Effect Of Long-range Dependence Research Articles

On the effect of long-range dependence on extreme value copula estimation with fixed marginals

ABSTRACTWe establish the existence of multivariate stationary processes with arbitrary marginal copula distributions and long-range dependence. The effect of long-range dependence on extreme value copula estimation is illustrated in the case of known marginals, by deriving functional limit theorems for a standard non parametric estimator of the Pickands dependence function and related parametric projection estimators. The asymptotic properties turn out to be very different from the case of iid or short-range dependent observations. Simulated and real data examples illustrate the results.

Fractional order fuzzy control of nuclear reactor power with thermal-hydraulic effects in the presence of random network induced delay and sensor noise having long range dependence

Nonlinear state space modeling of a nuclear reactor has been done for the purpose of controlling its global power in load following mode. The nonlinear state space model has been linearized at different percentage of reactor powers and a novel fractional order (FO) fuzzy proportional integral derivative (PID) controller is designed using real coded Genetic Algorithm (GA) to control the reactor power level at various operating conditions. The effectiveness of using the fuzzy FOPID controller over conventional fuzzy PID controllers has been shown with numerical simulations. The controllers tuned with the highest power models are shown to work well at other operating conditions as well; over the lowest power model based design and hence are robust with respect to the changes in nuclear reactor operating power levels. This paper also analyzes the degradation of nuclear reactor power signal due to network induced random delays in shared communication network and due to sensor noise while being fed-back to the Reactor Regulating System (RRS). The effect of long range dependence (LRD) which is a practical consideration for the stochastic processes like network induced delay and sensor noise has been tackled by optimum tuning of FO fuzzy PID controllers using GA, while also taking the operating point shift into consideration.

Wavelet deconvolution in a periodic setting with long-range dependent errors

In this paper, a hard thresholding wavelet estimator is constructed for a deconvolution model in a periodic setting that has long-range dependent noise. The estimation paradigm is based on a maxiset method that attains a near optimal rate of convergence for a variety of Lp loss functions and a wide variety of Besov spaces in the presence of strong dependence. The effect of long-range dependence is detrimental to the rate of convergence. The method is implemented using a modification of the WaveD-package in R and an extensive numerical study is conducted. The numerical study supplements the theoretical results and compares the LRD estimator with a naïve application of the standard WaveD approach.

The effect of long-range dependence on modelling extremes with the generalised extreme value distribution

Two effects arise for the modelling of block maxima from dependent time series: a reduced rate of convergence for the block maxima probability distribution towards the generalised extreme value distribution, and an increase in uncertainty of the parameter estimates compared to independent or short range dependent records. These effects are exemplified with a simulation study using a white noise, a short-range and a long-range dependent process. The two issues raised turned out to be relatively unproblematic for short-range dependent processes. For long-range dependent processes, especially the increased parameter uncertainty poses a problem. Incautious use of standard procedures would lead to a severe underestimation of the parameter uncertainty which implies a misconception of accuracy for derived quantities, such as return levels which are frequently used for risk assessment and dimensioning of hydraulic structures.

Kink estimation with correlated noise

In this article we study the estimation of the location of jump points in the first derivative (referred to as kinks) of a regression function f in the presence of noise that exhibits long-range dependence (LRD). The method is based on the zero-crossing technique and makes use of high-order kernels. The effect of LRD is seen to be detrimental to the rate of convergence. Using a fractional integration operator we draw a parallel with certain inverse problems which suggests optimality of our approach. The kink location and estimation technique is demonstrated on some simulated data and the detrimental effect of LRD is shown. We also apply our kink analysis on Australian temperature data.

Characterization of slice-based H.264/AVC encoded video traffic using token buckets

An explicit slice-based mode type selection scheme for use in H.264/AVC has recently been developed, which reduces the burstiness effect of standard frame-based H.264/AVC by breaking up the Group of Picture structure. In this paper, slice-based encoded video streams are characterized using the token bucket traffic model and compared to standard frame-based encoded streams. Both lossless, loss bounded and delay bounded token bucket models are investigated and the high quantiles are found for the amount of loss. Loss above the amount given by the high quantiles will happen only with a very small probability. It is shown that the reduced burstiness for the slice-based video encoding leads to lower token bucket parameters compared to frame-based video encoding for a stream without scene changes, and a larger reduction in the token bucket parameters compared to the frame-based video encoding when a small amount of delay or loss is allowed for the stream with scene changes. Next, reshuffling of the frames of the video streams with scene changes is employed to better understand the effects of long-range dependence on the token bucket parameters. Only small effects are found from reshuffling the scenes, but reshuffling of the frames inside the scenes leads to lower token bucket parameters. Finally, an approach to estimate the parameters for the token bucket model using simple characteristics of the slice-based stream is developed.

Impaction of aggregated network traffic on queueing performance

The impaction of aggregated network traffic on queueing system is studied in this paper. It shows that the network traffic stayed in buffer has different impaction on queueing performance when it is aggregated at different scales. And its influence is related not only to traffic parameters but also to system parameter, such as buffer size. The increased buffer size can absorb the effect of short-range dependence (SRD) in network traffic and only the effect of long-range dependence (LRD) is expressed. The queueing length is asymptotic Weibull distribution with increasing buffer size, which is irrespective with the effect of short-range dependence character. Monte-Carlo based simulation confirmed the validity of these results.

MODELS FOR FRACTIONAL RIESZ-BESSEL MOTION AND RELATED PROCESSES

This paper presents some stationary and stationary increment models for fractional Riesz-Bessel motion which permits the study of the effects of long-range dependence and second-order intermittency simultaneously. These effects are important features of data in finance and turbulence.

Nonparametric Density Estimation for a Long-Range Dependent Linear Process

We estimate the marginal density function of a long-range dependent linear process by the kernel estimator. We assume the innovations are i.i.d. Then it is known that the term of the sample mean is dominant in the MISE of the kernel density estimator when the dependence is beyond some level which depends on the bandwidth and that the MISE has asymptotically the same form as for i.i.d. observations when the dependence is below the level. We call the latter the case where the dependence is not very strong and focus on it in this paper. We show that the asymptotic distribution of the kernel density estimator is the same as for i.i.d. observations and the effect of long-range dependence does not appear. In addition we describe some results for weakly dependent linear processes.

Long-range dependence and self-similarity in World Wide Web proxy cache references

The existence of long-range dependence and self-similarity properties within World Wide Web proxy cache references is reported. Fractional ARIMA processes were used to generate long-range dependent cache hit/miss sequences in order to model the growth in cache occupancy. This model was compared to a model using independent cache hit/miss sequences and it was found that the results predicted by these models differed significantly. However, the results of the fractional ARIMA model resembled the growth of an actual cache. Trace simulations were carried out in order to investigate the effects of long-range dependence and self-similarity on cache replacement and garbage collection policies.

The effect of long-range dependence on change-point estimators

We study the asymptotic behaviour of a class of estimators of the time of change in the mean of Gaussian observations having long-range dependence. We prove that after a suitable normalization the estimators converge in distribution to functionals of fractional Brownian motion.

Convergence rates in density estimation for data from infinite-order moving average processes

The effect of long-range dependence in nonparametric probability density estimation is investigated under the assumption that the observed data are a sample from a stationary, infinite-order moving average process. It is shown that to first order, the mean integrated squared error (MISE) of a kernel estimator for moving average data may be expanded as the sum of MISE of the kernel estimator for a same-sizerandom sample, plus a term proportional to the variance of the moving average sample mean. The latter term does not depend on bandwidth, and so imposes a ceiling on the convergence rate of a kernel estimator regardless of how bandwidth is chosen. This ceiling can be quite significant in the case of long-range dependence. We show thatall density estimators have the convergence rate ceiling possessed by kernel estimators.