<A HREF="https://hal.inria.fr/hal-00370570/document">An explicit rough path construction for continuous paths with arbitrary Hölder exponent</A>, by Jeremie Unterberger (2009) [<a href="http://link.springer.com/article/10.1007%2Fs00220-010-1064-1">published</a> 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. The method is not limited to Brownian motion, because it does not rely on tools belonging exclusively to the Gaussian realm, namely, the equivalence of $L^p$-norms due to the hypercontractivity property of the Ornstein-Uhlenbeck process.

For a broader overview of this topic with many examples, starting from T. Lyon's seminal contributions, see Unterberger's <A HREF="http://www.iecn.u-nancy.fr/~unterber/book-rough-paths.pdf">Rough Path Theory</A>.