Linear multivariate models for physiological signal analysis: theory

Measuring Connectivity in Linear Multivariate Processes: Definitions, Interpretation, and Practical Analysis

“…Note that the definition in (1) limits to past values only the possible influences of one process to another, excluding instantaneous effects (i.e., effects occurring within the same lag). The absence of instantaneous effects is denoted as strict causality of the closed loop MV process [37, 38] and will be assumed henceforth. …”

“…Failure of fulfilling the white noise assumption means that the spectral properties of the signals are not fully described by the autoregression so that, for example, important power amounts in specific frequency bands could not be properly quantified. When the whiteness test is not passed, the experimenter should consider moving to different model structures, such as MV dynamic adjustment forms having the general structure of MVAR networks fed by individual colored AR noises at the level of each signal [37, 38]. …”

Autonomic mediation of the interdependence between variability signals of heart rate and blood pressure in the lizard Gallotia galloti

“…In the methodological approach used here, these variables are considered observed processes produced by the operation of a real system (Korhonen et al 1996). When observed processes are studied separately as univariate processes (i.e., using univariate methods), a complete description of the system operation is not achieved because no information on the joint probability distributions of processes is provided.…”

Assessing Frequency Domain Causality in Cardiovascular Time Series with Instantaneous Interactions

“…The MVAR model traditionally used to compute the PDC from multiple time series is strictly causal, in the sense that only lagged effects are modeled and instantaneous (i.e., not lagged) effects among the time series are not described by any model coefficients. However, neglecting instantaneous effects in MVAR models implies that zero-lag correlations among the time series are translated into correlations among the model residuals [7]. Although the PDC definition explicitly forsakes the cross-covariance matrix of the residuals, it is not clear whether and how the strictly causal description of multiple time series with significant zero-lag correlations may affect the frequency domain evaluation of causality.…”