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We apply the concepts of multifractal physics to financial time series in order to characterize the onset of crash for the Standard & Poor's 500 stock index x(t). It is found that within the framework of multifractality, the "analogous"…
Standard methods and theories in finance can be ill-equipped to capture highly non-linear interactions in financial prediction problems based on large-scale datasets, with deep learning offering a way to gain insights into correlations in…
We investigate the random walk of prices by developing a simple model relating the properties of the signs and absolute values of individual price changes to the diffusion rate (volatility) of prices at longer time scales. We show that this…
We consider a mean-reverting stochastic volatility model which satisfies some relevant stylized facts of financial markets. We introduce an algorithm for the detection of peaks in the volatility profile, that we apply to the time series of…
In this paper, a statistical analysis of high frequency fluctuations of the IPC, the Mexican Stock Market Index, is presented. A sample of tick-to-tick data covering the period from January 1999 to December 2002 was analyzed, as well as…
In an efficient stock market, the log-returns and their time-dependent variances are often jointly modelled by stochastic volatility models (SVMs). Many SVMs assume that errors in log-return and latent volatility process are uncorrelated,…
S&P 500 index data sampled at one-minute intervals over the course of 11.5 years (January 1989- May 2000) is analyzed, and in particular the Hurst parameter over segments of stationarity (the time period over which the Hurst parameter is…
The self-similar analysis of time series, suggested earlier by the authors, is applied to the description of market crises. The main attention is payed to the October 1929, 1987 and 1997 stock market crises, which can be successfully…
Stock price change in financial market occurs through transactions in analogy with diffusion in stochastic physical systems. The analysis of price changes in real markets shows that long-range correlations of price fluctuations largely…
Stock markets can become inefficient due to calendar anomalies known as day-of-the-week effect. Calendar anomalies are well-known in financial literature, but the phenomena remain to be explored in econophysics. In this paper we use…
We use rank correlations as distance functions to establish the interconnectivity between stock returns, building weighted signed networks for the stocks of seven European countries, the US and Japan. We establish the theoretical…
Specialized topics on financial data analysis from a numerical and physical point of view are discussed. They pertain to the analysis of crash prediction in stock market indices and to the persistence or not of coherent and random sequences…
Since the beginning of the new millennium, stock markets went through every state from long-time troughs, trade suspensions to all-time highs. The literature on asset pricing hence assumes random processes to be underlying the movement of…
We show that distinctive alterations in scaling parameters of Dst index time series occur as a strong magnetic storm approaches. These alterations reveal a gradual reduction of complexity as the catastrophic event approaches. The increase…
Based on theoretical argument and experimental evidence, we conjecture that structure functions of turbulent times series exhibit log-periodic modulations decorating their power law dependence. In order to provide ironclad experimental…
We study the temporal fluctuations in time-dependent stock prices (both individual and composite) as a stochastic phenomenon using general techniques and methods of nonequilibrium statistical mechanics. In particular, we analyze stock price…
The probability distribution of stock price changes is studied by analyzing a database (the Trades and Quotes Database) documenting every trade for all stocks in three major US stock markets, for the two year period Jan 1994 -- Dec 1995. A…
Using intraday data for the cross-section of individual stocks, we show that both transitory and persistent fluctuations in realized market and average idiosyncratic volatility, skewness and kurtosis are differentially priced in the…
A methodology is developed to identify, as units of study, each decrease in the value of a stock from a given maximum price level. A critical level in the amount of price declines is found to separate a segment operating under a random walk…
Multifractal analysis and extensive statistical tests are performed upon intraday minutely data within individual trading days for four stock market indexes (including HSI, SZSC, S&P500, and NASDAQ) to check whether the indexes (instead of…