Choosing between weekly and monthly volatility drivers within a Double Asymmetric GARCH-MIDAS model

Volatility in financial markets has both low and high–frequency components which determine its dynamic evolution. Previous modelling efforts in the GARCH context (e.g. the Spline–GARCH) were aimed at estimating the low frequency component as a smooth function of time around which short–term dynamics evolves. Alternatively, recent literature has introduced the possibility of considering data sampled at different frequencies to estimate the influence of macro–variables on volatility. In this paper, we extend a recently developed model, here labelled Double Asymmetric GARCH–MIDAS model, where a market volatility variable (in our context, VIX) is inserted as a daily lagged variable, and monthly variations represent an additional channel through which market volatility can influence individual stocks. We want to convey the idea that such variations (separately) affect the short– and long–run components, possibly having a separate impact according to their sign