Conversion from stationarity to non-stationarity
You've asked, if it's possible to convert a non-stationary signal into a stationary one and vice versa; the answer is yes it's possible to some extend as outlined below.

Indeed it forms the basis of a family of transform based signal compression algorithms. Specifically, for transform based signal compression, a block of time domain samples $x=\left[x_0,x_1,...,x_{N-1} \right]$ are taken, and transformed into a block of frequency domain coefficients $c=\left[c_0,c_1,...,c_{N-1}\right]$ practically via a DCT (discrete cosine transform) or similar and are re-quantized for furher processing.

Note that the time domain signal in the block is assumed to be WSS and correlated, as each sample $x[n]$ has the same variance $\sigma_x^2$, whereas the frequency domain coefficients are non-stationary with each coefficient $c[k]$ having a different variance, $\sigma_{c_k}^2$. This change in variance results in change in bit-resolution of the quantizer, hence compression. Furthermore, the compression efficieny is a direct consequence of the strength of the correlation in the time domain samples.

This non-stationary frequency transform coefficients $c[k]$ are made use of opimal quantization of those coefficients with larger variances (typically the lower frequency coefficients) assisted by the human visual system perceptual characteristics as well. That's a lossy compression. However, you don't have to compress anything, if all you need to get is non-stationary signal.

So this provides an answer for your question, but whether a sutiable method for your financial signal exists is up to you.

Have a look at the following books:

A Primer for Financial Engineering: Financial Signal Processing and Electronic Trading_AKANSU

Financial Signal Processing and Machine Learning_AKANSU