27 research outputs found

    Analysis of Binarized High Frequency Financial Data

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    A non-trivial probability structure is evident in the binary data extracted from the up/down price movements of very high frequency data such as tick-by-tick data for USD/JPY. In this paper, we analyze the Sony bank USD/JPY rates, ignoring the small deviations from the market price. We then show there is a similar non-trivial probability structure in the Sony bank rate, in spite of the Sony bank rate's having less frequent and larger deviations than tick-by-tick data. However, this probability structure is not found in the data which has been sampled from tick-by-tick data at the same rate as the Sony bank rate. Therefore, the method of generating the Sony bank rate from the market rate has the potential for practical use since the method retains the probability structure as the sampling frequency decreases.Comment: 8pages, 4figures, contribution to the 3rd International Conference NEXT-SigmaPh

    Waiting time analysis of foreign currency exchange rates: Beyond the renewal-reward theorem

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    We evaluate the average waiting time between observing the price of financial markets and the next price change, especially in an on-line foreign exchange trading service for individual customers via the internet. Basic technical idea of our present work is dependent on the so-called renewal-reward theorem. Assuming that stochastic processes of the market price changes could be regarded as a renewal process, we use the theorem to calculate the average waiting time of the process. In the conventional derivation of the theorem, it is apparently hard to evaluate the higher order moments of the waiting time. To overcome this type of difficulties, we attempt to derive the waiting time distribution Omega(s) directly for arbitrary time interval distribution (first passage time distribution) of the stochastic process P_{W}(tau) and observation time distribution P_{O}(t) of customers. Our analysis enables us to evaluate not only the first moment (the average waiting time) but also any order of the higher moments of the waiting time. Moreover, in our formalism, it is possible to model the observation of the price on the internet by the customers in terms of the observation time distribution P_{O}(t). We apply our analysis to the stochastic process of the on-line foreign exchange rate for individual customers from the Sony bank and compare the moments with the empirical data analysis.Comment: 8pages, 11figures, using IEEEtran.cl

    On the gap between an empirical distribution and an exponential distribution of waiting times for price changes in a financial market

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    We analyze waiting times for price changes in a foreign currency exchange rate. Recent empirical studies of high frequency financial data support that trades in financial markets do not follow a Poisson process and the waiting times between trades are not exponentially distributed. Here we show that our data is well approximated by a Weibull distribution rather than an exponential distribution in a non-asymptotic regime. Moreover, we quantitatively evaluate how much an empirical data is far from an exponential distribution using a Weibull fit. Finally, we discuss a phase transition between a Weibull-law and a power-law in the asymptotic long waiting time regime.Comment: 9 pages, 6 figures, submitted for a publication and under revie

    Fluctuations in time intervals of financial data from the view point of the Gini index

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    We propose an approach to explain fluctuations in time intervals of financial markets data from the view point of the Gini index. We show the explicit form of the Gini index for a Weibull distribution which is a good candidate to describe the first passage time of foreign exchange rate. The analytical expression of the Gini index gives a very close value with that of empirical data analysis.Comment: 6pages, 3figures, using elsart.cl

    Evaluating zero error noise thresholds by the replica method for Gallager code ensembles

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    The zero error noise threshold for Gallager code ensemblers were evaluated by using replica method (RM). The RM, which was invented in statistical physics, offered an option for calculating the bound. It was shown that the given approach provided more optimistic evaluations with respect to the evaluations provided by the information theory literature for sparse matrices

    Crossover between Levy and Gaussian regimes in first passage processes

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    We propose a new approach to the problem of the first passage time. Our method is applicable not only to the Wiener process but also to the non--Gaussian Leˊ\acute{\rm e}vy flights or to more complicated stochastic processes whose distributions are stable. To show the usefulness of the method, we particularly focus on the first passage time problems in the truncated Leˊ\acute{\rm e}vy flights (the so-called KoBoL processes), in which the arbitrarily large tail of the Leˊ\acute{\rm e}vy distribution is cut off. We find that the asymptotic scaling law of the first passage time tt distribution changes from t(α+1)/αt^{-(\alpha +1)/\alpha}-law (non-Gaussian Leˊ\acute{\rm e}vy regime) to t3/2t^{-3/2}-law (Gaussian regime) at the crossover point. This result means that an ultra-slow convergence from the non-Gaussian Leˊ\acute{\rm e}vy regime to the Gaussian regime is observed not only in the distribution of the real time step for the truncated Leˊ\acute{\rm e}vy flight but also in the first passage time distribution of the flight. The nature of the crossover in the scaling laws and the scaling relation on the crossover point with respect to the effective cut-off length of the Leˊ\acute{\rm e}vy distribution are discussed.Comment: 18pages, 7figures, using revtex4, to appear in Phys.Rev.

    Tighter decoding reliability bound for Gallager's error-correcting code

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    Statistical physics is employed to evaluate the performance of error-correcting codes in the case of finite message length for an ensemble of Gallager's error correcting codes. We follow Gallager's approach of upper-bounding the average decoding error rate, but invoke the replica method to reproduce the tightest general bound to date, and to improve on the most accurate zero-error noise level threshold reported in the literature. The relation between the methods used and those presented in the information theory literature are explored

    Non-linear Logit Model for High Frequency Currency Exchange

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