We have studied the empirical distribution of cancellation positions through
rebuilding the limit-order book using the order flow data of 23 liquid stocks
traded on the Shenzhen Stock Exchange in the year 2003. We find that the
probability density function (PDF) of relative price levels where cancellations
allocate obeys the log-normal distribution. We then analyze the PDF of
normalized relative price levels by removing the factor of order numbers stored
at the price level, and find that the PDF has a power-law behavior in the tails
for both buy and sell orders.

We propose a new set of stylized facts quantifying the structure of financial
markets. The key idea is to study the combined structure of both investment
strategies and prices in order to open a qualitatively new level of
understanding of financial and economic markets. We study the detailed order
flow on the Shenzhen Stock Exchange of China for the whole year of 2003.

There are a number of situations in which several signals are simultaneously
recorded in complex systems, which exhibit long-term power-law
cross-correlations. The multifractal detrended cross-correlation analysis
(MF-DCCA) approaches can be used to quantify such cross-correlations, such as
the MF-DCCA based on detrended fluctuation analysis (MF-X-DFA) method. We
develop in this work a class of MF-DCCA algorithms based on the detrending
moving average analysis, called MF-X-DMA.

Using a recently introduced method to quantify the time varying lead-lag
dependencies between pairs of economic time series (the thermal optimal path
method), we test two fundamental tenets of the theory of fixed income: (i) the
stock market variations and the yield changes should be anti-correlated; (ii)
the change in central bank rates, as a proxy of the monetary policy of the
central bank, should be a predictor of the future stock market direction.

The detrending moving average (DMA) algorithm is a widely used technique to
quantify the long-term correlations of non-stationary time series and the
long-range correlations of fractal surfaces, which contains a parameter
$\theta$ determining the position of the detrending window. We develop
multifractal detrending moving average (MFDMA) algorithms for the analysis of
one-dimensional multifractal measures and higher-dimensional multifractals,
which is a generalization of the DMA method.

There is convincing evidence showing that the probability distributions of
stock returns in mature markets exhibit power-law tails and both the positive
and negative tails conform to the inverse cubic law. It supports the
possibility that the tail exponents are universal at least for mature markets
in the sense that they do not depend on stock market, industry sector, and
market capitalization. We investigate the distributions of one-minute intraday
returns of all the A-share stocks traded in the Chinese stock market, which is
the largest emerging market in the world.

We study the dynamics of order flows around large intraday price changes
using ultra-high-frequency data from the Shenzhen Stock Exchange. We find a
significant reversal of price for both intraday price decreases and increases
with a permanent price impact. The volatility, the volume of different types of
orders, the bid-ask spread, and the volume imbalance increase before the
extreme events and decay slowly as a power law, which forms a well-established
peak.

The private car license plates issued in Shanghai are bestowed the title of
"the most expensive sheet iron all over the world", more expensive than gold. A
citizen has to bid in an monthly auction to obtain a license plate for his new
private car.

The superfamily phenomenon of time series with different dynamics can be
characterized by the motif rank patterns observed in the nearest-neighbor
networks of the time series in phase space. However, the determinants of
superfamily classification are unclear. We attack this problem by studying the
influence of linear temporal correlations and multifractality using fractional
Brownian motions (FBMs) and multifractal random walks (MRWs).

The order submission and cancelation processes are two crucial aspects in the
price formation of stocks traded in order-driven markets. We investigate the
dynamics of order cancelation by studying the statistical properties of
inter-cancelation durations defined as the waiting times between consecutive
order cancelations of 22 liquid stocks traded on the Shenzhen Stock Exchange of
China in year 2003.

By combining (i) the economic theory of rational expectation bubbles, (ii)
behavioral finance on imitation and herding of investors and traders and (iii)
the mathematical and statistical physics of bifurcations and phase transitions,
the log-periodic power law model has been developed as a flexible tool to
detect bubbles. The LPPL model considers the faster-than-exponential (power law
with finite-time singularity) increase in asset prices decorated by
accelerating oscillations as the main diagnostic of bubbles.