Intrinsic Time Directional-Change Methodology in Higher Dimensions

We extend the intrinsic time directional-change methodology to multidimensional space. The methodology is explored in the context of currencies where the currencies are orthogonal dimensions. The intrinsic time ticks whenever the price reverses from the local maximum/minimum by a certain percentage. We generalise the concept of the price move direction to the space of many dimensions. Scaling laws which were reported for one-dimensional Forex time series are now reproduced in the multidimensional space. We report the increased systematic curvature in the fitted Forex scaling law data. The increase in the curvature size is associated with dimensionality growth. We discuss how the novel methodology can be used as a method to estimate multidimensional volatility. The paper provides various ideas for practical applications of the multidimensional directional-change methodology for data analysis