Catálogo de publicaciones - libros

The fractal nature of financial data has been investigated through literature. The aim of this paper is to use the information given by the detection of the fractal measure of data in order to provide support for trading decisions when dealing with technical analysis signals that can be used to trigger buy/sell orders. Trendlines are considered as a case study.

FMDDF system based on the basic scientific ideas from Physics and Economics involved in the procedure for the dynamic probabilistic distribution function of the state () derivation for any financial market (). Price moving process defines dynamic FM. Price movement is defined by the volume imbalance V. The necessary condition for the dynamic FM is V ≠ 0 at the same price, while the sufficient condition is defined by nonzero price volatility σ. The total probabilistic distribution function of any FM is the sum of the two incompatible terms: the regular probabilistic distribution function () containing the mean value and PDFS. PDFS structured based on the adiabatic integrals of FM motion that include the existing or expected volume imbalance, price volatility and amount of shares or contracts. PDFS is not path dependable (the new trajectories’ invariant principle) in the special economic space E{ξ}. This fact is important in financial engineering, risk control, quantitative FM predictability and investment decision-making.

Among the long-term stationary (although complex) behavior characteristics of futures markets is a set of identifiable intermediate-length (2–21.5 days) price cycles. Using a two-parameter extrapolation technique, time and price objectives of these cycles are determined. The valley-to-valley time differences (wave-lengths) are more regular than those for top-to-top, with standard deviations of the former about 50% smaller than those of the latter. The substantial profitability in S&P futures trading based on these parameters can be further increased by including additional features.

The continuous time random walk (CTRW) has become a widely-used tool for studying the microstructure of random process appearing in many physical phenomena. We here report the CTRW analysis applied to the market dynamics which has been recently explored by physicists. We focuss on the mean exit problem.

By using regular time-steps we define discrete-time random walks and flights on subordinate (directed) Continuous-Time Hierarchical (or Weierstrass) Walks and Flights, respectively. The obtained results can be considered as a kind of warning that indicates some persistent non-linear long-term autocorrelations (artifacts) accompanying the recording of empirical high-frequency financial time-series by regular time-steps, indeed.

It is now well established that the probability distribution of relative price changes of stock market aggregates has two prominent features. First, in its central region, the distribution closely resembles a Levy stable distribution with exponent α ≅ 1.4. Secondly, it has power-law tails with exponent ≤ 4. Both these results follow from relatively low resolution analyses of the data. In this paper we present the results of a high-resolution analysis of a database consisting of 132,000 values of the S&P 500 index taken at 10 minute intervals. We find a third prominent feature, a delta function at the origin the amplitude of which shows power-law decay over time with an exponent ≅ 2 / 3. We show that Continuous-Time Random-Walk (CTRW) theory can account for all three features, but predicts subdiffusion with a growth of the variance of the ln(price) as the power of time. We find instead superdiffusion with an exponent ≅ 9/8 instead of 2/3. We conclude that CTRW theory must be extended to incorporate the effects of “Price Momentum”.

The purpose of this study is to examine the deterministic structure of financial time series of prices in presence of chaos and a low-dimensional attractor. The methodology used consists of transforming the observed system, typically exhibiting higher dimensional characteristics, into its , via attractor or phase space reconstruction method, with subsequent intersection of the reconstructed attractor with the best two-dimensional (2D) hyperplane. The 2D system resulting from this slicing operation can be used for financial market analysis applications, by means of the determination of the .

A set of finance literature shows that asset return processes are characterized by a GARCH class conditional volatility and fat-tail distributed disturbances, such as mixture of normal distributions and -distribution (Watanabe 2000; Watanabe and Asai 2004). This paper finds that this type of complicated process arises by aggregating returns of a risky asset traded in a limit order market. The conditional volatility of generated return series can be modeled as a GARCH class since the volatility gradually diminishes as the price assimilates the new information about the future asset return. The reason why the error term of estimated model is fat-tail distributed is that the return of transaction prices is distributed as a mixture of normals; one of the two distributions represents the drift of the price process, and the other represents the liquidity effect.

Using a Gibbs distribution developed in the theory of statistical physics and a long-range percolation theory, we present a new model of a stock price process for explaining the fat tail in the distribution of stock returns.

We consider two types of traders, Group A and Group B: Group A traders analyze the past data on the stock market to determine their present trading positions. The way to determine their trading positions is not deterministic but obeys a Gibbs distribution with interactions between the past data and the present trading positions. On the other hand, Group B traders follow the advice reached through the long-range percolation system from the investment adviser. As the resulting stock price process, we derive a Lévy process.

Foundations of Flicker-Noise Spectroscopy (FNS) which is a new phenomenological approach to extract information hidden in chaotic signals are presented. The information is formed by sequences of distinguished types of signal irregularities — spikes, jumps, and discontinuities of derivatives of different orders — at all space-time hierarchical levels of systems. The ability to distinguish irregularities means that parameters or patterns characterizing the totality of properties of the irregularities are distinguishably extracted from the power spectra () ( — frequency) and difference moments Ф() ( — temporal delay) of the order. It is shown that FNS method can be used to solve the problems of two types: to show of the parameters characterizing dynamics and peculiarities of structural organization of open complex systems; to reveal the precursors of the sharpest changes in the states of open dissipative systems of various nature on the base of a priori information about their dynamics. Applications of the FNS for getting information hidden in economical data (daily market prices for the Nasdaq- and Nikkei-Index time series) are presented.