Instantaneous volatility seasonality of high-frequency markets in directional-change intrinsic time

We propose a novel intraday instantaneous volatility measure which utilises sequences of drawdowns and drawups non-equidistantly spaced in physical time as indicators of high-frequency activity of financial markets. The sequences are re-expressed in terms of directional-change intrinsic time which ticks only when the price curve changes the direction of its trend by a given relative value. We employ the proposed measure to uncover weekly volatility seasonality patterns of three Forex and one Bitcoin exchange rates, as well as a stock market index. We demonstrate the long memory of instantaneous volatility computed in directional-change intrinsic time. The provided volatility estimation method can be adapted as a universal multiscale risk-management tool independent of the discreteness and the type of analysed high-frequency data.