Statistical properties of the moving average price in dollar–yen exchange rates

We introduce a weighted-moving-average analysis for the tick-by-tick data of yen–dollar exchange rates. The weights are determined automatically for given data by applying the Yule–Walker formula for autoregressive model. Although the data are non-stationary, the resulting moving average gives a quite nice property that the deviation around the moving-average becomes a white noise. The weights decay exponentially with time scale less than 2 min implying that dealers are watching only very recent market state.