The Experts below are selected from a list of 103338 Experts worldwide ranked by ideXlab platform
Weixing Zhou - One of the best experts on this subject based on the ideXlab platform.
-
multifractal detrending Moving Average cross correlation analysis
Physical Review E, 2011Co-Authors: Zhiqiang Jiang, Weixing ZhouAbstract:There are a number of situations in which several signals are simultaneously recorded in complex systems, which exhibit long-term power-law cross correlations. The multifractal detrended cross-correlation analysis (MFDCCA) approaches can be used to quantify such cross correlations, such as the MFDCCA based on the detrended fluctuation analysis (MFXDFA) method. We develop in this work a class of MFDCCA algorithms based on the detrending Moving-Average analysis, called MFXDMA. The performances of the proposed MFXDMA algorithms are compared with the MFXDFA method by extensive numerical experiments on pairs of time series generated from bivariate fractional Brownian motions, two-component autoregressive fractionally integrated Moving-Average processes, and binomial measures, which have theoretical expressions of the multifractal nature. In all cases, the scaling exponents h(xy) extracted from the MFXDMA and MFXDFA algorithms are very close to the theoretical values. For bivariate fractional Brownian motions, the scaling exponent of the cross correlation is independent of the cross-correlation coefficient between two time series, and the MFXDFA and centered MFXDMA algorithms have comparative performances, which outperform the forward and backward MFXDMA algorithms. For two-component autoregressive fractionally integrated Moving-Average processes, we also find that the MFXDFA and centered MFXDMA algorithms have comparative performances, while the forward and backward MFXDMA algorithms perform slightly worse. For binomial measures, the forward MFXDMA algorithm exhibits the best performance, the centered MFXDMA algorithms performs worst, and the backward MFXDMA algorithm outperforms the MFXDFA algorithm when the moment order q 0. We apply these algorithms to the return time series of two stock market indexes and to their volatilities. For the returns, the centered MFXDMA algorithm gives the best estimates of h(xy)(q) since its h(xy)(2) is closest to 0.5, as expected, and the MFXDFA algorithm has the second best performance. For the volatilities, the forward and backward MFXDMA algorithms give similar results, while the centered MFXDMA and the MFXDFA algorithms fail to extract rational multifractal nature.
-
multifractal detrending Moving Average cross correlation analysis
Physical Review E, 2011Co-Authors: Zhiqiang Jiang, Weixing ZhouAbstract:There are a number of situations in which several signals are simultaneously recorded in complex systems, which exhibit long-term power-law cross-correlations. The multifractal detrended cross-correlation analysis (MF-DCCA) approaches can be used to quantify such cross-correlations, such as the MF-DCCA based on detrended fluctuation analysis (MF-X-DFA) method. We develop in this work a class of MF-DCCA algorithms based on the detrending Moving Average analysis, called MF-X-DMA. The performances of the MF-X-DMA algorithms are compared with the MF-X-DFA method by extensive numerical experiments on pairs of time series generated from bivariate fractional Brownian motions, two-component autoregressive fractionally integrated Moving Average processes and binomial measures, which have theoretical expressions of the multifractal nature. In all cases, the scaling exponents $h_{xy}$ extracted from the MF-X-DMA and MF-X-DFA algorithms are very close to the theoretical values. For bivariate fractional Brownian motions, the scaling exponent of the cross-correlation is independent of the cross-correlation coefficient between two time series and the MF-X-DFA and centered MF-X-DMA algorithms have comparative performance, which outperform the forward and backward MF-X-DMA algorithms. We apply these algorithms to the return time series of two stock market indexes and to their volatilities. For the returns, the centered MF-X-DMA algorithm gives the best estimates of $h_{xy}(q)$ since its $h_{xy}(2)$ is closest to 0.5 as expected, and the MF-X-DFA algorithm has the second best performance. For the volatilities, the forward and backward MF-X-DMA algorithms give similar results, while the centered MF-X-DMA and the MF-X-DFA algorithms fails to extract rational multifractal nature.
-
detrending Moving Average algorithm for multifractals
Physical Review E, 2010Co-Authors: Weixing ZhouAbstract:The detrending Moving Average (DMA) algorithm is a widely used technique to quantify the long-term correlations of nonstationary time series and the long-range correlations of fractal surfaces, which contains a parameter $\ensuremath{\theta}$ determining the position of the detrending window. We develop multifractal detrending Moving Average (MFDMA) algorithms for the analysis of one-dimensional multifractal measures and higher-dimensional multifractals, which is a generalization of the DMA method. The performance of the one-dimensional and two-dimensional MFDMA methods is investigated using synthetic multifractal measures with analytical solutions for backward $(\ensuremath{\theta}=0)$, centered $(\ensuremath{\theta}=0.5)$, and forward $(\ensuremath{\theta}=1)$ detrending windows. We find that the estimated multifractal scaling exponent $\ensuremath{\tau}(q)$ and the singularity spectrum $f(\ensuremath{\alpha})$ are in good agreement with the theoretical values. In addition, the backward MFDMA method has the best performance, which provides the most accurate estimates of the scaling exponents with lowest error bars, while the centered MFDMA method has the worse performance. It is found that the backward MFDMA algorithm also outperforms the multifractal detrended fluctuation analysis. The one-dimensional backward MFDMA method is applied to analyzing the time series of Shanghai Stock Exchange Composite Index and its multifractal nature is confirmed.
-
detrending Moving Average algorithm for multifractals
Research Papers in Economics, 2010Co-Authors: Weixing ZhouAbstract:The detrending Moving Average (DMA) algorithm is a widely used technique to quantify the long-term correlations of non-stationary time series and the long-range correlations of fractal surfaces, which contains a parameter $\theta$ determining the position of the detrending window. We develop multifractal detrending Moving Average (MFDMA) algorithms for the analysis of one-dimensional multifractal measures and higher-dimensional multifractals, which is a generalization of the DMA method. The performance of the one-dimensional and two-dimensional MFDMA methods is investigated using synthetic multifractal measures with analytical solutions for backward ($\theta=0$), centered ($\theta=0.5$), and forward ($\theta=1$) detrending windows. We find that the estimated multifractal scaling exponent $\tau(q)$ and the singularity spectrum $f(\alpha)$ are in good agreement with the theoretical values. In addition, the backward MFDMA method has the best performance, which provides the most accurate estimates of the scaling exponents with lowest error bars, while the centered MFDMA method has the worse performance. It is found that the backward MFDMA algorithm also outperforms the multifractal detrended fluctuation analysis (MFDFA). The one-dimensional backward MFDMA method is applied to analyzing the time series of Shanghai Stock Exchange Composite Index and its multifractal nature is confirmed.
Zhiqiang Jiang - One of the best experts on this subject based on the ideXlab platform.
-
multifractal detrending Moving Average cross correlation analysis
Physical Review E, 2011Co-Authors: Zhiqiang Jiang, Weixing ZhouAbstract:There are a number of situations in which several signals are simultaneously recorded in complex systems, which exhibit long-term power-law cross correlations. The multifractal detrended cross-correlation analysis (MFDCCA) approaches can be used to quantify such cross correlations, such as the MFDCCA based on the detrended fluctuation analysis (MFXDFA) method. We develop in this work a class of MFDCCA algorithms based on the detrending Moving-Average analysis, called MFXDMA. The performances of the proposed MFXDMA algorithms are compared with the MFXDFA method by extensive numerical experiments on pairs of time series generated from bivariate fractional Brownian motions, two-component autoregressive fractionally integrated Moving-Average processes, and binomial measures, which have theoretical expressions of the multifractal nature. In all cases, the scaling exponents h(xy) extracted from the MFXDMA and MFXDFA algorithms are very close to the theoretical values. For bivariate fractional Brownian motions, the scaling exponent of the cross correlation is independent of the cross-correlation coefficient between two time series, and the MFXDFA and centered MFXDMA algorithms have comparative performances, which outperform the forward and backward MFXDMA algorithms. For two-component autoregressive fractionally integrated Moving-Average processes, we also find that the MFXDFA and centered MFXDMA algorithms have comparative performances, while the forward and backward MFXDMA algorithms perform slightly worse. For binomial measures, the forward MFXDMA algorithm exhibits the best performance, the centered MFXDMA algorithms performs worst, and the backward MFXDMA algorithm outperforms the MFXDFA algorithm when the moment order q 0. We apply these algorithms to the return time series of two stock market indexes and to their volatilities. For the returns, the centered MFXDMA algorithm gives the best estimates of h(xy)(q) since its h(xy)(2) is closest to 0.5, as expected, and the MFXDFA algorithm has the second best performance. For the volatilities, the forward and backward MFXDMA algorithms give similar results, while the centered MFXDMA and the MFXDFA algorithms fail to extract rational multifractal nature.
-
multifractal detrending Moving Average cross correlation analysis
Physical Review E, 2011Co-Authors: Zhiqiang Jiang, Weixing ZhouAbstract:There are a number of situations in which several signals are simultaneously recorded in complex systems, which exhibit long-term power-law cross-correlations. The multifractal detrended cross-correlation analysis (MF-DCCA) approaches can be used to quantify such cross-correlations, such as the MF-DCCA based on detrended fluctuation analysis (MF-X-DFA) method. We develop in this work a class of MF-DCCA algorithms based on the detrending Moving Average analysis, called MF-X-DMA. The performances of the MF-X-DMA algorithms are compared with the MF-X-DFA method by extensive numerical experiments on pairs of time series generated from bivariate fractional Brownian motions, two-component autoregressive fractionally integrated Moving Average processes and binomial measures, which have theoretical expressions of the multifractal nature. In all cases, the scaling exponents $h_{xy}$ extracted from the MF-X-DMA and MF-X-DFA algorithms are very close to the theoretical values. For bivariate fractional Brownian motions, the scaling exponent of the cross-correlation is independent of the cross-correlation coefficient between two time series and the MF-X-DFA and centered MF-X-DMA algorithms have comparative performance, which outperform the forward and backward MF-X-DMA algorithms. We apply these algorithms to the return time series of two stock market indexes and to their volatilities. For the returns, the centered MF-X-DMA algorithm gives the best estimates of $h_{xy}(q)$ since its $h_{xy}(2)$ is closest to 0.5 as expected, and the MF-X-DFA algorithm has the second best performance. For the volatilities, the forward and backward MF-X-DMA algorithms give similar results, while the centered MF-X-DMA and the MF-X-DFA algorithms fails to extract rational multifractal nature.
Young-han Kim - One of the best experts on this subject based on the ideXlab platform.
-
Feedback capacity of the first-order Moving Average Gaussian channel
IEEE Transactions on Information Theory, 2006Co-Authors: Young-han KimAbstract:Despite numerous bounds and partial results, the feedback capacity of the stationary nonwhite Gaussian additive noise channel has been open, even for the simplest cases such as the first-order autoregressive Gaussian channel studied by Butman, Tiernan and Schalkwijk, Wolfowitz, Ozarow, and more recently, Yang, Kavccaronicacute, and Tatikonda. Here we consider another simple special case of the stationary first-order Moving Average additive Gaussian noise channel and find the feedback capacity in closed form. Specifically, the channel is given by Yi=Xi+Zi, i=1,2,..., where the input {X i} satisfies a power constraint and the noise {Zi} is a first-order Moving Average Gaussian process defined by Zi=alphaUi-1+Ui, |alpha|les 1, with white Gaussian innovations Ui, i=0,1,.... We show that the feedback capacity of this channel is CFB=-log x0 where x0 is the unique positive root of the equation rhox2=(1-x2)(1-|alpha|x)2 and rho is the ratio of the Average input power per transmission to the variance of the noise innovation Ui. The optimal coding scheme parallels the simple linear signaling scheme by Schalkwijk and Kailath for the additive white Gaussian noise channel-the transmitter sends a real-valued information-bearing signal at the beginning of communication and subsequently refines the receiver's knowledge by processing the feedback noise signal through a linear stationary first-order autoregressive filter. The resulting error probability of the maximum likelihood decoding decays doubly exponentially in the duration of the communication. Refreshingly, this feedback capacity of the first-order Moving Average Gaussian channel is very similar in form to the best known achievable rate for the first-order autoregressive Gaussian noise channel given by Butman
-
feedback capacity of the first order Moving Average gaussian channel
International Symposium on Information Theory, 2005Co-Authors: Young-han KimAbstract:The feedback capacity of the stationary Gaussian additive noise channel has been open, except for the case where the noise is white. Here we obtain the closed-form feedback capacity of the first-order Moving Average additive Gaussian noise channel. Specifically, the channel is given by Yi = Xi + Zi, i = 1,2,..., where the input {Xi} satisfies Average power constraint and the noise {Zi} is a first-order Moving Average Gaussian process defined by Zi = alphaUi-1 + U i, |alpha| les 1, with white Gaussian innovation {Ui }i=0 infin. We show that the feedback capacity of this channel is -log x0, where x0 is the unique positive root of the equation rhox2 = (1 - x2)(1 - |alpha|x)2, and rho is the ratio of the Average input power per transmission to the variance of the noise innovation Ui. The optimal coding scheme parallels the simple linear signalling scheme by Schalkwijk and Kailath for the additive white Gaussian noise channel; the transmitter sends a real-valued information-bearing signal at the beginning of communication, then subsequently processes the feedback noise process through a simple linear stationary first-order autoregressive filter to help the receiver recover the information by maximum likelihood decoding. The resulting probability of error decays doubly exponentially in the duration of the communication. This feedback capacity of the first-order Moving Average Gaussian channel is very similar in form to the best known achievable rate for the first-order autoregressive Gaussian noise channel studied by Butman, Wolfowitz, and Tiernan, although the optimality of the latter is yet to be established
-
feedback capacity of the first order Moving Average gaussian channel
arXiv: Information Theory, 2004Co-Authors: Young-han KimAbstract:The feedback capacity of the stationary Gaussian additive noise channel has been open, except for the case where the noise is white. Here we find the feedback capacity of the stationary first-order Moving Average additive Gaussian noise channel in closed form. Specifically, the channel is given by $Y_i = X_i + Z_i,$ $i = 1, 2, ...,$ where the input $\{X_i\}$ satisfies a power constraint and the noise $\{Z_i\}$ is a first-order Moving Average Gaussian process defined by $Z_i = \alpha U_{i-1} + U_i,$ $|\alpha| \le 1,$ with white Gaussian innovations $U_i,$ $i = 0,1,....$ We show that the feedback capacity of this channel is $-\log x_0,$ where $x_0$ is the unique positive root of the equation $ \rho x^2 = (1-x^2) (1 - |\alpha|x)^2,$ and $\rho$ is the ratio of the Average input power per transmission to the variance of the noise innovation $U_i$. The optimal coding scheme parallels the simple linear signalling scheme by Schalkwijk and Kailath for the additive white Gaussian noise channel -- the transmitter sends a real-valued information-bearing signal at the beginning of communication and subsequently refines the receiver's error by processing the feedback noise signal through a linear stationary first-order autoregressive filter. The resulting error probability of the maximum likelihood decoding decays doubly-exponentially in the duration of the communication. This feedback capacity of the first-order Moving Average Gaussian channel is very similar in form to the best known achievable rate for the first-order \emph{autoregressive} Gaussian noise channel studied by Butman, Wolfowitz, and Tiernan, although the optimality of the latter is yet to be established.
Geert Leus - One of the best experts on this subject based on the ideXlab platform.
-
Autoregressive Moving Average Graph Filtering
IEEE Transactions on Signal Processing, 2017Co-Authors: Elvin Isufi, Andreas Loukas, Andrea Simonetto, Geert LeusAbstract:One of the cornerstones of the field of signal processing on graphs are graph filters, direct analogs of classical filters, but intended for signals defined on graphs. This paper brings forth new insights on the distributed graph filtering problem. We design a family of autoregressive Moving Average (ARMA) recursions, which are able to approximate any desired graph frequency response, and give exact solutions for specific graph signal denoising and interpolation problems. The philosophy to design the ARMA coefficients independently from the underlying graph renders the ARMA graph filters suitable in static and, particularly, time-varying settings. The latter occur when the graph signal and/or graph topology are changing over time. We show that in case of a time-varying graph signal, our approach extends naturally to a two-dimensional filter, operating concurrently in the graph and regular time domain. We also derive the graph filter behavior, as well as sufficient conditions for filter stability when the graph and signal are time varying. The analytical and numerical results presented in this paper illustrate that ARMA graph filters are practically appealing for static and time-varying settings, as predicted by theoretical derivations.
-
Autoregressive Moving Average graph filter design
2017 IEEE Global Conference on Signal and Information Processing (GlobalSIP), 2017Co-Authors: Elvin Isufi, Geert LeusAbstract:In graph signal processing, signals are processed by explicitly taking into account their underlying structure, which is generally characterized by a graph. In this field, graph filters play a major role to process such signals in the so-called graph frequency domain. In this paper, we focus on the design of autoregressive Moving Average (ARMA) graph filters and basically present two design approaches. The first approach is inspired by Prony's method, which considers a modified error between the modeled and the desired frequency response. The second approach is based on an iterative method, which finds the filter coefficients by iteratively minimizing the true error (instead of the modified error) between the modeled and the desired frequency response. The performance of the proposed design algorithms is evaluated and compared with finite impulse response (FIR) graph filters. The obtained results show that ARMA filters outperform FIR filters in terms of approximation accuracy even for the same computational cost.
-
distributed autoregressive Moving Average graph filters
arXiv: Social and Information Networks, 2015Co-Authors: Andreas Loukas, Andrea Simonetto, Geert LeusAbstract:We introduce the concept of autoregressive Moving Average (ARMA) filters on a graph and show how they can be implemented in a distributed fashion. Our graph filter design philosophy is independent of the particular graph, meaning that the filter coefficients are derived irrespective of the graph. In contrast to finite-impulse response (FIR) graph filters, ARMA graph filters are robust against changes in the signal and/or graph. In addition, when time-varying signals are considered, we prove that the proposed graph filters behave as ARMA filters in the graph domain and, depending on the implementation, as first or higher ARMA filters in the time domain.
-
Distributed Autoregressive Moving Average Graph Filters
IEEE Signal Processing Letters, 2015Co-Authors: Andreas Loukas, Andrea Simonetto, Geert LeusAbstract:We introduce the concept of autoregressive Moving Average (ARMA) filters on a graph and show how they can be implemented in a distributed fashion. Our graph filter design philosophy is independent of the particular graph, meaning that the filter coefficients are derived irrespective of the graph. In contrast to finite-impulse response (FIR) graph filters, ARMA graph filters are robust against changes in the signal and/or graph. In addition, when time-varying signals are considered, we prove that the proposed graph filters behave as ARMA filters in the graph domain and, depending on the implementation, as first or higher order ARMA filters in the time domain.
Mikis D Stasinopoulos - One of the best experts on this subject based on the ideXlab platform.
-
generalized autoregressive Moving Average models
Journal of the American Statistical Association, 2003Co-Authors: Michael A. Benjamin, Robert A Rigby, Mikis D StasinopoulosAbstract:A class of generalized autoregressive Moving Average (GARMA) models is developed that extends the univariate Gaussian ARMA time series model to a flexible observation-driven model for non-Gaussian time series data. The dependent variable is assumed to have a conditional exponential family distribution given the past history of the process. The model estimation is carried out using an iteratively reweighted least squares algorithm. Properties of the model, including stationarity and marginal moments, are either derived explicitly or investigated using Monte Carlo simulation. The relationship of the GARMA model to other models is shown, including the autoregressive models of Zeger and Qaqish, the Moving Average models of Li, and the reparameterized generalized autoregressive conditional heteroscedastic GARCH model (providing the formula for its fourth marginal moment not previously derived). The model is demonstrated by the application of the GARMA model with a negative binomial conditional distribution to ...
