201 research outputs found
Estimation of Scale and Hurst Parameters of Semi-Selfsimilar Processes
The characteristic feature of semi-selfsimilar process is the invariance of
its finite dimensional distributions by certain dilation for specific scaling
factor. Estimating the scale parameter and the Hurst index of such
processes is one of the fundamental problem in the literature. We present some
iterative method for estimation of the scale and Hurst parameters which is
addressed for semi-selfsimilar processes with stationary increments. This
method is based on some flexible sampling scheme and evaluating sample variance
of increments in each scale intervals , . For such iterative method we find the initial estimation for the
scale parameter by evaluating cumulative sum of moving sample variances and
also by evaluating sample variance of preceding and succeeding moving sample
variance of increments. We also present a new efficient method for estimation
of Hurst parameter of selfsimilar processes. As an example we introduce simple
fractional Brownian motion (sfBm) which is semi-selfsimilar with stationary
increments. We present some simulations and numerical evaluation to illustrate
the results and to estimate the scale for sfBm as a semi-selfsimilar process.
We also present another simulation and show the efficiency of our method in
estimation of Hurst parameter by comparing its performance with some previous
methods.Comment: 15 page
Aggregation and long memory: recent developments
It is well-known that the aggregated time series might have very different
properties from those of the individual series, in particular, long memory. At
the present time, aggregation has become one of the main tools for modelling of
long memory processes. We review recent work on contemporaneous aggregation of
random-coefficient AR(1) and related models, with particular focus on various
long memory properties of the aggregated process
Local Holder regularity-based modeling of RR intervals
International audienceWe analyze the local regularity of RR traces from ECG through the computation of the so-called Hölder exponents. These exponents are at the basis of multifractal analysis, which has been shown to be relevant in the study of RR data. While multifractal analysis yields a global picture of the (statistical) distribution of regularity, we focus here on its time evolution. We show that this evolution is strongly correlated with the signal itself, a feature that seems to have remained unnoticed so far. We use this fact to build realistic synthetic RR traces
Application of Chaos Theory in the Prediction of Motorised Traffic Flows on Urban Networks
In recent times, urban road networks are faced with severe congestion problems as a result of the accelerating demand for mobility. One of the ways to mitigate the congestion problems on urban traffic road network is by predicting the traffic flow pattern. Accurate prediction of the dynamics of a highly complex system such as traffic flow requires a robust methodology. An approach for predicting Motorised Traffic Flow on Urban Road Networks based on Chaos Theory is presented in this paper. Nonlinear time series modeling techniques were used for the analysis of the traffic flow prediction with emphasis on the technique of computation of the Largest Lyapunov Exponent to aid in the prediction of traffic flow. The study concludes that algorithms based on the computation of the Lyapunov time seem promising as regards facilitating the control of congestion because of the technique’s effectiveness in predicting the dynamics of complex systems especially traffic flow
Gohberg-Semencul Estimation of Toeplitz Structured Covariance Matrices and Their Inverses
When only few data samples are accessible, utilizing structural prior
knowledge is essential for estimating covariance matrices and their inverses.
One prominent example is knowing the covariance matrix to be Toeplitz
structured, which occurs when dealing with wide sense stationary (WSS)
processes. This work introduces a novel class of positive definiteness ensuring
likelihood-based estimators for Toeplitz structured covariance matrices (CMs)
and their inverses. In order to accomplish this, we derive positive
definiteness enforcing constraint sets for the Gohberg-Semencul (GS)
parameterization of inverse symmetric Toeplitz matrices. Motivated by the
relationship between the GS parameterization and autoregressive (AR) processes,
we propose hyperparameter tuning techniques, which enable our estimators to
combine advantages from state-of-the-art likelihood and non-parametric
estimators. Moreover, we present a computationally cheap closed-form estimator,
which is derived by maximizing an approximate likelihood. Due to the ensured
positive definiteness, our estimators perform well for both the estimation of
the CM and the inverse covariance matrix (ICM). Extensive simulation results
validate the proposed estimators' efficacy for several standard Toeplitz
structured CMs commonly employed in a wide range of applications
Architectures for virtualization and performance evaluation in software defined networks
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