J. R. M. Hosking, "Fractional differencing, " Biometrika, vol. 68, no. 1, pp. 163-176, 1981.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....spectrum; even in these cases, though, the FSD model did a good job of summarizing dependence for the purpose of studying long range dependence. An FSD model consists of the sum of two Gaussian time series, independent of one another a dependent time series that is either a fractional ARIMA [31] or short range dependent, and a white noise time series. Suppose z u is an FSD time series. The dependent component, s u ,is #I B# s u # u # u## where u is Gaussian white noise with mean zero and variance # d## d# #### #d# (which makes the variance of s u equal to 1) B ....

J. R. M. Hosking, "Fractional Differencing," Biometrika, vol. 68, pp. 165--176, 1981.

....the joint distributions of all finite subsets of the time series are multivariate normal. Let # s u # # n u ; where s u and n u are independent of one another and each has mean 0 and variance 1. n u is white noise, that is, an uncorrelated time series. s u is a fractional ARIMA (FARIMA) model [31] s u # u # u## where Bs u # s u## , # d #:#,and u is white noise with mean 0 and variance # d## d# #### #d# to make the variance of s u equal to 1. z u is an FSD model. We coined this term because the model for z u can be written as a combination of fractional and ....

J. R. M. Hosking, "Fractional Differencing," Biometrika, vol. 68, pp. 165--176, 1981.

....ARMA model that can capture the longrange dependence of self similar signals. In some sense, these signals are borderline stationary. The AR, MA, ARMA, and ARIMA models are classical time series models described by Box, et al. [3] ARFIMA models are well covered in more recent literature [7, 6, 2]. The RPS technical report [5] also provides an explanation of these models as well as a detailed description of the implementations we use here. The same implementations are used for offline and online analysis in RPS. It is important to point out that we do not follow the Box Jenkins ....

HOSKING, J. R. M. Fractional differencing. Biometrika 68, 1 (1981), 165--176.

....for the predictions to the variance of the second half of the signal. This is basically the noise to signal ratio of the predictor. The smaller the ratio, the better the predictability. We use a wide range of models, including the classical AR, MA, ARMA, and ARIMA models [7] fractional ARIMAs [20], 18] and simple models such as LAST and a windowed average. Our prediction tools are currently available as part of our RPS Toolbox [15] Our Tsunami wavelet toolbox, which we describe further in Sections IV and V, will also soon be released. The earliest work in predicting network ....

....The ARFIMA(4, 1,4) model is a fractionally integrated ARMA model that can capture the long range dependence of self similar signals. AR, MA, ARMA, and ARIMA models are classical time series models well covered by Box, et al. [7] ARFIMA models are well covered in more recent literature [20], 18] 5] The RPS technical report [15] also provides an explanation of these models as well as a detailed description of the implementations we use here. The same implementations are used for offline and online analysis in RPS. For each of the 34 AUCKLAND traces, we performed the analysis ....

HOSKING, J. R. M. Fractional differencing. Biometrika 68,1 (1981), 165--176.

....[6] AR, MA, ARMA, and ARIMA classes might be appropriate for predicting load. On the other hand, the existence of self similarity induced long range dependence suggested that such models might require an impracti cal number of parameters or that the much more com plex ARFIMA model class [20,16,4], which explicitly captures long range dependence, might be more appro priate. Since it is not obvious which model is best, we empirically evaluated the predictive power of the AR, MA, ARMA, ARIMA, and ARFIMA model classes, as well as that of a simple ad hoc windowed mean predic tor called BM ....

....parameters in the range of 0.5 to 1.0 indicate self similarity with positive near neighbor correlations. This result tells us that load varies in complex ways on all time scales and has long range dependence. Long range dependence suggests that using the fractional ARIMA (ARFIMA) modeling approach [20,16,4] may be appropriate. 6) The traces display what we term epochal behavior. The local frequency content (measured by using a spectrogram) of the load signal remains quite stable Unpredictable Random Signal a, WhtteNotse (0. cr ) Fixed Linear Filter Partially Predictable Signal a ....

[Article contains additional citation context not shown here]

HOSKING, J. R. M. Fractional differencing. Biometrika 68, i (1981), 165-176.

....spectrum; even in these cases, though, the FSD model did a good job of summarizing dependence for the purpose of studying long range dependence. An FSD model consists of the sum of two Gaussian time series, independent of one another a dependent time series that is either a fractional ARIMA [31] or short range dependent, and a white noise time series. Suppose z u is an FSD time series. The dependent component, s u ,is #I # B# d s u # u # u## where u is Gaussian white noise with mean zero and variance # # ## # d## # ## # d# #### # #d# (which makes the variance ....

J. R. M. Hosking, "Fractional Differencing," Biometrika, vol. 68, pp. 165--176, 1981.

....loess to choose a parametric family that approximates the true spectrum locally was well as possible. FARIMA models have an additive term in the log spectrum consisting of a constant times A which introduces substantial curvature in the log spectrum near the origin, but is smooth elsewhere [15]. Since our packet spectra exhibit this behavior, the P F are smoothed by loess as a function of P F , using a quadratic as the local regression function. The fit, though, is then plotted against P F . This results in a much better fit than smoothing directly as a quadratic function ....

J. R. M. Hosking. Fractional Differencing. Biometrika, 68:165--176, 1981.

....are zero if k d and d is an integer. The representation in Eq. 25 for d is equivalent to an infinite order autoregressive process (all pole filter with an infinite order) F ARIMA(0, d, 0) process with 0 d 1 2, is stationary and long range dependent, with an auto correlation function [29] (26) Observe that for 0 d 1 2, the hyperbolic decay will produce persistence. By comparing Eq. 26 to Eq. 21, d = 1 a) 2 = H 0.5. F ARIMA processes can model short range and long range dependence. If Gaussian white noise is used, then the F ARIMA has a Gaussian distribution. This ....

J. Hosking, "Fractional Differencing," Biometrica, 1981, pp. 165--76.

....a parametric family that approximates the true spectrum locally was well as possible. FARIMA models have an additive term in the log spectrum consisting of a constant times g(u) log(4 sin 2 ( u) which introduces substantial curvature in the spectrum near the origin, but is smooth elsewhere [16]. Since our packet spectra exhibit this behavior, the L( fk ) are smoothed by loess as a function of g( fk ) using a quadratic as the local regression function. The fit, p(f) is then plotted against f . This results in a much better fit than smoothing directly as a quadratic function ....

J. R. M. Hosking. Fractional Differencing. Biometrika, 68:165--176, 1981.

....GPH test is sometimes designated as a semiparametric test. The dominant parametric discrete time model that exhibits hyperbolic decay of its autocorrelation function is the fractional integrated autoregressive moving average model (ARFIMA) introduced independently by Granger and Joyeux (1980) and Hosking (1981) see Viano, Deniau, and Oppenheim (1994) for a continuous time version. For Gamma0:5 d :5, X t is said to follow an ARFIMA(p,d,q) model if it is the unique stationary solution to the equation (1 Gamma B) d OE(B)X t = B)j t ; j t iidN(0; oe 2 j ) where B is the backshift operator ....

Hosking, J. (1981),"Fractional differencing," Biometrika 68, 165-176.

....originally introduced in [83] for social measurement purposes. However, initial sizeable empirical success of the long range dependence (LRD) concept in economics is certainly related to the autoregressive fractionally integrated moving average model (hereafter ARFIMA) proposed simultaneously by [64]and [51] and the increased flexibility it brings to the Box Jenkins linear time series methodology, in particular for modeling macroeconomic time series since [30] The relative success of the LRD concept in economics may also be attributed to the development of a rationale for its presence in ....

Hosking, J. (1981): "Fractional differencing," Biometrika, 68, 165--176.

.... goes to infinity.To obtain the results of this paper we formally define a stationary process X t as having long memory if the process s theoretical autocorrelation function ae X ( j j 2d;1 L( # where d 2 ( 1# 1=2) and L( isaslowvarying function at infinity [Granger and Joyeux (1980) Hosking (1981), Brockwell and Davis (1993) and Baillie (1996) 4 In contrast to a short memory ARMA process (d = 0) whose autocorrelation function decays geometrically fast to zero, the notable feature of long memory is a autocorrelation function that decays hyperbolically to zero when d 6=0. When d 0, ....

Hosking, J.R. (1981) "Fractional Differencing," Biometrika, 68, 165-176.

....as is typical for long range processes. The best known models for long range correlated processes are the increments of selfsimilar processes as mentioned above which are called fractional noise, and fractional ARIMA(p,d,q) processes, where d is between 0 and 1 2 (Granger and Joyeux 1980, Hosking 1981). For near Gaussian fractional noise, statistical methods have been worked out and programmed, including confidence and prediction intervals for the mean ( onesample t test for long range correlated data , see Beran 1986, 1989) For a more detailed survey of these statistical methods see Beran ....

....variation and bounded away from zero. 3:7) Condition (3.7) implies (3.6) see Zygmund (1959, Chap. V.2) In (3.6) stationarity is not required. The two most common models with long range correlations, fractional noise (Mandelbrot and van Ness, 1968) and fractional ARIMA (p,d,q) processes (Hosking, 1981), satisfy (3.7) see Sinai (1976) in the former and Hosking (1981) in the latter case. If the treatments are allocated in space as for instance in agriculture, the index t becomes multidimensional, i.e. the t 0 s are then a random field. We expect our results to generalize to this case. 3.4 ....

[Article contains additional citation context not shown here]

Hosking, J. R. M. (1981). Fractional differencing. Biometrika 68, 165-176.

....family that approximates the true spectrum locally was well as possible. FARIMA models have an additive term in the log spectrum consisting of a constant times g(u) log 10 (4 sin 2 ( u) which introduces substantial curvature in the log spectrum near the origin, but is smooth elsewhere [15]. Since our packet spectra exhibit this behavior, the L( fk ) are smoothed by loess as a function of g( fk ) using a quadratic as the local regression function. The fit, though, is then plotted against fk . This results in a much better fit than smoothing directly as a quadratic ....

J. R. M. Hosking. Fractional Differencing. Biometrika, 68:165--176, 1981.

....and Ebens (2000) 2.2. Fractionally integrated white noise 6 An important example of a long memory process is a stochastic process t y that requires fractional differencing to obtain a set of independent and identically distributed residuals t e . Following Granger and Joyeux (1980) and Hosking (1981), such a process is defined using the filter ( 3 ) 2 ) 1 ( 2 ) 1 ( 1 1 3 2 = L d d d L d d dL L d (6) where L is the usual lag operator, so that 1 = t t y Ly . Then a fractionally integrated white noise (FIWN) process t y is defined by ( t t d y L e = 1 ....

....e = 1 (7) with the t e assumed to have zero mean and variance 2 e s . Throughout this paper it is assumed that the differencing parameter d is constrained by 1 0 d . The mathematical properties of FIWN are summarised in Baillie (1996) and were first derived by Granger and Joyeux (1980) and Hosking (1981). The process is covariance stationary if 2 1 d and then the following results apply. First, the autocorrelations are given by ( 3 2 1 2 1 , 2 1 1 , 1 3 2 1 d d d d d d d d d d d d = r r r (8) or, in terms of the Gamma function, ....

[Article contains additional citation context not shown here]

Hosking, J., 1981, Fractional differencing, Biometrika 68, 165-176.

No context found.

J. R. M. Hosking, "Fractional differencing, " Biometrika, vol. 68, no. 1, pp. 163-176, 1981.

No context found.

Hosking, J.R.M. (1981). Fractional differencing, Biometrika, 68, 165-176.

No context found.

J. R. M. Hosking (1981). Fractional Differencing. Biometrika, 68:165--176.

No context found.

HOSKING, J. R. M. Fractional differencing. Biometrika 68,1 (1981), 165--176.

No context found.

J. R. M. Hosking. Fractional differencing. Biometrika, 68(1):165-176, 1981.

No context found.

HOSKING, J. R. M. Fractional differencing. Biometrika 68, 1 (1981), 165--176.

No context found.

J. R. M. Hosking. Fractional Differencing. Biometrika,

No context found.

Hosking, J. R. (1981) Fractional differencing . Biometrika 68, 165--176.

No context found.

J.R.M. Hosking (1981). "Fractional differencing," Biometrika 68, 165-176.

No context found.

Hosking, J. (1981): "Fractional Differencing", Biometrika, 68, 165-176.

First 50 documents  Next 50

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC