We present the results of a simulation study into the properties of 12 different estimators of the hurst parameter, h, or the fractional integration parameter, d, in long memory time series. About 10 years ago, the introduction of longrange dependence lrd and selfsimilarity revolutionized our under. Montanari diiar, politecnico di milano, piazza leonardo da vinci 32 1203 milano, italy m. A major issue in financial economics is the behavior of asset returns over long horizons. A fractional fourier transform frft based estimation method is introduced in this paper to analyze the long range dependence lrd in time series. An empirical study author links open overlay panela. Longrange dependence and sea level forecasting ali. Mathematical and computer modelling, 29 1999 217228. First, long range dependence may exist even, if the estimators have different estimates of the hurst exponent in the interval 0. We report the effects of four different normalization methods using a large set of microarray data on childhood leukemia in addition to several sets of simulated data. A model for a financial asset is constructed with two types of agents. To take into account parameter uncertainty one can use the bootstrap method, see e.
Simulation results produce quantiles and document the finitesample size properties of the estimators, and a few empirical applications demonstrate the utility of the new methods. To discover the ones that work best, we apply the differentmethods to. Robustness of estimators of longrange dependence and self. The degree of lrd can be characterized by the hurst parameter.
It is reasonably straightforward to extend the asymptotic results for the robust scale estimator to the corresponding robust autocovariance estimators. In an empirical investigation of log absolute daily index returns, we find evidence of longrange dependence with values of the memory parameter in the range between 0. Various methods for estimating the selfsimilarity parameter andor the intensity of longrange dependence in a time series are available. This study shows that the caspian sea level time series possess long range dependence even after removing linear trends, based on analyses of the hurst statistic, the sample autocorrelation functions, and the periodogram of the series. First, longrange dependence may exist even, if the estimators have different estimates of the hurst exponent in the interval 0. Large sample behaviour of some wellknown robust estimators under longrange dependence article pdf available in statistics. A rst guard against model misspeci cation is a comprehensive empirical analysis, which will typically restrict the class of stochastic models we use. Recent studies have shown that many physiological and behavioral processes.
Citeseerx document details isaac councill, lee giles, pradeep teregowda. Zitikis, distributional analysis of empirical volatility in garch processes journal of statistical inference and planning, 8, 35783589, 2008 pdf file. Estimation of dynamic parameters, motivated by gaussianity 3. Various estimators of longrange dependence have been proposed. Various methods for estimating the selfsimilarity parameter andor the inten sity of longrange dependence in a time series are available.
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. Experimental queuing analysis with long range dependent packet traffic. A class of semiparametric estimators for longrange dependent. The effects of normalization on the correlation structure of. In this study, we report on different estimators of h and d implemented in r, a popular and freely available.
A number of estimators of longrange dependence have been proposed in the literature. Estimating longrange dependence in the presence of periodicity. Craig mackinlay princeton university press princeton, new jersey. To discover the ones that work best, we apply the different methods to simulated sequences of fractional gaussian noise and fractional arima0.
Such networks have distinctive empirical properties and a wealth of new models have emerged to capture them. Optimal rate of convergence for nonparametric changepoint estimators for nonstationary sequences hariz, samir ben, wylie, jonathan j. The paper presents a systematic study of correlation between the tstatistics associated with different genes. The empirical queuing analysis confirms the long range dependence detected through direct analysis by showing that the queue behavior at high level of aggregation still diverges greatly from that predicted by poisson model. Another alternative, which we adopt in this study, is the smallsample correction proposed inko et al. The results of the simulations are presented in sec. We also study the fitness of various analytical models to the traffic traces. Longrange dependence and sea level forecasting ali ercan. The goal of this paper is to provide benchmarks to the practitioner for measuring the intensity of longrange dependence in time series. Parametric estimation under longrange dependence by liudas giraitis and peter m robinson london school of economics and political science contents. Various estimators of long range dependence have been proposed. Various methods for estimating the selfsimilarity parameter andor the intensityof longrange dependence in a time series are available. Mar 24, 2017 simulation results produce quantiles and document the finitesample size properties of the estimators, and a few empirical applications demonstrate the utility of the new methods. However, despite its interesting structure, this estimate of dhas a limit.
Statistical properties of estimators for longrange dependence and selfsimilarity are critically assessed. Internet traffic and topology characteristics from a national isp perspective artan salihu, mst university of pittsburgh, 2016. The oldest and bestknown is the socalled rescaled range rs analysis popularized by mandelbrot and wallis and based on previous hydrological findings of hurst. 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. A number of estimators of long range dependence have been proposed in the literature. Recent studies have shown that many physiological and behavioral processes can be characterized by longrange correlations. Read trend stationarity versus longrange dependence in time series analysis, journal of econometrics on deepdyve, the largest online rental service for scholarly research with thousands of academic publications available at your fingertips. Some of the authors of this publication are also working on these related projects. We test r s analysis, detrended fluctuation analysis and periodogram regression methods on samples.
The empirical properties of some popular estimators of long. Understanding the limitations of estimation methods for. Estimating long range dependence in the presence of periodicity. This rigorous introduction to network science presents random graphs as models for realworld networks. Maximum likelihood estimators for arma and arfima models. Their conclusion is based on empirical data of www traffic collected. A class of semiparametric estimators for long range dependent multivariate processes s lvia r.
For example, this property has been observed in data pertaining to electronics, econometrics, hydrology and biomedical signals. Nine estimators were discussed in some detail by taqqu et al. Marcinkiewicz law of large numbers for outer products of heavytailed, longrange dependent data kouritzin, michael a. Also, we reveal information about the topology structure of internet at ip level, from the perspective of our data. The estimators are compared in terms of pileup effect, mean square error, bias, and empirical confidence level. A journal of theoretical and applied statistics 451 february. Various results from this chapter have been presented at asc 2012 and ems 20. Lopes and guilherme pumi federal university of rio grande do sul, porto alegre, rs, brazil. Cyclical long memory, kernel spectral estimator, long range dependence, spectral confidence bands. Mathematical and computer modelling pergamon mathematical and computer modelling 29 1999 217228 estimating longrange dependence in the presence of periodicity. Statistics of regional surface temperatures post year 1900. 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. Longrange versus shortrange dependence, and signi cance of warming trends. Kokoszka, wavelet domain test for longrange dependence in the presence of a trend statistics, 42, 1011, 2008 pdf file l.
Recent studies have shown that many physiological and behavioral processes can be characterized by long range correlations. We believe that the new method can be used as an online estimation tool for the longrange dependence parameter and thus be incorporated in the new tcp algorithms that exploit the known selfsimilar and longrange dependent nature of network trac. It is found that the most popular estimators can be biased in the presence of important features of many natural systems like trends and multiplicative noise. Optimal rate of convergence for nonparametric changepoint estimators for nonstationary sequences hariz, samir ben, wylie, jonathan. In an empirical investigation of log absolute daily index returns, we find evidence of long range dependence with values of the memory parameter in the range between 0. Authors in 9 showed that causes of selfsimilarity are associated with heavytailed distribution of file transfers.
It provides a detailed comparison of eight estimators for longrange dependence, using simulated farimap. The frftbased estimation of hurst parameter proposed in this paper can be implemented efficiently allowing very large data set. A regularised estimator for longrange dependent processes. Second, long range dependence is unlikely to exist, if there are several estimators that fail to es timate the hurst exponent. Estimation of longrange dependence research explorer. There exist several estimation methods for finding model parameters that help explain the set of observations exhibiting longrange dependence. Nevertheless, there is a likelihood of missing, or ignoring, some. We also provide here a theoretical justification for the method of residuals of regression. The effects of normalization on the correlation structure. There are different methodological approaches, and their respective statistical parameters, to capture fractality.
The hurst exponent h of fractal analysis and the fractionaldifferencing parameter d of the arfima methodology are useful for capturing serial correlations. Numerous procedures for measuring the fractal parameters. We test rs analysis, detrended fluctuation analysis and periodogram regression methods on. Understanding the limitations of estimation methods for long. Panel data with crosssectional dependence characterized by a. There is significant interest in longrange dependent processes since they occur in a wide range of phenomena across different areas of study. The majority of the studies performed on the topic of long range dependence are aimed at revealing long range dependence in empirical data whereas only a smaller part of this. Second, longrange dependence is unlikely to exist, if there are several estimators that fail to es timate the hurst exponent. There are no indications of longrange dependence in the case of the original index returns. Classroom tested for over ten years, this text places recent advances in a unified framework to enable systematic study. However, the authors tested estimators on rather long time series 0 elements, whereas in practice we often have to perform analysis of. Bubbles and long range dependence in asset prices volatilities.
Table table1 1 includes estimators that are available in software packages traditionally used by psychologists r, spss, and sas. Therefore, further important goals of fractal analyses are to test for the effective presence of genuine longrange correlations and provide an accurate estimation of their strength. Marcinkiewicz law of large numbers for outer products of heavytailed, long range dependent data kouritzin, michael a. Pdf large sample behaviour of some wellknown robust. Longrange dependence and sea level forecasting ali ercan, m. Longrange dependence of internet traffic has been mostly attributed to file transfer sizes. 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. 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.
Many methods for estimating the selfsimilarity parameter h or the intensity of longrange dependence in a time. Even though some have known asymptotic properties, it is important to test their accuracy by using simulated series of different lengths. The empirical queuing analysis confirms the longrange dependence detected through direct analysis by showing that the queue behavior at high level of aggregation still diverges greatly. Based on the available models capable of describing longrange dependence, various parameter estimation methods have been developed. Teverovsky department of mathematics, boston university, 111 cummington street boston. Teverovsky and taqqu 1999 showed in a simulation study that the di. Panel data with crosssectional dependence characterized.
Such a study was presented in, using ideal models that display longrange dependence, i. Measures of central tendency, variability, introduction to sampling distributions, sampling distribution of the mean, introduction to estimation, degrees of freedom learning objectives. Oscillations of empirical distribution functions under dependence wu, wei biao, high dimensional probability, 2006. The tapered version of the whittle likelihood turns out to be a reliable estimator for arma and arfima models. Estimation of dynamic parameters, motivated by nongaussianity 4. This result is used to yield the asymptotic uniform linearity of a class of rank statistics in linear regression models with. We compare and contrast their performance on simulated fractional gaussian noises and fractionally integrated series with lengths between 100 and 10,000 data points and h values between 0. Rea and les oxley and marco reale and jennifer brown, year2009. On estimating the intensity of longrange dependence in. Network performance implications of variability in data.
Estimating longrange dependence in the presence of. Deucalion view project ntua civil engineering team for egu 2017 view project hristos tyralis. Hristos tyralis, panayiotis dimitriadis, and demetris koutsoyiannis national technical university of athens itia. To estimate the model, i follow the ideas mentioned before to. 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. There are no indications of long range dependence in the case of the original index returns. An improved hurst parameter estimator based on fractional. May 01, 2002 read trend stationarity versus long range dependence in time series analysis, journal of econometrics on deepdyve, the largest online rental service for scholarly research with thousands of academic publications available at your fingertips.
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