R. Dahlhaus (1989). "Efficient parameter estimation for self-similar processes," Ann. Statist. 17, 1749-1766.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... on asymptotic theory relevant (in particular) to parametric estimation of the ARFIMA model is 4 Marc Henry,Paolo Zaffaroni given in [100] Exact maximum likelihood is efficient in the Fr echet DarmoisCram er Rao (hereafter FDCR) sense when the t s are normally and identically distributed ([26]) The Whittle approximate likelihood is asymptotically efficient under Gaussianity ( 38] and remains p n consistent and asymptotically normal for possibly non normal identically and independently distributed t s ( 46] A result that is particularly relevant to macroeconomic time series is ....

Dahlhaus, R. (1989): "Efficient parameter estimation for self-similar processes, " Annals of Statistics, 17, 1749--1766.

....par LM. Par la suite, on suppose connus X 0 ; X 1 ; XN , o u (X k ) est une s erie chronologique stationnaire. En premier lieu, si l on revient sur les estimateurs param etriques, il nous semble que deux r ef erences importantes devraient etre ajout ees. La premi ere est l article de Dahlhaus (1989) concernant l estimateur du maximum de vraisemblance, qui montre, dans le cas gaussien, l efficacit e de cet estimateur et de l estimateur par minimum de contraste (ou maximum de vraisemblance avec approximation de type Whittle) pr esent e dans Fox et Taqqu (1986) ou Avram (1988) La seconde est ....

R. Dahlhaus. Efficient parameter estimation for self-similar processes. Annals of Statistics, 17: 1749--1746, 1989.

....dT. d d SE( d) f x (T) k) SE( d) d. 3 (3) 4) spectral density function in terms of the parameters of the model and then calculating the autocovariance function at lag k by The exact maximum likelihood estimator of d, for d 0, has an asymptotic normal distribution; see Dahlhaus (1989). This allows for hypothesis testing based on the Wald statistic where d is the value of the fractional integration parameter under the null hypothesis and is the maximum likelihood estimate of the standard error of The rejection region is set up based upon a one sided alternative hypothesis. 3. ....

Dahlhaus, R., 1989, Efficient parameter estimation for self-similar processes, Annals of Statistics, 17, 1749-1766.

....of g( fi 0 ) For Gaussian (X t ) t2Z the estimator fi n is closely related to least squares and maximum likelihood estimators and it is a standard estimator for ARMA processes with finite variance. The idea goes back to Whittle (1953) see also Dzhaparidze (1986) Fox and Taqqu (1986) and Dahlhaus (1989). It is wellknown that in the classical case fi n is consistent and asymptotically normal (cf. Brockwell and Davis (1991) We showed in Mikosch et al. 1994) that fi n is also for ARMA processes with infinite variance a weakly consistent estimator for the true parameter vector fi 0 (see also ....

Dahlhaus, R. (1989). Efficient parameter estimation for self-similar processes.

....(1.3) or approximations to (1. 3) and has been discussed by Boes, Davis and Gupta (1989) Brockwell and Davis (1987) Fox and Taqqu (1986) Hosking (1981, 1984) Luce no (1993) and Sowell (1992) Some properties of the maximum likelihood estimators are discussed in Fox and Taqqu (1986, 1987) Dahlhaus (1989) and Cheung and Deibold (1994) The study of asymptotic inference for the ARF IMA(p; d; q) process is of considerable current research interest. The use of differential geometry to characterize statistical inference has been widely studied in the last two decades and an excellent review was given ....

....of s fi (w) at w = 0. In Section 2, we briefly review some differential geometrical concepts and present the geometrical framework for the ARF IMA(p; d; q) 3 process. We describe the derivation of the geometrical quantities by utilizing properties of Toeplitz forms and a result due to Dahlhaus (1989). The complete set of quantities is presented in the Appendix. In Section 3, we discuss asymptotic inference for the ARF IMA(p; d; q) processes, indicating the role of geometry. 2 GEOMETRY OF ARFIMA PROCESSES This section describes the geometry of the ARF IMA(p; d; q) process. A brief review of ....

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Dahlhaus, R. (1989) Efficient parameter estimation for self-similar processes.

....BBSRC EPSRC Grant 96 MMI09785. 1 Introduction Until recently much of time series modeling has been confined to linear ARMA models (Box and Jenkins 1970) Although the original ARMA framework has been enlarged to include long range dependence with fractional ARMA (Granger and Joyeux 1980, and Dahlhaus 1989), multivariate VARMA and VARMAX models (Hannan and Deistler 1988) and random walk nonstationarities via cointegration (Engle and Granger 1987) there still exist so called nonlinear features beyond the capacity of linear ARMA modeling. For example, various non standard phenomena such as ....

Dahlhaus, R. (1989). Efficient parameter estimation for self similar processes. The Annals of Statistics, 17, 1749-1766.

....substantial improvement of the paper. 1 Introduction Until recently much of time series modeling has been confined to linear ARMA models (Box and Jenkins 1970) Although the original ARMA framework has been enlarged to include long range dependence with fractional ARMA (Granger and Joyeux 1980; Dahlhaus 1989), multivariate VARMA and VARMAX models (Hannan and Deistler 1988) and random walk nonstationarities via cointegration (Engle and Granger 1987) there still exist so called nonlinear features beyond the capacity of linear ARMA modeling. For example, various non standard phenomena such as ....

Dahlhaus, R. (1989), "Efficient parameter estimation for self similar processes," The Annals of Statistics, 17, 1749-1766.

....fl( Z Gamma 1 g( e Gammai d : 24) On the basis of the periodogram I( 1 2 T Gamma1 X = GammaT 1 fl( e Gamma : 25) an alternative representation of (24) is given by oe 2 T ( Z Gamma I( g( d : 26) which is known as the Whittle estimator. Dahlhaus (1989) shows its asymptotic normality and efficiency. However, as the numerical integration of the fraction containing the periodogram in (26) is cumbersome and possibly inaccurate, Tschernig (1994) suggests an alternative computation method of the Whittle estimator that avoids the integration of the ....

Dahlhaus, Rainer. "Efficient parameter estimation for self-similar processes.", The Annals of Statistics, 17 (1989): 1749 -- 1766.

....d. Several authors have considered this problem, generally from two perspectives; firstly by a maximum likelihood method, and secondly by some form of regression on estimates of the log spectrum. Asymptotic normality of the maximum likelihood estimator has been proved by Yajima (1988) and Dahlhaus (1989). Efficient maximum likelihood estimation has been outlined by several authors including Li McLeod (1986) Fox Taqqu (1986) Deriche Tewfik (1993) and Haslett Raftery (1989) Geweke Porter Hudak (1983) suggest estimating d via least squares regression, using only the lowest frequency ....

Dahlhaus R. (1989). Efficient parameter estimation for self-similar processes.

....to be able to estimate the spectral exponent fl from an observed sample path. Many methods to achieve this have been proposed. They range from least squares estimation of the slope of log axes plots of sample periodograms [26, 17] through to approximate and exact maximum likelihood estimation [7, 16, 26, 28] and direct measuring of fractal dimension of observed sample paths [17, 12, 14] Aside from the maximum likelihood (ML) based schemes, these methods assume that the sample path observation fx k g is not corrupted by any other noise sources. Various convergence results (which will be surveyed) are ....

.... results (by employing stronger assumptions on OE( that disallow estimation with white noise corrupted measurements) to also hold for fl 2 (1; 2) and have estimated the mean square rate of convergence of the approximate ML method as Var fbflg = o 1 N as N 1: For fl 2 (0; 1) Dalhaus [7] has shown the same distributional results, but only weak consistency for the exact ML scheme. These results would appear to also be of relevance to various ML estimation methods [9, 10] that have been developed around the fractional differencing model (3) In x5, the purpose of this paper will be ....

R. Dahlhaus, Efficient parameter estimation for self similar processes, The Annals of Statistics, 17 (1989), pp. 1749--1766.

....0 C b (2; 2) log 2 (h(H) 0 ] 2 (2.26) for N j 1 large with C b defined in (2.22) and h in (2.11) The variance of the estimators is of order 1=N j 1 . Long memory processes can also be modeled via state space models. Maximum likelihood estimators (MLE) for such models are analyzed in [3, 7]. 2.7 Illustration of precision The above result on the distribution of the estimators may be validated by numerical simulation. We generate synthetic realizations of fractional Brownian motion with known parameters. Then we use the above algorithm to estimate these parameters and compare the ....

R. Dahlhaus, Efficient parameter estimation for self-similar processes, Ann. Statist., 17, pp. 1749-1766, 1989.

....refined statistical analyses based on Maximum Likelihood Estimate (MLE) methods are used to estimate H when fX t g comes from a Gaussian distribution. These methods and their approximations are based on the spectral density of X t and properties of the MLEs are discussed by a number of authors [4, 10, 37]. One specific method that has been used extensively is Whittle s approximate MLE (e.g. see [23] Most of the approximate MLEs are defined via quadratic forms which make them quite sensitive to deviations from normality. However, transformation of the data may sometimes alleviate these types of ....

....smtp in Mode A) The above studies were performed using the heuristic tools of R S analysis, V T plots, and Periodogram plots. These were followed by rigorous estimation of H using Whittle s approximate MLE, and estimating oe 2 H through a corresponding Central Limit Theorem due to Dahlhaus (see [10, 23]) For each aggregation level m; the aggregate time series fX (m) g yielded point estimates for H (m) oe 2 H (m) and the 95 confidence intervals ( H (m) Sigma 1:96oe H (m) H (m) and its 95 confidence intervals were then plotted as a function of m for the packet level ....

R. Dahlhaus, "Efficient parameter estimation for self-similar processes," Annals of Statistics, vol. 17, pp. 1749-1766, 1989.

....listing additional techniques. More specifically, R S analysis is discussed in [18, 24, 26, 28, 130, 200, 258, 272, 273, 286, 288, 290 292, 302, 310, 394] see also [10,131] variance time analysis in [24,26,77,258,310,331,394,399] and for spectral domain methods using periodograms, see [24,26,48,84,140,149,157, 159,183,203,204,206,249,253,353,357 366,393,407, 418]. Examples of new statistical techniques in this area include [3, 7, 20,21,25,27, 52, 53, 57, 58, 80 82, 86, 98, 99, 154, 155, 189, 190, 197, 247, 258, 381, 382, 410, 415] For a practical evaluation of the different techniques see [392 394] The paper [76] provides a general overview on the ....

R. Dahlhaus. Efficient parameter estimation for self similar processes. The Annals of Statistics, 17(4):1749--1766, 1989.

.... of Pisa Via Diotisalvi 2, I 56126 Pisa Italy Abstract: Teletraffic models based on self similar processes are emerging as promising mathematical representation of real broadband traffic [1] This statistical characterization was confirmed over LAN [2] MAN [3] WANs [4] and VBR video sequences [5][6] The most common approaches for the generation and representation of self similar processes are fractional Gaussian noises, ARIMA processes and chaotic maps generated processes. Although better fitting of the process could be obtained using more complex self similar reprentation, the use of ....

....based on a Maximum Likelihood Estimation is proposed. This method could be employed also for a broader class of stationary processes which exhibit a long range dependence showing an hyperbolic decay of the spectral density and with Gaussian distributions. 1. INTRODUCTION The Hurst parameter [1][5] is one of the most interesting metric in describing the relevant properties of self similar traffic processes exhibiting long range dependence. It can be qualitatively estimated using some graphical methods based on the determination of the power spectral density at low frequency or on the ....

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R. Dahlhaus "Efficient parameter estimation for self-similar processes" The Annals of Statistics 1989 vol.17. pp. 1749-1766

....fractional Gaussian noise or fractional ARIMA by appealing to a central limit theorem for weighted quadratic forms whose weights are chosen in such a way as to compensate for the long range dependence. Fox and Taqqu s result, which was later generalized to the full maximum likelihood by Dahlhaus [2], is the basis of one of the most commonly used techniques for estimating 1. Semi parametric graphical estimation techniques for long memory data. 7 the intensity of long range dependence in Gaussian time series (see Beran [1] Giraitis and Surgailis [5] extended Fox and Taqqu s result to ....

R. Dahlhaus. Efficient parameter estimation for self similar processes. The Annals of Statistics, 17(4):1749--1766, 1989.

....d; fi 1 ; Delta Delta Delta ; fi q ) are available: the (approximative) spectral (Whittle) maximum likelihood, and the exact Gaussian maximum likelihood method. Both methods yield p n consistent, asymptotically normal and asymptotically efficient parameter estimates. See Fox and Taqqu(1986) Dahlhaus(1989) and Giraitis and Surgailis (1990) for the Whittle estimator, and Dahlhaus(1989) and An, Bloomfield and Pantula (1992) for the exact maximum likelihood. The small sample properties of four estimators will be investigated: the exact Gaussian likelihood, the modified profile likelihood derived by An ....

....(Whittle) maximum likelihood, and the exact Gaussian maximum likelihood method. Both methods yield p n consistent, asymptotically normal and asymptotically efficient parameter estimates. See Fox and Taqqu(1986) Dahlhaus(1989) and Giraitis and Surgailis (1990) for the Whittle estimator, and Dahlhaus(1989) and An, Bloomfield and Pantula (1992) for the exact maximum likelihood. The small sample properties of four estimators will be investigated: the exact Gaussian likelihood, the modified profile likelihood derived by An and Bloomfield(1993) according to the proposal of Cox and Reid(1987) the ....

Dahlhaus, R., 1989, Efficient parameter estimation for self-similar processes, The Annals of Statistics, 17, 1749-1766.

....of H. Several periodogram based estimators can be found in the literature. In this paper we will focus on an MLE as presented in [1, 13] which is based on Whittle s approximate MLE for Gaussian processes [12] For Gaussian sequences this estimator is asymptotically normal and efficient [4, 3]. The spectral density of the self similar process is denoted by f( where the parameter vector of the process = 1 ; M ) is structured as follows. 1 = oe 2 ffl is a scale parameter, where oe 2 ffl is the variance of the innovation ffl of the infinite AR representation of ....

R. Dahlhaus. Efficient parameter estimation for self-similar processes. The Annals of Statistics, 17(4):1749--1766, 1989.

....whereby [x] denotes the largest integer not exceeding x. 2.2 The trimmed Whittle likelihood Another spectral estimator developed for the estimation of ARFIMA models is based on the Whittle likelihood, which is shown [for d 0] by Fox and Taqqu(1986) to be consistent and asymptotically normal. Dahlhaus(1989) proves its asymptotic efficiency under Gaussian innovations [cp. also Giraitis and Surgailis(1990) In small samples this estimator has a smaller bias and mean squared error for most d than the exact maximum likelihood method applied to mean corrected data [Hauser(1994) In case of pure ....

Dahlhaus, Rainer, 1989, Efficient parameter estimation for self-similar processes, The Annals of Statistics 17, 1749-1766.

....fractional ARIMA, long memory, stable distributions, heavy tails. to a central limit theorem for weighted quadratic forms whose weights are chosen in such a way as to compensate for the long range dependence. Fox and Taqqu s result, which was later generalized to the full maximum likelihood by Dahlhaus (1989), is the basis of one of the most commonly used techniques for estimating the intensity of long range dependence in Gaussian time series (see Beran (1994) Giraitis and Surgailis (1990) extended Fox and Taqqu s result to finite variance innovations without Gaussian assumptions and Heyde and Gay ....

Dahlhaus, R. (1989), `Efficient parameter estimation for self similar processes', The Annals of Statistics 17(4), 1749--1766.

....= 1 (Fox and Taqqu (1987) to show that the Whittle estimator of the long range dependence parameter in Gaussian time series is asymptotically normal. This result, as well as the subsequent work of Giraitis and Surgailis (1990) has had a wide impact on the statistical literature (see for example Dahlhaus (1989), Robinson (1994a, 1994b, 1995) Introducing different kernels b is useful when considering misspecified models, integrated periodograms, etc . Kluppelberg and Mikosch(1995, 1996) In many real life situations, e.g. in the Ethernet studies (Leland, Taqqu, Willinger, Wilson (1993, 1994) the ....

Dahlhaus, R. (1989), `Efficient parameter estimation for self similar processes', The Annals of Statistics 17(4), 1749--1766.

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R. Dahlhaus (1989). "Efficient parameter estimation for self-similar processes," Ann. Statist. 17, 1749-1766.

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R. Dahlhaus (1989). "Efficient parameter estimation for self-similar processes," Ann. Statist. 17, 1749-1766.

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R. Dahlhaus, "Efficient Parameter Estimation for Self-Similar Processes", Ann. Statist. 17, 1749-1766, 1989.

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R. Dahlhaus, "Efficient parameter estimation for self-similar processes," Annals of Statistics, vol. 17, pp. 1749-1766, 1989.

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R. Dahlhaus, "Efficient Parameter Estimation for SelfSimilar Processes", Ann. Statist. 17, 1749-1766, 1989.

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R. Dahlhaus (1989) Efficient parameter estimation for self-similar processes. Ann. Statist., 17(4):1749--1766.

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