Density estimation methods based on aggregating several estimators are described and compared over several simula tion models. The existence of lrd is usually indicated by the hurst parameters. The tail empirical process for some long memory sequences. An improved hurst parameter estimator based on fractional. We show that aggregation gives rise in general to better estimators than simple methods like histograms or kernel density estimators.
Taqqu and teverovsky 35 present an empirical study that compares estimators for longrange dependence. We make detailed study of a waveletdomain pseudo maximum likelihood estimator mle, for which we provide an asymptotic and. We use wavelet scale spectra because they provide a timescale decomposition of. Longrange dependence lrd is discovered in time series arising from different fields, especially in network traffic and econometrics. Thus, a regression of the log of the periodogram on the log of gives a coefficient of 1 2h. We have extended their study to a larger number of parameters, higher number of replications and two additional estimators as detailed in section 2 below.
Estimation and inference in fractional ornsteinuhlenbeck. Empirical studies have demonstrated that the rsstatistic has the ability to detect longrange dependence in the data. Up to now, many hurst parameter estimators have been proposed. We applyall 12 estimators to the campito mountain data and estimate the accuracyof their estimates using the beran goodness of. Stock market prices and longrange dependence long memory. A second related question is whether and how the estimators of longrange dependence are affected by aggregation. The hurst exponent is used as a measure of longterm memory of time series. Statistics large sample behaviour of some wellknown. From each of six real populations, 1,000 simple random samples, 1,000 restricted random samples, and three nonrandom samples of size 32 are drawn. 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.
We test rs analysis, detrended fluctuation analysis and periodogram regression methods on samples drawn. On the minimax optimality of block thresholded wavelet. Noncentral limit theorems for quadratic forms in random variables having longrange dependence fox, robert and taqqu, murad s. The periodogram is an estimator of the spectral density, thus a series with longrange dependence should have a periodogram proportional to lal1 2 when close to the origin. The fractional vasicek model with longrange dependence is assumed to be driven by a fractional brownian motion with the hurst parameter greater than or equal to one half. Taqqu, vadim teverovsky, walter willinger, 1995 various methods for estimating the selfsimilarity parameter andor the intensity of longrange dependence in a time series are available. Financial econometrics boston college, spring 20 christopher f baum bc diw arfima long memory models boston college, spring 20 1 44. To discover the ones that work best, we apply the different methods to simulated sequences of fractional gaussian noise and fractional arima0. A read is counted each time someone views a publication summary such as the title, abstract, and list of authors, clicks on a figure, or views or downloads the fulltext. An empirical study of the ratio estimator and estimators. We focus our attention on the logperiodogram regression estimator of geweke and porterhudak gph and on the local whittle lw estimator. On the minimax optimality of block thresholded wavelet estimators with long memory data. System estimation of panel data models under longrange.
Various estimators of longrange dependence have been proposed. They also carried out an empirical study of these estimators for a single series length, ve values of both h and d,and50 replications. A number of estimators of longrange dependence have been proposed in. Citeseerx document details isaac councill, lee giles, pradeep teregowda. Longin and solnik, 2001, very few results formally characterize tail memory in garch data. One approach exploits the fact that garch class 1 belongs to the maximum domain of attraction. In particular, we derive minimax lower bounds for the risk of the nonparametric empirical bayes estimator for a general conditional distribution. 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.
Wavelet based estimation of local kolmogorov turbulence. Understanding the limitations of estimation methods for long. Recent studies show that very high resolutions are needed to. Robust rs analysis of long run serial correlation 1979. This paper reports results from an empirical study of the ratio estimator for a finite population total. Estimating longrange dependence in the presence of. The notion of long range dependence can also be applied to di. Rescaled range is a measure of the variability of a time series and is calculated by.
Smalltime scaling behaviors of internet backbone traffic. Pdf or denotes a file in adobes portable document format. A minimax study rida benhaddoua, rafal kulikb, marianna penskya,n, theofanis sapatinasc a department of mathematics, university of central florida, usa b department of mathematics and statistics, university of ottawa, canada c department of mathematics and statistics, university of cyprus, cyprus. Introduction the seminal papers reporting empirical evidence for longrange dependence and selfsimilarity in network traffic first appeared around ten years ago 20. Multichannel deconvolution with longrange dependence a. This article develops an asymptotic theory for estimators of two parameters in the. Rea and les oxley and marco reale and jennifer brown, year2009. We suggest three new simple algorithms which aggregate histograms and compare very well. With the identification of longrange dependence lrd in network.
To discover the ones that work best, we apply the differentmethods to. From an empirical point of view we would thus anticipate that the equilibrium. Choosing among regularized estimators in empirical economics. The method results in likelihood ratios which can be used to build nonparametric, asymptotically correct con. Strong dependence, global dependence, long range dependence, hurst parameter estimators. Maximum empirical likelihood estimators are possible as well as tests of spectral moment conditions. Download averaged one dependence estimators aode for free. To the best of our knowledge, only few papers study fractional longrange dependence in panel data models. We also explore the impact that longrange dependence has on empirical estimates of the mean, standard deviation, and variance of spike counts in neural activity. A dynamical systems explanation of the hurst effect and. Strong dependence, global dependence, longrange dependence, hurst parameter estimators.
Studies involving the hurst exponent were originally developed in hydrology. Much empirical model choice has been based on the idea of parsimony. We test rs analysis, detrended fluctuation analysis and periodogram. Teverovsky and taqqu 1999 showed in a simulation study that the di. 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. The impact of longrange dependence on the empirical tail process was considered in kulik and soulier 2011, and was extended by mcelroy and jach 2012a to nj time series. When measured through linear correlation, many of these systems exhibit a slow correlation decaya phenomenon often referred to as longmemory or longrange dependence.
In the case of the nonparametric empirical bayes estimation, we carried out a complete minimax study. Datadriven choice of regularization parameters the second part the article turns to feature ii of machine learning estimators and studies. A fractional fourier transform frft based estimation method is introduced in this paper to analyze the long range dependence lrd in time series. Even though some have known asymptotic properties, it is important to test their accuracy by using simulated series of different lengths. The notion of long range dependence has, clearly, something to do with memory in a stochastic process. Understanding the limitations of estimation methods for. Various methods for estimating the selfsimilarity parameter andor the intensityof longrange dependence in a time series are available.
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. Detecting the presence and the intensity of lrd plays a crucial role in timeseries analysis and fractional system identification. Understanding the limitations of estimation methods for longrange dependence thomas karagiannis, mart molle, michalis faloutsos. Averaged n dependence estimators a1de and a2de achieves highly accurate classification by averaging over all of a small space of alternative naivebayeslike models that have weaker and hence less detrimental independence assumptions than naive bayes. It relates to the autocorrelations of the time series, and the rate at which these decrease as the lag between pairs of values increases. With the identification of longrange dependence lrd in network traffic, the research community has undergone a mental shift from. Like many other estimators of longrange dependence, though, thersstatistic has been shown to be excessively sensitive to shortrange dependence. As empirical evidence suggests that nancial time series are highly nonlinear, in particular volatility processes exhibit a combination of nonlinearity, longrange dependence and changepoints, we study in this chapter the es. Since then available computer power has increased considerably. Our linking to these sites does not constitute an endorsement of any products, services or the information found on them. It is argued that univariate long memory estimates based on ex post data tend to underestimate the persistence of ex ante variables and, hence, that of the ex post variables themselves because of the presence of unanticipated shocks whose short. The degree of lrd can be characterized by the hurst parameter. Although empirical studies of extremal dependence in random volatility processes abound e.
Nonparametric and empirical bayes estimation methods. A major issue in financial economics is the behavior of asset returns over long horizons. Various estimators of long range dependence have been proposed. Fredholm determinant of a positive definite kernel of a special type and its application sukhatme. A frequency domain empirical likelihood for short and. Understanding the fisher equation sun 2004 journal. The frftbased estimation of hurst parameter proposed in this paper can be implemented efficiently allowing very large data set. Multichannel deconvolution with longrange dependence. Several methods for measuring the longrange dependence parameter. Longrange dependence in a changing internet traffic mix. Various methods for estimating the selfsimilarity parameter andor the intensity of longrange dependence in a time series are available.