The closest orthogonal transform I know of that might meet your needs is the [Slant Transform][1]. It's based on sawtooth(ish) waves, but some of the basis functions do resemble triangle waves:

![Slant Basis Functions][2]

(source: [Applied Fourier transform][3])

It was developed for image coding/compression, but it seems like a reasonable first approach for the analysis of long-term linear trends/reversals in financial data. It doesn't seem like many of the [key papers][4] describing the transform are available [for free] online, but the following paper probably has sufficient detail to implement something:

> A Truncation Method for Computing Slant Transforms with Applications
> to Image Processing. M. M. Anguh, R. R. Martin. IEEE Trans.
> Communications 43 (6), 2103-2110, 1995. ([author link][6]) ([pdf link][7])

Specifically, see Section III which gives the recursion relations used to construct the transform matrix.


  [1]: https://ieeexplore.ieee.org/document/1092335
  [2]: https://i.sstatic.net/e6Ko6.jpg
  [3]: https://books.google.com/books?id=wJF_nJQz0MsC&pg=PA220#v=onepage&q&f=false
  [4]: https://www.tandfonline.com/doi/abs/10.1080/00207167608803122#preview 
  [6]: https://web.archive.org/web/20210506225151/http://ralph.cs.cf.ac.uk/publications.html
  [7]: https://web.archive.org/web/20210506201530/http://ralph.cs.cf.ac.uk/papers/Geometry/TruncationSlant.pdf