Purchasing power parity and triangular arbitrage

External question — Economics Stack Exchange Author: Pavel Filip Original post: https://economics.stackexchange.com/questions/57997 License: CC BY-SA 4.0 — https://creativecommons.org/licenses/by-sa/4.0/ Adaptation: HTML converted to plain text; contact email addresses removed. Does no arbitrage in the FX market have any implications for purchasing power parity (PPP) tests? To be more specific, suppose you have currencies A, B and C and you can form three currency pairs (exchange rates) AB, BC and AC. Only two of those can be independent of each other. Suppose you run a test on each currency pair to see whether or not PPP holds and only two of the tests indicate a PPP relationship. Is this result consistent with a no-arbitrage FX market? I would lean towards a yes, but I am not entirely sure.