Short run and long run causality in time series: Inference

We propose methods for testing hypotheses of non-causality at various horizons, as defined in Dufour and Renault (1998, Econometrica). We study in detail the case of VAR models and we propose linear methods based on running vector autoregressions at different horizons. While the hypotheses considered are nonlinear, the proposed methods only require linear regression techniques as well as standard Gaussian asymptotic distributional theory. Bootstrap procedures are also considered. For the case of integrated processes, we propose extended regression methods that avoid nonstandard asymptotics. The methods are applied to a VAR model of the U.S. economy.

fNIRS-EEG study of focal interictal epileptiform discharges

Functional near-infrared spectroscopy (fNIRS) acquired with electroencephalography (EEG) is a relatively new non-invasive neuroimaging technique with potential for long term monitoring of the epileptic brain. Simultaneous EEG-fNIRS recording allows the spatio-temporal reconstruction of the hemodynamic response in terms of the concentration changes in oxy-hemoglobin (HbO) and deoxy-hemoglobin (HbR) associated with recorded epileptic events such as interictal epileptic discharges (IEDs) or seizures. While most previous studies investigating fNIRS in epilepsy had limitations due to restricted spatial coverage and small sample sizes, this work includes a sufficiently large number of channels to provide an extensive bilateral coverage of the surface of the brain for a sample size of 40 patients with focal epilepsies. Topographic maps of significant activations due to each IED type were generated in four different views (dorsal, frontal, left and right) and were compared with the epileptic focus previously identified by an epileptologist. After excluding 5 patients due to the absence of IEDs and 6 more with mesial temporal foci too deep for fNIRS, we report that significant HbR (respectively HbO) concentration changes corresponding to IEDs were observed in 62% (resp. 38%) of patients with neocortical epilepsies. This HbR/HbO response was most significant in the epileptic focus region among all the activations in 28%/21% of patients.