This question has been addressed here: Can Principal Component Analysis be used on stock prices / non-stationary data?
In his answer Jon Egil wrote
please make sure you analyse returns not prices
and referenced a paper by Attilio Meucci. In another of Attilio Meucci's papers (which is very nice incidentally), Review of Statistical Arbitrage, Cointegration, and Multivariate Ornstein-Uhlenbeck (2009) Attilio applies PCA to prices (or in this case yields) rather than returns. He even supplies code and data here.
Even just looking at the code you can see he measures the covariance and then applies the PCA directly to this matrix. The results he gets are good, producing the level, slope and curve you would expect.
So it seems that in some cases PCA can be applied successfully to prices.
I'd just like to understand better when it can be applied to prices and what it can't? Is this case was the detrending inherent in the covariance estimation sufficient to produce stationarity?
What are the best tests to apply to whether a particular time-series is suitable for PCA analysis or not?