The cause of an integral correction mechanism of the real exchange rate

I find that Rabanal and Rubio-Ramirez (2015)'s international real business cycle model can explain an integral correction mechanism of the real exchange rate. An input adjustment cost in their model implies that the real exchange appreciates following a positive domestic productivity shock and reverts to steady state quickly, but presents a long-run cyclical movement. These particular dynamics help explain the PPP puzzle.