Time lags will be denoted by the greek letter typically. The farima models, which have longrangedependence lrd, are widely used in many areas. The farima models, which have long range dependence lrd, are widely used in many areas. Consequently, accurate and reliable measurement, analysis and control of internet traffic are vital. Recent studies have shown that many physiological and behavioral processes can be. Authors in 9 showed that causes of selfsimilarity are associated with heavytailed distribution of file transfers. It is usually characterized by the hurst parameter h. Nine estimators were discussed in some detail by taqqu et al. Per definition 2, this time domain powerlaw decay at infinity is equivalent to a powerlaw divergence of. Wavelet analysis is a common method for signal processing, and has been used for estimation of hurst parameter. Nonparametric and empirical bayes estimation methods.
It relates to the autocorrelations of the time series, and the rate at which these decrease as the lag between pairs of values increases. The signals in numerous fields usually have scaling behavior longrange dependence and selfsimilarity which has been recognized as a key property for data characterization and decision making see e. We propose an estimator for the change point and prove consistency properties of this estimator. First, long range dependence may exist even, if the estimators have different estimates of the hurst exponent in the interval 0. To take into account parameter uncertainty one can use the bootstrap method, see e. Robustness of estimators of longrange dependence and self. Per definition 2, this time domain powerlaw decay at infinity is equivalent to a powerlaw divergence of the spectral density in the frequency domain near 0.
However, the authors tested estimators on rather long time series 0 elements, whereas in practice we often have to perform analysis of much shorter data sets. Q f volume p i p empirical properties of asset returns. A class of semiparametric estimators for long range dependent multivariate processes s lvia r. Recent studies have shown that many physiological and behavioral processes can be characterized by long range correlations. Robustness of whittle type estimators for time series with longrange dependence. Benhaddou, rida, nonparametric and empirical bayes estimation methods 20. Longrange dependence lrd and nongaussianity are ubiquitous in. Through the derivation of a precise characterization of the spectrum and variance time function, we show that this family is very atypical among lrd processes, being extremely close to the fractional gaussian noise in a precise sense which results in ultra. Our empirical results evidence the proxy of absolute return and archtype volatility model provides better performances in both the estimation and forecasting evaluations. Nonparametric beta kernel estimator for long memory time series. Interpreting the empirical findings properly with the help of the results of our simulation study, we conclude that the log absolute returns are longrange dependent with the memory parameter in the range between 0. It is known that the queuing system consists of three basic components. Comparing the performance of fa, dfa and dma using different.
A frequency domain empirical likelihood for short and longrange dependence nordman, daniel j. A class of semiparametric estimators for longrange. Empirical likelihood methods with weakly dependent processes kitamura, yuichi, annals of statistics, 1997. Even though some have known asymptotic properties, it is important to test their accuracy by using simulated series of di.
Studies involving the hurst exponent were originally developed in hydrology for the practical matter of determining optimum dam sizing for the nile rivers volatile rain and. We run extensive monte carlo simulations to find out how rescaled range analysis rs, multifractal detrended fluctuation analysis mfdfa, detrending moving average dma and generalized hurst exponent approach ghe estimate hurst exponent on independent. Understanding the limitations of estimation methods for. Various methods for estimating the selfsimilarity parameter andor the intensity of longrange dependence in a time series are available. Second, longrange dependence is unlikely to exist, if there are several estimators that fail to es timate the hurst exponent.
This paper establishes the uniform closeness of a weighted residual empirical process to its natural estimate in the linear regression setting when the errors are gaussian, or a function of gaussian random variables, that are strictly stationary and long range dependent. Interpreting the empirical findings properly with the help of the results of our simulation study, we conclude that the log absolute returns are long range dependent with the memory parameter in the range between 0. Fractional bivariate exponential fbexp estimator is proposed for long range dependence parameter estimation in random fields observed on a regular lattice. A class of semiparametric estimators for longrange dependent multivariate processes s lvia r. We do not limit our consideration to a speci c type of longrange dependence, rather we assume that the. The most significant techniques for performance evaluation include theoretical analysis, simulation, and empirical study based on measurement. In this study, we report on different estimators of h and d implemented in r, a. Furthermore, some efforts have been made to evaluate the accuracy and validity of the hurst estimators for lrd processes. Our work is intended as a survival guide and howto manual for. First, longrange dependence may exist even, if the estimators have different estimates of the hurst exponent in the interval 0. To discover the ones that work best, we apply the different methods to simulated sequences of fractional gaussian noise and.
The estimation and application of long memory time series models. Optimal uniform convergence rates and asymptotic normality. Longrange dependence and nongaussianity are ubiquitous in many natural systems like ecosystems, biological systems and climate. Table table1 1 includes estimators that are available in software packages traditionally used by psychologists r, spss, and sas. The hurst 20 exponent provides a measure for long term memory and fractality 21 of a time series. Entropy free fulltext a note on waveletbased estimator. Estimating longrange dependence parameter of a random field, which provides a measure for the extent of longrange dependence, is a challenging problem. Several books and monographs are available on the topic. We run extensive monte carlo simulations to find out how rescaled range analysis rs, multifractal detrended fluctuation analysis mfdfa, detrending moving average dma and generalized hurst exponent approach ghe estimate. University of central florida, 2007 a dissertation submitted in partial ful llment of the requirements for the degree of doctor of philosophy in the department of mathematics in the college of science at the university of central florida orlando, florida summer term 20. An empirical study william rea, marco reale and jennifer brown department of mathematics and statistics university of canterbury christchurch new zealand december, 2007 abstract we present the results of a simulation study into the properties of 11 di erent. In this paper, we show how the sampling properties of the hurst exponent methods of estimation change with the presence of heavy tails. Another alternative, which we adopt in this study, is the smallsample correction proposed inko et al.
This result is used to yield the asymptotic uniform linearity of a class of rank statistics in linear. Long memory, or long range dependent time series is. Rangebased volatility, longrange dependence, econometrics, financial time series introduction f rec ent literatures of longrange dependence1,5. The study of time series with long range dependence have been extensively developed for applications in nature sciences, as well as in dna sequences, cardiac dynamics, internet traffic 18 and finance 19. This result is used to yield the asymptotic uniform linearity of a class of rank statistics in linear regression models with.
Reassessment of longrange dependence of volatility by the estimation of volatility spectrum using highfrequency data chen, richard y. The presence and the nature of longrange dependent lrd are usually characterised by the hurst parameter. Longrange dependence of internet traffic has been mostly attributed to file transfer sizes. Range based volatility, long range dependence, econometrics, financial time series introduction f rec ent literatures of long range dependence 1,5. Estimating long range dependence in the presence of periodicity. The signals in numerous fields usually have scaling behaviors long range dependence and selfsimilarity which is characterized by the hurst parameter h. In this study, we report on different estimators of h and d implemented in r, a popular and freely available. Rea and les oxley and marco reale and jennifer brown, journalarxiv. The hurst exponent is used as a measure of longterm memory of time series. Spectral density, long range dependence, nonparametric estimation, periodogram, kernel smoothing, beta kernel, crossvalidation 1 introduction the estimation of a spectral density often requires to know whether the observed stationary time series is short or long memory. Long range dependence and nongaussianity are ubiquitous in many natural systems like ecosystems, biological systems and climate.
Pdf we present the results of a simulation study into the properties of 12 different. We also provide here a theoretical justification for the method of residuals of regression. Fractal brownian motion fbm plays an important role in modeling signals with selfsimilarity and long range dependence. Longrange dependence lrd and nongaussianity are ubiquitous in many natural systems such as ecosystems, biological systems and climate. A class of semiparametric estimators for longrange dependent. Understanding the limitations of estimation methods for long. This provides evidence for long range dependence and sensitive dependence of the evolution of the network on the initial evolution of the process. Mathematical and computer modelling, 29 1999 217228. A frequency domain empirical likelihood for short and long range dependence nordman, daniel j. Their conclusion is based on empirical data of www traffic collected at local area network web server ncsa mosaic. Various estimators of long range dependence have been proposed. The efficient market hypothesis, where asset prices follow a random walk and incorporate all relevant information, is often invoked in financial economics.
Here, a brief overview of the probabilistic foundations and statistical methods is given. Such a study was presented in, using ideal models that display longrange dependence, i. Quantifying long range dependence in language and user behavior to improve rnns kdd 19, august 48, 2019, anchorage, ak, usa function 38. Pdf on hurst exponent estimation under heavytailed. The study of time series with longrange dependence have been extensively developed for applications in nature sciences, as well as in dna sequences, cardiac dynamics, internet traffic 18 and finance 19. Longrange dependence, selfsimilar processes, and stabledistribution are very closely related sun07. We apply all 12 estimators to the campito mountain data and estimate the accuracy of their estimates using the beran goodness of fit test for long memory time series. Recent studies have shown that many physiological and behavioral processes can be characterized by longrange correlations. Fractional bivariate exponential estimator for longrange.
Mathematically this leads to limit theorems that differ from the short. A survey of performance evaluation and control for self. Statistical analysis and evaluation of hurst coefficient. Quantifying long range dependence in language and user. Statistics of regional surface temperatures post year 1900.
Statistical analysis and evaluation of hurst coefficient for. In order to meet the requirements of analysing the lrd processes, a number of practical estimation methods have been proposed in the literature. Second, long range dependence is unlikely to exist, if there are several estimators that fail to es timate the hurst exponent. Note that all these methods have a multifractal version 16,17,18,19,20 and can be generalized to handle highdimensional fractals and multifractals 20,21,22. We focus on how lrd is defined, which typical models may. Through the derivation of a precise characterization of the spectrum and variance time function, we show that this family is very atypical among lrd processes, being extremely close to the fractional gaussian noise in a precise sense which results in ultrafast convergence to fgn.
Nonparametric beta kernel estimator for long memory time. The hurst exponent h of fractal analysis and the fractionaldifferencing parameter d of the arfima methodology are useful for capturing serial correlations. When t is smallfor example of the order of minutesone speaks of. Queue performance in presence of longrange dependencies an. In an empirical study comparing 27 german stocks included in the dax, sun, rachev, and fabozzi sun07 conclude that an armagarch model assuming a fractional stable. However, it is not always appreciated that the two phenomena may occur together in natural systems and that selfsimilarity in a system can be a superposition of both phenomena.
Comparing the performance of fa, dfa and dma using. Various methods for estimating the selfsimilarity parameter andor the intensity of long range dependence in a time series are available. Fractional bivariate exponential fbexp estimator is proposed for longrange dependence parameter estimation in random fields observed on a regular lattice. Estimating longrange dependence in the presence of periodicity. The optimal performance of system can be achieved only in the case when all components are matched. There is some evidence however to suggest that some asset prices do not follow random walks but display long. Lopes and guilherme pumi federal university of rio grande do sul, porto alegre, rs, brazil corresponding author. The smoothness of stochastic volatility consequentially influences the applications and practice of. Robustness of whittle type estimators for time series with long range dependence.
Teverovsky and taqqu 1999 showed in a simulation study that the di. Citeseerx document details isaac councill, lee giles, pradeep teregowda. The queuing, as an inherent feature of each real system, plays a very important role in teletraffic networks as well. Reassessment of long range dependence of volatility by the estimation of volatility spectrum using highfrequency data chen, richard y. Nonparametric and empirical bayes estimation methods rida benhaddou. To discover the ones that work best, we apply the different methods to simulated sequences of fractional gaussian noise and fractional arima 0, d, 0. Nonparametric and empirical bayes estimation methods by rida benhaddou m. Queue performance in presence of longrange dependencies. Effects of trends and seasonalities on robustness of the. Such systematic behavior of past returns is of interest to traders.
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