Choosing the frequency of volatility components within the Double Asymmetric GARCH–MIDAS–X model

The Double Asymmetric GARCH–MIDAS (DAGM) model has the advantage of modelling volatility as the product of two components: a slow–moving term involving variables sampled at lower frequencies and a short–run part, each with an asymmetric behavior in volatility dynamics. Such a model is extended in three directions: first, by including a market volatility index as a daily lagged variable in the short–run component (the so-called “–X” term); second, by adding the same variable in the long–run component as variations of data aggregated at any desired frequency; third, by proposing a data-driven method to find the optimal number of lags to be included in the positive and negative parts of the long–run component. The resulting model, labelled as DAGM–X–2K, is extensively evaluated under several alternative configurations, producing satisfactory evidence when applied to the S&P 500 and NASDAQ indices. The out–of–sample results show that the “–X” addition significantly improves the performance, making the proposed DAGM–X–2K model enter the Model Confidence Set, even for large forecasting horizons (for 1 to 60 days).