Citations: Long-Range Dependence: A Review

149 citations found. Retrieving documents...

D. Cox, "Long-range dependence: A review," Statistics: An Appraisal, pp. 55--74, 1984.

Home/Search Document Not in Database Summary Related Articles Check

This paper is cited in the following contexts:

First 50 documents Next 50

Multiscale Queuing Analysis of Long-Range-Dependent.. - Ribeiro, Riedi.. (2000) (9 citations) (Correct)

....X [t] which is obtained by summing X [t] over non overlapping blocks of length m [t] X [tm m 1] X [tm] 2) Denote the auto covariance of X by r X . The process X is said to exhibit LRD if its auto covariance decays slowly enough to render P 1 k=1 r X [k] infinite [33]. Two additional equivalent definitions of LRD require that r X [0] m 1 as m 1 or that the power spectrum SX (f) is singular at f = 0 [33] One example of an LRD process is fractional Gaussian noise G (fGn) the increment process of the fractional Brownian motion B (fBm) G[k] B [ k ....

....auto covariance of X by r X . The process X is said to exhibit LRD if its auto covariance decays slowly enough to render P 1 k=1 r X [k] infinite [33] Two additional equivalent definitions of LRD require that r X [0] m 1 as m 1 or that the power spectrum SX (f) is singular at f = 0 [33]. One example of an LRD process is fractional Gaussian noise G (fGn) the increment process of the fractional Brownian motion B (fBm) G[k] B [ k 1) B [k ] with a constant time lag. fGn s autocorrelation is given by r G [k] j j jk 1j 2jkj jk 1j 2H (3) with ....

[Article contains additional citation context not shown here]

D. Cox, "Long-range dependence: A review," Statistics: An Appraisal, pp. 55--74, 1984.

Multiscale Queuing Analysis of Long-Range-Dependent.. - Ribeiro, Riedi.. (2000) (9 citations) (Correct)

....X [t] which is obtained by summing X [t] over non overlapping blocks of length m [t] X [tm m 1] X [tm] 2) Denote the auto covariance of X by r X . The process X is said to exhibit LRD if its auto covariance decays slowly enough to render P 1 k=1 r X [k] infinite [33]. Two additional equivalent definitions of LRD require that r X [0] m 1 as m 1 or that the power spectrum SX (f) is singular at f = 0 [33] One example of an LRD process is fractional Gaussian noise G (fGn) the increment process of the fractional Brownian motion B (fBm) G[k] B [ k ....

....auto covariance of X by r X . The process X is said to exhibit LRD if its auto covariance decays slowly enough to render P 1 k=1 r X [k] infinite [33] Two additional equivalent definitions of LRD require that r X [0] m 1 as m 1 or that the power spectrum SX (f) is singular at f = 0 [33]. One example of an LRD process is fractional Gaussian noise G (fGn) the increment process of the fractional Brownian motion B (fBm) G[k] B [ k 1) B [k ] with a constant time lag. fGn s autocorrelation is given by r G [k] j j jk 1j 2jkj jk 1j (3) with = ....

[Article contains additional citation context not shown here]

D. Cox, "Long-range dependence: A review," Statistics: An Appraisal, pp. 55--74, 1984.

Multifractal Processes - Riedi (1999) (7 citations) (Correct)

....Indeed, if X(k) are i.i.d. then X (k) has variance (1 m )var(X 0 . Xm 1 ) 1 m)var(X) For G we find, due to (1.1) and BH (0) 0, 0) var BH (m#) var BH (#) m var (G(0) 1.17) For H 1 2 this expression decays indeed much slower than 1 m. As is shown in [19] is equivalent to r X (k) and so, G(k) is indeed LRD for H 1 2 (this follows also directly from (7.3) Let us demonstrate with fGn how to relate LRD with multifractal analysis using only that it is a zero mean processes, not (1.1) To this end let # = 2 n denote the finest ....

....of as being the increment process of Y with this property ( k r X (k) is said to exhibit long range dependence (LRD) since it exhibits strong correlations at large lags. LRD can be equivalently characterized in terms of the behavior of the aggregated processes X(i) 7. 19) As [19] shows, r X (k) is equivalent to var(X(k) n] So, we are lead to define: Definition 7.6. We say that X is asymptotically second order self similar with parameter H var if the following limit exists: H var : 1 1 2 log [var(X ) var(X ) log m (7.20) As an example ....

D. Cox. Long-range dependence: A review. Statistics: An Appraisal, pages 55--74, 1984.

Unknown - (Correct)