The necessary and sufficient condition to test for 'overall causality', i.e., the presence of Granger-causality and instantaneous causal relations, in a bivariate and trivariate autoregressive model with recursive form is discussed. It is argued that the conventional AR model (the reduced form...

Causal forces are a way of summarizing forecasters' expectations about what will happen to a time series in the future. Contrary to the common assumption for extrapolation, time series are not always subject to consistent forces that point in the same direction. Some are affected by conflicting...

Decomposing Granger causality over the spectrum allows to disentangle potentially different Granger causality relationships over different frequencies. This may yield new and complementary insights compared to traditional versions of Granger causality. In this paper, we compare two existing...

Many researchers appear to operate under the impression that causal models lead to more accurate forecasts than those provided by naive models (or “projections”). This study was based on the premise that causal models lead to better forecasts than do naive models in certain situations. The...

Volatility forecasts play a central role among equity risk measures. Besides traditional statistical models, modern forecasting techniques, based on machine learning, can readily be employed when treating volatility as a univariate, daily time-series. However, econometric studies have shown that...