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Asset and Liability Management: Recent Advances
Published in George Anastassiou, Handbook of Analytic-Computational Methods in Applied Mathematics, 2019
Generating scenarios that realistically represent the future uncertainty is important for the validity of the results of stochastic programming based ALM models. The assumption underlying the above described scenario generation methods is the normal distribution. The validity of normal distribution has been questioned in the finance and macroeconomics literature. The financial data exhibit heavy tails, time varying volatility, and long-range dependence. The macroeconomic variables exhibit significant kurtosis and asymmetry. The leptokurtic (heavy tailed and peaked) and asymmetric nature of the economic variables can be better captured by using stable distribution as opposed to normal distribution. The conditional heteroskedastic models (ARMA-GARCH) utilizing stable distributions can be used to describe the time varying volatility along with the asymmetric and leptokurtic behavior. In addition to these, the long-range dependence can also be modeled if fractional-stable GARCH models are employed.
Broadband Networks
Published in Naoaki Yamanaka, High-Performance Backbone Network Technology, 2020
Self-similar phenomena were observed in traces of LAN traffic [9] and VBR video services [10]. This led to the proposal of a class of self-similar traffic models with long-range dependence such as fractional Brownian motion and fractional ARIMA processes [11]. Unfortunately, these processes are difficult to analyze in queueing models. Recently, some papers have questioned the importance of long-range dependence on multiplexer performance (cf. [12]).
Using Power Laws and the Hurst Exponent to Identify Stock Market Trading Bubbles
Published in Gunilla SundstrÖm, Erik Hollnagel, Governance and Control of Financial Systems, 2018
Rossitsa Yalamova, Bill McKelvey
Long-range dependency relates to the rate of decay of statistical dependence measured by the autocorrelation function, with the implication that slower than an exponential decay typically means a power-law indicated decay rate.
Dynamics of Premixed Flames Near Lean and Rich Blowout
Published in Combustion Science and Technology, 2022
Somnath De, Sabyasachi Mondal, Arijit Bhattacharya, Sirshendu Mondal, Achintya Mukhopadhyay, Swarnendu Sen
Hurst exponent also measures the long-term memory or correlation of a time series and thus, it can also be referred to as ‘index of long-range dependence’ (Mishura and Zili 2018). H can quantify the tendency of a time series to regress strongly to mean (anti-persistent or mean reversion) or to cluster (persistent or trending pattern) in a specific direction (Kantelhardt et al. 2002). Generally, H < 0.5 signifies the anti-persistent nature of time signal where long-term switching between high and low values in adjacent pairs can be observed. The trending or persistent nature of signal (H > 0.5) indicates the long-term positive auto-correlation where high value can be followed by another high value in the time series. For an uncorrelated time series, H is 0.5.
On uniqueness and existence of solutions to stochastic set-valued differential equations with fractional Brownian motions
Published in Systems Science & Control Engineering, 2020
Jialu Zhu, Yong Liang, Weiyin Fei
Next, let us recall the fBm. Since real systems are complex, a noise-disturbed system has a long range dependence (strong aftereffect, long memory) which shows it is no more a classical Brownian motion, just a fractional Brownian motion (see e.g. Mandelbrot & van Ness, 1968; Shiryaev, 1999). Later, the fBm and its applications are extensively investigated. Especially, a kind of stochastic differential equations with an fBm is characterized. Recently, there is much literature which attempts to solve stochastic differential equations for an fBms (see e.g. Boufoussi & Hajji, 2012; Fei, 2007c; Fei et al., 2013; Hu et al., 2008; Hu & Peng, 2009; Le Breton, 1998; Yan & Yang, 2008, and references therein). However, the multivalued processes have not been considered which have early been discussed many scholars (see e.g. Hiai & Umegaki, 1977; Li et al., 2010, and references therein).
A case study on Discrete Wavelet Transform based Hurst exponent for epilepsy detection
Published in Journal of Medical Engineering & Technology, 2018
Saiby Madan, Kajri Srivastava, A. Sharmila, P. Mahalakshmi
Hurst exponent (HE) is a classical parameter to quantify the correlation of points in a time series. HE <0.5 indicates that the sequences are long range anti correlations and anti-persistent while HE >0.5 indicates the sequences with long range correlations. Therefore, HE is widely applied to assess the presence or absence of long-range dependence and its degree in a time series. As the HE can classify time series based on their predictability and chaos levels, it may be a useful tool in identifying deviations from the normal pattern of brain activity during interruptions of seizures [23]. Hurst type (HE) is an established parameter that is utilised as a part of this case for nonlinear analysis. In a time series, this parameter is used to quantify the correlation of points. The presence or absence of long-range dependence and its degree in a time series is assessed through HE. During interruption of seizures, HE is very much useful in identifying deviations from the normal pattern of brain activity. Commonly, HE can be estimated using rescaled range analysis (R/S) of which the equation is defined below where R is the difference between the maximum and minimum of deviation and S represents the standard deviation of the time series. T denotes the duration of the sample data [26].