Gross & Net Flows
There is evidence of this in the available data over how much securities the Fed holds on behalf of foreign central banks. In the year to June 25, these foreign central bank holdings increased $347 billion to $2,322 billion. $347 billion over a year means approximately $29 billion per month, which means that roughly half of the U.S. trade deficit was financed by these central bank purchases.
By August 6, foreign central bank holdings had increased to $2,396 billion, and the annual increase had increased to $389 billion. If you add translate that 6 week acceleration of $42 billion in monthly terms, $30 billion, and add this to the original $29 billion monthly accumulation, this means that foreign central banks went from covering half of the U.S. trade deficit to covering all of it.
While this wasn't the only factor behind the dollar rally, it was clearly a important reason. Steve Saville, according to Mike Shedlock, however disagrees, using arguments that indicate failure to understand currency markets.
"It should also be noted that the weekly volume on the foreign exchange market exceeds 10 TRILLION dollars, so it really makes no sense to assert that a $28B purchase could affect this market's trend so dramatically."
But what matters for exchange rate movements is not gross flows, but net flows. If banks both sell and buy $1 trillion, that will have no effect at all on exchange rates because the effects of the sales and purchases cancel each other out. If by contrast, you buy, and don't sell, $60 billion a month that will have a big impact on exchange rates because then prices will have to rise enough to convince net holders of $60 billion to "permanently" get rid of their USD assets. Whether that net number simply involves $60 billion of sellers, 0r $1.06 trillion of sellers and $1 trillion of buyers doesn't really matter. Exactly how big that price increase need to be vary somewhat depending on what the prevalent market psychology is, but given the tendency of some to be more eager to buy something when it rises in price, that could in some circumstances be big.
The empirical correlation is likely to be even weaker considering that there are always other important factors involved sometimes counteracting and sometimes reinforcing the effects of the interventions, but it should be clear that the ceteris paribus (other things being equal) net effect can sometimes be big. While, again, these accelerated central bank purchases of U.S. assets isn't the only factor explaining the market moves, it is clear that they are one of the factors involved.