systematic sampling of periodic ARMA processes

The aim of this work is to investigate the effects of temporal aggregation and systematic sampling on periodic autoregressive moving average (PARMA) time series. Firstly, it is shown that the class of weak PARMA processes, i.e. with uncorrelated but possibly dependent errors, is closed under a particular class of linear transformations that include both temporal aggregation and systematic sampling. This extends a similar result for autoregressive moving average processes; see [Wei, W.W.S., 2006. Time Series Analysis: Univariate and Multivariate Methods, second ed. Addison-Wesley, New York (Chapter 20)] for a review on the subject. Secondly, the properties of the noise of the transformed process are investigated. A sufficient condition is given under which aggregation and systematic sampling of a strong PARMA process, i.e. with independent errors, give rise in general to a weak PARMA process. Under that condition, the noise of the transformed process is neither strong nor a martingale difference. This result points out that the assumption of strong PARMA should not be used without careful considerations when analyzing aggregated time series that naturally occur in many scientific fields. The sufficient condition for non-independent errors is illustrated with the PARMA(1,1) model. A simulation study underlines the practical relevance of our findings and the importance of taking into account the dependence of the errors when fitting a PARMA model to an aggregated time series.

Optimal Tests of Noncorrelation Between Multivariate Time Series

The problem of testing noncorrelation between two multivariate time series is considered. Assuming that the global process admits a joint vector autoregressive (VAR) representation, noncorrelation between the two component series is equivalent to the hypothesis that all off-diagonal blocks in the matrix coefficients and the innovation covariance of the joint VAR representation are zero. We establish an adequate local asymptotic normality (LAN) property for this VAR model in the vicinity of noncorrelation. This LAN structure allows construction of optimal pseudo-Gaussian tests—that is, tests that are locally and asymptotically optimal under Gaussian innovations, but remain valid under non-Gaussian ones—for the null hypothesis of noncorrelation and for comparing their local asymptotic powers with those of the heuristic tests (Haugh–El Himdi–Roy and Koch–Yang–Hallin–Saidi) proposed in the literature.