Suppose that we have (daily) open, high, low and close exchange rates over a long period of time. How can we formally test whether the exchange rate market is manipulated by the central banks?
I hope you may be interested in this paper even if it is on Libor manipulation...:
J Fouquau, P Spieser "Statistical evidence about Libor manipulation": A Sherlock Holmes investigation", Journal of banking and finance, 2015, 50, p 632 -643.