Search results for "PROBABILITY DENSITY"
showing 10 items of 187 documents
Stationary and non-stationary probability density function for non-linear oscillators
1997
A method for the evaluation of the stationary and non-stationary probability density function of non-linear oscillators subjected to random input is presented. The method requires the approximation of the probability density function of the response in terms of C-type Gram-Charlier series expansion. By applying the weighted residual method, the Fokker-Planck equation is reduced to a system of non-linear first order ordinary differential equations, where the unknowns are the coefficients of the series expansion. Furthermore, the relationships between the A-type and C-type Gram-Charlier series coefficient are derived.
Non-Gaussian probability density function of SDOF linear structures under wind actions
1998
Abstract Wind velocity is usually analytically described adding a static mean term to a zero mean fluctuation stationary process. The corresponding aerodynamic alongwind force acting on a single degree of freedom (SDOF) structure can be considered as a sum of three terms proportional to the mean wind velocity, to the product between mean and fluctuating part of the wind velocity and to the square power of the fluctuating wind velocity, respectively. The latter term, often neglected in the literature, is responsible for the non-Gaussian behaviour of the response. In this paper a method for the evaluation of the stationary probability density function of SDOF structures subjected to non-Gauss…
Power-law relaxation in a complex system: Omori law after a financial market crash
2003
We study the relaxation dynamics of a financial market just after the occurrence of a crash by investigating the number of times the absolute value of an index return is exceeding a given threshold value. We show that the empirical observation of a power law evolution of the number of events exceeding the selected threshold (a behavior known as the Omori law in geophysics) is consistent with the simultaneous occurrence of (i) a return probability density function characterized by a power law asymptotic behavior and (ii) a power law relaxation decay of its typical scale. Our empirical observation cannot be explained within the framework of simple and widespread stochastic volatility models.
Statistical Properties of Statistical Ensembles of Stock Returns
1999
We select n stocks traded in the New York Stock Exchange and we form a statistical ensemble of daily stock returns for each of the k trading days of our database from the stock price time series. We analyze each ensemble of stock returns by extracting its first four central moments. We observe that these moments are fluctuating in time and are stochastic processes themselves. We characterize the statistical properties of central moments by investigating their probability density function and temporal correlation properties.
Variety and volatility in financial markets
2000
We study the price dynamics of stocks traded in a financial market by considering the statistical properties both of a single time series and of an ensemble of stocks traded simultaneously. We use the $n$ stocks traded in the New York Stock Exchange to form a statistical ensemble of daily stock returns. For each trading day of our database, we study the ensemble return distribution. We find that a typical ensemble return distribution exists in most of the trading days with the exception of crash and rally days and of the days subsequent to these extreme events. We analyze each ensemble return distribution by extracting its first two central moments. We observe that these moments are fluctua…
Testing Goodness-of-Fit with the Kernel Density Estimator: GoFKernel
2015
To assess the goodness-of-fit of a sample to a continuous random distribution, the most popular approach has been based on measuring, using either L∞ - or L2 -norms, the distance between the null hypothesis cumulative distribution function and the empirical cumulative distribution function. Indeed, as far as I know, almost all the tests currently available in R related to this issue (ks.test in package stats, ad.test in package ADGofTest, and ad.test, ad2.test, ks.test, v.test and w2.test in package truncgof) use one of these two distances on cumulative distribution functions. This paper (i) proposes dgeometric.test, a new implementation of the test that measures the discrepancy between a s…
Applications of statistical mechanics to finance
1999
Abstract We discuss some apparently “universal” aspects observed in the empirical analysis of stock price dynamics in financial markets. Specifically we consider (i) the empirical behavior of the return probability density function and (ii) the content of economic information in financial time series.
Probabilistic characterization of nonlinear systems under α-stable white noise via complex fractional moments
2015
Abstract The probability density function of the response of a nonlinear system under external α -stable Levy white noise is ruled by the so called Fractional Fokker–Planck equation. In such equation the diffusive term is the Riesz fractional derivative of the probability density function of the response. The paper deals with the solution of such equation by using the complex fractional moments. The analysis is performed in terms of probability density for a linear and a non-linear half oscillator forced by Levy white noise with different stability indexes α . Numerical results are reported for a wide range of non-linearity of the mechanical system and stability index of the Levy white nois…
Empirical investigation of stock price dynamics in an emerging market
1999
Abstract We study the development of an emerging market – the Budapest Stock Exchange – by investigating the time evolution of some statistical properties of heavily traded stocks. Moving quarter by quarter over a period of two and a half years we analyze the scaling properties of the standard deviation of intra-day log-price changes. We observe scaling using both seconds and ticks as units of time. For the investigated stocks a Levy shape is a good approximation to the probability density function of tick-by-tick log-price changes in each quarter: the index of the distribution follows an increasing trend, suggesting it could be used as a measure of market efficiency.
Stock market dynamics and turbulence: parallel analysis of fluctuation phenomena
1997
Abstract We report analogies and differences between the fluctuations in an economic index and the fluctuations in velocity of a fluid in a fully turbulent state. Specifically, we systematically compare (i) the statistical properties of the S&P 500 cash index recorded during the period January 84–December 89 with (ii) the statistical properties of the velocity of turbulent air measured in the atmospheric surface layer about 6 m above a wheat canopy in the Connecticut Agricultural Research Station. We find non-Gaussian statistics, and intermittency, for both processes (i) and (ii) but the deviation from a Gaussian probability density function are different for stock market dynamics and turbu…