Markov reconstruction of financial time series

The availability of high-frequent price data in foreign exchange market, the biggest financial market in the world, attracts researchers to study its logarithm return time series quantitatively. Non-Markov processes prevail to model the time series, but non-Markov processes are difficult to model and characterize. In this paper, we use our proposed method to reconstruct the time series with Markov model. Our reconstruction repeats the fat-tailed transition probability density of the time series. From the reconstruction, we find that the underlying Markov process is mean-reverting, and more volatile and more tendentious to the mean when further from the mean. EUR/USD is more disciplinary than AUD/USD.