Extraction of phase information in daily stock prices
Yoshi Fujiwara · AIP conference proceedings · 2000
It is known that, in an intermediate time-scale such as days, stock market fluctuations possess several statistical properties that are common to different markets. Namely, logarithmic returns of an asset price have (i) truncated Pareto-Lévy distribution, (ii) vanishing linear correlation, (iii) volatility clustering and its power-law autocorrelation. The fact (ii) is a consequence of nonexistence of arbitragers with simple strategies, but this does not mean statistical independence of market fluctuations. Little attention has been paid to temporal structure of higher-order statistics, although it contains some important information on market dynamics. We applied a signal separation technique, called Independent Component Analysis (ICA), to actual data of daily stock prices in Tokyo and New York Stock Exchange (TSE/NYSE). ICA does a linear transformation of lag vectors from time-series to find independent components by a nonlinear algorithm. We obtained a similar impulse response for these dataset. If it were a Martingale process, it can be shown that impulse response should be a delta-function under a few conditions that could be numerically checked and as was verified by surrogate data. This result would provide information on the market dynamics including speculative bubbles and arbitrating processes.