The goal of this paper is to provide benchmarks to the practitioner for measuring the intensity of longrange dependence in time series. For example, this property has been observed in data pertaining to electronics, econometrics, hydrology and biomedical signals. Central limit theorem for the empirical process of a linear sequence with long memory. Statistics large sample behaviour of some wellknown robust. Queue performance in presence of longrange dependencies an. There exist several estimation methods for finding model parameters that help explain the set of observations exhibiting longrange dependence. Recent studies have shown that many physiological and behavioral processes can be characterized by longrange correlations. Abstract we investigate the performance of several waveletbased estimators of the fractional difference parameter. A class of semiparametric estimators for longrange. Multichannel deconvolution with longrange dependence a. On the minimax optimality of block thresholded wavelet.
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. The literature on longrange dependence is very extensive, see, e. The obtained values dier largely from heuristic values pro. Estimation of the selfsimilarity parameter using the wavelet transform. Effects of trends and seasonalities on robustness of the. Even though some have known asymptotic properties, it is important to test their accuracy by using simulated series of di. A class of semiparametric estimators for long range dependent multivariate processes s lvia r. Even though some have known asymptotic properties, it is important to test their accuracy by usingsimulated series of dier. 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.
We focus on the hodgeslehmann location estimator 1, the shamosbickel scale estimator 2,3 and the rousseeuwcroux scale. Various methods for estimating the selfsimilarity parameter andor the intensityof longrange dependence in a time series are available. A class of semiparametric estimators for longrange dependent multivariate processes s lvia r. To account for this, a great deal of papers on long range dependence lrd has been developed. In section 2, a variety of hurst parameter estimators are. Longrange dependence lrd and nongaussianity are ubiquitous in many natural systems such as ecosystems, biological systems and climate. Robustness of estimators of longrange dependence and self. Various methods for estimating the selfsimilarity parameter andor the intensity of longrange dependence in a time series are available. We present the results of a simulation study into the properties of 12 different estimators of the hurst parameter, h, or the fractional integra tion. Calibration of the empirical likelihood method for a vector mean emerson, sarah c. The estimation and application of long memory time series models. Understanding the limitations of estimation methods for. Estimating longrange dependence in the presence of periodicity. We conclude that the tapered version of the whittle likelihood is a reliable estimator for arma and arfima models.
The paper includes computer simulation in order to examine how well the estimators perform at nite sample sizes. On estimating the intensity of longrange dependence in. Nonparametric and empirical bayes estimation methods. 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. We present confidence intervals estimates for rescaled range and modified rescaled range. In this study, we report on different estimators of h and. To account for this, a great deal of papers on longrange dependence lrd has been developed. The queuing, as an inherent feature of each real system, plays a very important role in teletraffic networks as well. Change point estimation based on wilcoxon tests in. For example, hall and hart 1990 showed that the convergence rates of mean. About 10 years ago, the introduction of longrange dependence lrd and selfsimilarity revolutionized our under. Various estimators of long range dependence have been proposed. It provides a detailed comparison of eight estimators for longrange dependence, using simulated farimap. We consider situations where, in addition to long range dependence, the time series exhibit heavy tails and are perturbed by polynomial and changepoint trends.
Several methods for measuring the longrange dependence parameter. We consider situations where, in addition to longrange dependence, the time series exhibit heavy tails and are perturbed by polynomial and changepoint trends. Lopes and guilherme pumi federal university of rio grande do sul, porto alegre, rs, brazil corresponding author. When t is smallfor example of the order of minutesone speaks of. However, empirical evidence has shown that even at large lags, the correlation structure in the errors can decay at a hyperbolic rate, rather than an exponential rate. Rea and les oxley and marco reale and jennifer brown, year2009. Extensive simulation studies show that the proposed estimators perform well. A major issue in financial economics is the behavior of asset returns over long horizons. Recent studies have shown that many physiological and behavioral processes can be characterized by long range correlations.
Time lags will be denoted by the greek letter typically. Understanding the limitations of estimation methods for long. Estimation and inference in fractional ornsteinuhlenbeck. Teverovsky and taqqu 1999 showed in a simulation study that the di. Discriminating longrange dependence from single or multiple change points is a very active research area in statistics, see e. We also provide here a theoretical justification for the method of residuals of regression. The optimal performance of system can be achieved only in the case when all components are matched together.
Estimating longrange dependence in the presence of. We test rs analysis, detrended fluctuation analysis and periodogram regression methods on samples drawn. 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. To discover the ones that work best, we apply the different methods to simulated sequences of fractional gaussian noise and fractional arima0. A note on waveletbased estimator of the hurst parameter. The presence and the nature of long range dependent lrd are usually characterised by the hurst parameter. Mostly used estimators of hurst exponent for detection of long range dependence are biased by presence of short range dependence in the underlying time series.
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. Mathematical and computer modelling pergamon mathematical and computer modelling 29 1999 217228 estimating long range dependence in the presence of periodicity. This means that the stationarity assumption of hydrological time series, which has been widely used in the past, cannot be further advocated. Various methods for estimating the selfsimilarity parameter andor the intensityof long range dependence in a time series are available. Estimation for data with longrange dependence is quite di. Maximum likelihood estimators for arma and arfima models. A class of semiparametric estimators for longrange dependent. Mostly used estimators of hurst exponent for detection of longrange dependence are biased by presence of shortrange dependence in the underlying time series.
Mathematical and computer modelling pergamon mathematical and computer modelling 29 1999 217228 estimating longrange dependence in the presence of periodicity. Estimation of longrange dependence research explorer. We test r s analysis, detrended fluctuation analysis and periodogram regression methods on samples. Various methods for estimating the selfsimilarity parameter andor the intensity of long range dependence in a time series are available. In this study, we report on different estimators of h and d implemented in r, a popular and freely available. We present the results of a simulation study into the properties of 12 different estimators of the hurst. Even though some have known asymptotic properties, it is important to test their accuracy by using simulated series of different lengths.
Distinguishing between short and long range dependence. Our empirical results evidence the proxy of absolute return and archtype volatility model provides better performances in both the estimation and forecasting evaluations. Influence of the longrange dependence in rainfall in. Montanari diiar, politecnico di milano, piazza leonardo da vinci 32 1203 milano, italy m. The presence and the nature of longrange dependent lrd are usually characterised by the hurst parameter. Then the estimators are compared with respect to their mean square error, bias, and empirical confidence level. We show that the difference in expected values and confidence intervals enables us to use both methods together to clearly distinguish. 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. This paper formulates a penalized empirical likelihood pel method for inference on the population mean when the dimension of the observations may grow faster than the sample size. Q f volume p i p empirical properties of asset returns. Rangebased volatility, longrange dependence, econometrics, financial time series introduction f. However, the authors tested estimators on rather long time series 0 elements, whereas in practice we often have to perform analysis of.
Such a study was presented in, using ideal models that display longrange dependence, i. To discover the ones that work best, we apply the differentmethods to. 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. 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. Statistics large sample behaviour of some wellknown.
The term long range dependence is often taken to imply stationarity, but of course many nonstationary series, such as unit root ones, exhibit even longer range dependence. It is known that the queuing system consists of three basic components. We test rs analysis, detrended fluctuation analysis and periodogram regression methods on. Our work is intended as a survival guide and howto manual for. Journal of statistical planning and inference, special issue on long range dependence posted. Robustness of whittle type estimators for time series with long range dependence. Citeseerx document details isaac councill, lee giles, pradeep teregowda.
Various estimators of longrange dependence have been proposed. The hurst parameter is slightly but statistically signi. A realvalued stochastic process fztgt2r is selfsimilar with index h 0 if, for any a 0, fzatgt2r d fahztgt2r where d denotes equality of the. Queue performance in presence of longrange dependencies. The most wellknown methods are the rs method 28, 23, variancetime analysis 23, 24, the periodogram method 23, 24.
In this study, we critically reevaluate four popular methods for measuring d and two for measuring h. The second part involves computer simulation to see how well the methods perform at. A frequency domain empirical likelihood method for irregularly spaced spatial data bandyopadhyay, soutir, lahiri, soumendra. Nonparametric and empirical bayes estimation methods by rida benhaddou m. The hurst exponent h of fractal analysis and the fractionaldifferencing parameter d of the arfima methodology are useful for capturing serial correlations. Teverovsky department of mathematics, boston university, 111 cummington street boston, ma 02215, u. Nine estimators were discussed in some detail by taqqu et al.