Does the monetary theory of exchange rates apply to the dollar and the euro?

According to the monetary theory of exchange rates, the exchange rate varies with changes in the relative levels of money supply (adjusted for the relative levels of real GDP). Can this be observed between the dollar and the euro? Have shifts to greater monetary expansion in the United States or in the euro zone led to a depreciation of the dollar or the euro? This question can be examined using the central bank money supply (M0, the monetary base) or the money supply for non-bank economic agents (M2, banknotes and deposits). We find that the monetary theory of exchange rates seems to apply between the United States and the euro zone since 2010, but not beforehand.