Short and long run causality measures: Theory and inference

Nonparametric estimation and inference for conditional density based Granger causality measures

“…This concept is defined in terms of predictability at horizon one of a (vector) variable Y from its own past, the past of another (vector) variable X, and possibly a vector Z of auxiliary variables. The theory of Wiener-Granger causality has generated a considerable literature; for review see Dufour and Taamouti (2010). Wiener-Granger analysis distinguishes between three basic types of causality:…”

“…Polasek (1994Polasek ( , 2002 showed how causality measures can be computed using the Akaike Information 1 Criterion (AIC) and a Bayesian approach. Dufour and Taamouti (2010) proposed short and long run causality measures based on vector autoregressive and moving average models. The estimation of most existing causality measures has been done based on parametric mean regression models.…”

Exchange Rates and Commodity Prices: Measuring Causality at Multiple Horizons

“…More generally, significance tests (for noncausality) are inappropriate for that purpose: it is well known that a large effect (from an economic viewpoint) may not be statistically significant because the data do not allow one to measure it precisely (e.g., due a multicollinearity or a small size), and an economically negligible effect may be statistically significant because the effect, while small, can be very precisely estimated. It is much more informative to parameterize the relevant effects, compute point estimates for these parameters, and eventually confidence sets; see Dufour and Taamouti (2010) and Dufour, Garcia and Taamouti (2012). Non-causality tests can provide evidence of the presence or absence of forecast improvements available from inclusion of the past of other variables, but do not indicate the magnitudes of forecast improvements.…”

“…In particular, they should allow for a wide spectrum of dynamic structures, such as relatively general VAR or VARMA models. For that purpose, we will use here the approach developed in Dufour and Taamouti (2010) and .…”

“…Further, to avoid the overly simplifying features of pure significance tests for non-causality, we compute measures at many horizons because they allow one to assess in a much more precise way the underlying linkages when causality at different horizons in different directions is present. The measures used are based on the concepts and statistical methodology -including both point estimates (of causality measures) and confidence intervals -described in Dufour and Taamouti (2010) for a general time-series framework, and in the context of high-frequency data (as in this paper). In particular, the statistical setup we consider allows for general assumptions, such as stationary invertible vector autoregressive moving average (VARMA) models.…”