Why is the yen getting stronger even with negative interest rates? Checking this graph we can see that 1 Yen is worth increasingly more dollars this past week. 

I wonder why is this, specially when the BoJ has imposed negative nominal interest rates.

It seems a bit strange...
Negative interest rates are not incompatible with appreciation of the local currency. As pointed out by the economist (Why investors buy bonds with negative yields), some investors buy bonds to place bets on currencies. Thus, it does not matter so much that the interest rate is negative.

Thus, the variation of the yen reflects other trends. It is very tricky to point out at one event or idea in particular, but here are a few possible drivers of the appreciation of the Yen:


The dollar is weakening, following the release of the minutes of the Fed meeting which showed that the central bank does not intend to raise interest rates in April.
Japan is running out of options to put downward pressure on the yen. The central bank already buys everything in sight, and thus would have difficulties to increase the money supply. The feeling that central banks are loosing grip is very tangible since a few months (if not years)
G20 countries recently agreed to not proceed to competitive devaluations of their currency. Therefore, investors might expect that Yen won't go down easily, and that the most logical path is unpward.
Japan's Prime Minister Shinzo Abe seems to hesitate to proceed to planned increase in sale tax. The first increase had a desastrous short-term effect on the economy, and most firms have a pessimistic outlook (latest PMI 49.1). Therefore, it becomes more and more likely that the government will delay the increase in sale tax, and potentially also try to stimulate the economy further.


These are all guesses. It might be that one or more of the above guesses actually moved the Yen. Or maybe it didn't and something else is happening. Maybe investors aren't as rational as we think they are and they just bet on the Yen because of their gut without logical reasons.