Instability caused by the cubic potential in the foreign exchange market observed at the intervention by the Bank of Japan

It is widely known that market prices in the financial markets are approximated by random walks, however, in some special occasions we can find peculiar price motions. Here, we pay attention to the event of the largest intervention in the foreign exchange market, the US dollar-Japanese yen market, on October 31, 2011 and analyze the extraordinary time series of exchange rates by applying the new data analysis method based on the particle-filter version of the PUCK model. Through this data analysis we can detect deviation from the pure random walk quantitatively, and the functional form of underlying potential force is estimated accordingly. It is found that a nonlinear potential force, which causes a directional motion, appeared right after the start of the intervention.