统计金融
We compare systematically several classes of stochastic volatility models of stock market fluctuations. We show that the long-time return distribution is either Gaussian or develops a power-law tail, while the short-time return distribution…
Probability distributions of money, income, and energy consumption per capita are studied for ensembles of economic agents. The principle of entropy maximization for partitioning of a limited resource gives exponential distributions for the…
Based on criteria of mathematical simplicity and consistency with empirical market data, a model with volatility driven by fractional noise has been constructed which provides a fairly accurate mathematical parametrization of the data.…
We discuss some methods to quantitatively investigate the properties of correlation matrices. Correlation matrices play an important role in portfolio optimization and in several other quantitative descriptions of asset price dynamics in…
We investigate the temporal correlations and multifractal nature of trading volume of 22 liquid stocks traded on the Shenzhen Stock Exchange in 2003. We find that the trading volume exhibit size-dependent non-universal long memory and…
We consider a statistical model for pairs of traded assets, based on a Cointegrated Vector Auto Regression (CVAR) Model. We extend standard CVAR models to incorporate estimation of model parameters in the presence of price series level…
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 $\theta$…
We investigate the probability distributions of the recurrence intervals $\tau$ between consecutive 1-min returns above a positive threshold $q>0$ or below a negative threshold $q<0$ of two indices and 20 individual stocks in China's stock…
To define oscillatory movements of securities market, we put in the non-local extension of Ito- equation for wavelet-images of random processes. It is proposed an algorithm of creation of evolutionary equation and a model of prediction of…
While the use of volatilities is pervasive throughout finance, our ability to determine the instantaneous volatility of stocks is nascent. Here, we present a method for measuring the temporal behavior of stocks, and show that stock prices…
We analyze the Bombay stock exchange (BSE) price index over the period of last 12 years. Keeping in mind the large fluctuations in last few years, we carefully find out the transient, non-statistical and locally structured variations. For…
We briefly review our recent studies on stochastic processes modelling internet on-line trading. We present a way to evaluate the average waiting time between the observation of the price in financial markets and the next price change,…
The investigations of financial markets from a complex network perspective have unveiled many phenomenological properties, in which the majority of these studies map the financial markets into one complex network. In this work, we…
We decompose the exchange rates returns of 41 currencies (incl. gold) into their sign and amplitude components. Then we group together all exchange rates with a common base currency, construct Minimal Spanning Trees for each group…
We study the statistical properties of the recurrence intervals $\tau$ between successive trading volumes exceeding a certain threshold $q$. The recurrence interval analysis is carried out for the 20 liquid Chinese stocks covering a period…
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…
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…
We present a method to compensate statistical errors in the calculation of correlations on asynchronous time series. The method is based on the assumption of an underlying time series. We set up a model and apply it to financial data to…
We discuss a weighted estimation of correlation and covariance matrices from historical financial data. To this end, we introduce a weighting scheme that accounts for similarity of previous market conditions to the present one. The…
We show that log-periodic power-law (LPPL) functions are intrinsically very hard to fit to time series. This comes from their sloppiness, the squared residuals depending very much on some combinations of parameters and very little on other…