An Improved Hurst Parameter Estimator Based on Fractional Fourier Transform

Author(s):  
YangQuan Chen ◽  
Rongtao Sun ◽  
Anhong Zhou

A fractional Fourier transform (FrFT) based estimation method is introduced in this paper to analyze the long range dependence (LRD) in time series. The degree of LRD can be characterized by the Hurst parameter. The FrFT-based estimation of Hurst parameter proposed in this paper can be implemented efficiently allowing very large data set. We used fractional Gaussian noises (FGN) which typically possesses long-range dependence with known Hurst parameters to test the accuracy of the proposed Hurst parameter estimator. For justifying the advantage of the proposed estimator, some other existing Hurst parameter estimation methods, such as wavelet-based method and a global estimator based on dispersional analysis, are compared. The proposed estimator can process the very long experimental time series locally to achieve a reliable estimation of the Hurst parameter.

Sensors ◽  
2019 ◽  
Vol 19 (6) ◽  
pp. 1477 ◽  
Author(s):  
Xinqun Liu ◽  
Tao Li ◽  
Xiaolei Fan ◽  
Zengping Chen

The Nyquist folding receiver (NYFR) can achieve a high-probability interception of an ultra-wideband (UWB) signal with fewer devices, while the output of the NYFR is converted into a hybrid modulated signal of the local oscillator (LO) and the received signal, which requires the matching parameter estimation methods. The linear frequency modulation (LFM) signal is a typical low probability of intercept (LPI) radar signal. In this paper, an estimation method of both the Nyquist Zone (NZ) index and the chirp rate for the LFM signal intercepted by NYFR was proposed. First, according to the time-frequency characteristics of the LFM signal, the accurate NZ and the rough chirp rate was estimated based on least squares (LS) and random sample consensus (RANSAC). Then, the information of the LO was removed from the hybrid modulated signal by the known NZ, and the precise chirp rate was obtained by using the fractional Fourier transform (FrFT). Moreover, a fast search method of FrFT optimal order was presented, which could obviously reduce the computational complexity. The simulation demonstrated that the proposed method could precisely estimate the parameters of the hybrid modulated output signal of the NYFR.


2014 ◽  
Vol 7 (6) ◽  
pp. 1547-1570 ◽  
Author(s):  
C. Viatte ◽  
K. Strong ◽  
K. A. Walker ◽  
J. R. Drummond

Abstract. We present a five-year time series of seven tropospheric species measured using a ground-based Fourier transform infrared (FTIR) spectrometer at the Polar Environment Atmospheric Research Laboratory (PEARL; Eureka, Nunavut, Canada; 80°05' N, 86°42' W) from 2007 to 2011. Total columns and temporal variabilities of carbon monoxide (CO), hydrogen cyanide (HCN) and ethane (C2H6) as well as the first derived total columns at Eureka of acetylene (C2H2), methanol (CH3OH), formic acid (HCOOH) and formaldehyde (H2CO) are investigated, providing a new data set in the sparsely sampled high latitudes. Total columns are obtained using the SFIT2 retrieval algorithm based on the optimal estimation method. The microwindows as well as the a priori profiles and variabilities are selected to optimize the information content of the retrievals, and error analyses are performed for all seven species. Our retrievals show good sensitivities in the troposphere. The seasonal amplitudes of the time series, ranging from 34 to 104%, are captured while using a single a priori profile for each species. The time series of the CO, C2H6 and C2H2 total columns at PEARL exhibit strong seasonal cycles with maxima in winter and minima in summer, in opposite phase to the HCN, CH3OH, HCOOH and H2CO time series. These cycles result from the relative contributions of the photochemistry, oxidation and transport as well as biogenic and biomass burning emissions. Comparisons of the FTIR partial columns with coincident satellite measurements by the Atmospheric Chemistry Experiment Fourier Transform Spectrometer (ACE-FTS) show good agreement. The correlation coefficients and the slopes range from 0.56 to 0.97 and 0.50 to 3.35, respectively, for the seven target species. Our new data set is compared to previous measurements found in the literature to assess atmospheric budgets of these tropospheric species in the high Arctic. The CO and C2H6concentrations are consistent with negative trends observed over the Northern Hemisphere, attributed to fossil fuel emission decrease. The importance of poleward transport for the atmospheric budgets of HCN and C2H2 is highlighted. Columns and variabilities of CH3OH and HCOOH at PEARL are comparable to previous measurements performed at other remote sites. However, the small columns of H2CO in early May might reflect its large atmospheric variability and/or the effect of the updated spectroscopic parameters used in our retrievals. Overall, emissions from biomass burning contribute to the day-to-day variabilities of the seven tropospheric species observed at Eureka.


2018 ◽  
Vol 173 ◽  
pp. 03044
Author(s):  
FAN Junhui ◽  
PENG Hua ◽  
WEI Chi

To overcome the performance degradation of conventional Chirp parameters estimation methods in underwater acoustic multipath channels, a novel parameters estimation method based on Fractional Fourier transform (FRFT) and Fourier transform (FFT) was proposed. Firstly, the Chirp rate was estimated by searching for the best degree of Chirp after Fractional Fourier transform. Secondly, the Chirp signal turned into a single-frequency signal by means of Chirp rate equalization. Finally, FFT was applied to estimate the initial frequency. The simulation experiment show that the proposed algorithm enhanced about 1dB RMSE performance on Chirp initial frequency compared with FRFT while the computational complexity is similar to FRFT.


Author(s):  
Jan Beran ◽  
Britta Steffens ◽  
Sucharita Ghosh

AbstractWe consider nonparametric regression for bivariate circular time series with long-range dependence. Asymptotic results for circular Nadaraya–Watson estimators are derived. Due to long-range dependence, a range of asymptotically optimal bandwidths can be found where the asymptotic rate of convergence does not depend on the bandwidth. The result can be used for obtaining simple confidence bands for the regression function. The method is illustrated by an application to wind direction data.


Entropy ◽  
2016 ◽  
Vol 18 (1) ◽  
pp. 23 ◽  
Author(s):  
Qing Li ◽  
Steven Liang ◽  
Jianguo Yang ◽  
Beizhi Li

2021 ◽  
Author(s):  
Ginno Millan ◽  
manuel vargas ◽  
Guillermo Fuertes

Fractal behavior and long-range dependence are widely observed in measurements and characterization of traffic flow in high-speed computer networks of different technologies and coverage levels. This paper presents the results obtained when applying fractal analysis techniques on a time series obtained from traffic captures coming from an application server connected to the internet through a high-speed link. The results obtained show that traffic flow in the dedicated high-speed network link exhibited fractal behavior since the Hurst exponent was in the range of 0.5, 1, the fractal dimension between 1, 1.5, and the correlation coefficient between -0.5, 0. Based on these results, it is ideal to characterize both the singularities of the fractal traffic and its impulsiveness during a fractal analysis of temporal scales. Finally, based on the results of the time series analyzes, the fact that the traffic flows of current computer networks exhibited fractal behavior with a long-range dependence was reaffirmed.


Symmetry ◽  
2020 ◽  
Vol 12 (7) ◽  
pp. 1157
Author(s):  
Faheem Aslam ◽  
Saima Latif ◽  
Paulo Ferreira

The use of multifractal approaches has been growing because of the capacity of these tools to analyze complex properties and possible nonlinear structures such as those in financial time series. This paper analyzes the presence of long-range dependence and multifractal parameters in the stock indices of nine MSCI emerging Asian economies. Multifractal Detrended Fluctuation Analysis (MFDFA) is used, with prior application of the Seasonal and Trend Decomposition using the Loess (STL) method for more reliable results, as STL separates different components of the time series and removes seasonal oscillations. We find a varying degree of multifractality in all the markets considered, implying that they exhibit long-range correlations, which could be related to verification of the fractal market hypothesis. The evidence of multifractality reveals symmetry in the variation trends of the multifractal spectrum parameters of financial time series, which could be useful to develop portfolio management. Based on the degree of multifractality, the Chinese and South Korean markets exhibit the least long-range dependence, followed by Pakistan, Indonesia, and Thailand. On the contrary, the Indian and Malaysian stock markets are found to have the highest level of dependence. This evidence could be related to possible market inefficiencies, implying the possibility of institutional investors using active trading strategies in order to make their portfolios more profitable.


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