An explicit rough path construction for continuous paths with arbitrary Hölder exponent, by Jeremie Unterberger (2009) [published with a different title]:
We construct an explicit geometric rough path over arbitrary $d$-dimensional paths with finite $1/\alpha$-variation for any $\alpha\in (0, 1)$. The method generalizes to arbitrary $\alpha$-Hölder paths the previous constructions that were limited to fractional Brownian motion. Our generalization may be coined as Fourier normal ordering since it consists in a regularization obtained after permuting the order of integration in iterated integrals so that innermost integrals have highest Fourier frequencies.
For a broader overview of this topic, starting from T. Lyon's seminal contributions, see Unterberger's Rough path theory.