scholarly journals NONPARAMETRIC ANALYSES OF LOG-PERIODIC PRECURSORS TO FINANCIAL CRASHES

2003 ◽  
Vol 14 (08) ◽  
pp. 1107-1125 ◽  
Author(s):  
WEI-XING ZHOU ◽  
DIDIER SORNETTE
Keyword(s):  
Time Series ◽  
Fourier Transform ◽  
Power Law ◽  
Hilbert Transform ◽  
Strong Evidence ◽  
Unpublished Report ◽  
Dow Jones Industrial Average ◽  
The Hilbert Transform ◽  
Financial Indices ◽  
Good Agreement

We apply two nonparametric methods to further test the hypothesis that log-periodicity characterizes the detrended price trajectory of large financial indices prior to financial crashes or strong corrections. The term "parametric" refers here to the use of the log-periodic power law formula to fit the data; in contrast, "nonparametric" refers to the use of general tools such as Fourier transform, and in the present case the Hilbert transform and the so-called (H, q)-analysis. The analysis using the (H, q)-derivative is applied to seven time series ending with the October 1987 crash, the October 1997 correction and the April 2000 crash of the Dow Jones Industrial Average (DJIA), the Standard & Poor 500 and Nasdaq indices. The Hilbert transform is applied to two detrended price time series in terms of the ln (tc-t) variable, where tcis the time of the crash. Taking all results together, we find strong evidence for a universal fundamental log-frequency f=1.02±0.05 corresponding to the scaling ratio λ=2.67±0.12. These values are in very good agreement with those obtained in earlier works with different parametric techniques. This note is extracted from a long unpublished report with 58 figures available at , which extensively describes the evidence we have accumulated on these seven time series, in particular by presenting all relevant details so that the reader can judge for himself or herself the validity and robustness of the results.

Model of multicomponent narrow-band periodical non-stationary random signal

2020 ◽  
Vol 2020 (48) ◽  
pp. 17-24
Author(s):  
I.M. Javorskyj ◽  
◽  
R.M. Yuzefovych ◽  
P.R. Kurapov ◽  
◽  
...  
Keyword(s):  
Time Series ◽  
Real Time ◽  
Hilbert Transform ◽  
Spectral Properties ◽  
Narrow Band ◽  
Analytic Signal ◽  
Random Signal ◽  
Hilbert Transformation ◽  
The Hilbert Transform

The correlation and spectral properties of a multicomponent narrowband periodical non-stationary random signal (PNRS) and its Hilbert transformation are considered. It is shown that multicomponent narrowband PNRS differ from the monocomponent signal. This difference is caused by correlation of the quadratures for the different carrier harmonics. Such features of the analytic signal must be taken into account when we use the Hilbert transform for the analysis of real time series.

scholarly journals Phase Synchronization Is the Amplified Result by the Hilbert Transform

2015 ◽  
Vol 2015 ◽  
pp. 1-3 ◽  
Author(s):  
Ming-Chi Lu ◽  
Hsing-Chung Ho ◽  
Chen-An Chan ◽  
Chia-Ju Liu ◽  
Jiann-Shing Lih ◽  
...  
Keyword(s):  
Time Series ◽  
Dynamical Systems ◽  
Hilbert Transform ◽  
Phase Synchronization ◽  
Nonlinear Dynamical Systems ◽  
The State ◽  
Nonlinear Dynamical ◽  
Large Correlation ◽  
Current Usage ◽  
The Hilbert Transform

We investigate the interplay between phase synchronization and amplitude synchronization in nonlinear dynamical systems. It is numerically found that phase synchronization intends to be established earlier than amplitude synchronization. Nevertheless, amplitude synchronization (or the state with large correlation between the amplitudes) is crucial for the maintenance of a high correlation between two time series. A breakdown of high correlation in amplitudes will lead to a desynchronization of two time series. It is shown that these unique features are caused essentially by the Hilbert transform. This leads to a deep concern and criticism on the current usage of phase synchronization.

The properties of generalized offset linear canonical Hilbert transform and its applications

2017 ◽  
Vol 15 (04) ◽  
pp. 1750031 ◽  
Author(s):  
Shuiqing Xu ◽  
Li Feng ◽  
Yi Chai ◽  
Youqiang Hu ◽  
Lei Huang
Keyword(s):  
Signal Processing ◽  
Fourier Transform ◽  
Hilbert Transform ◽  
Analytic Signal ◽  
Linear Canonical Transform ◽  
Single Sideband ◽  
Generalized Hilbert Transform ◽  
Offset Linear Canonical Transform ◽  
The Fourier Transform ◽  
The Hilbert Transform

The Hilbert transform is tightly associated with the Fourier transform. As the offset linear canonical transform (OLCT) has been shown to be useful and powerful in signal processing and optics, the concept of generalized Hilbert transform associated with the OLCT has been proposed in the literature. However, some basic results for the generalized Hilbert transform still remain unknown. Therefore, in this paper, theories and properties of the generalized Hilbert transform have been considered. First, we introduce some basic properties of the generalized Hilbert transform. Then, an important theorem for the generalized analytic signal is presented. Subsequently, the generalized Bedrosian theorem for the generalized Hilbert transform is formulated. In addition, a generalized secure single-sideband (SSB) modulation system is also presented. Finally, the simulations are carried out to verify the validity and correctness of the proposed results.

The Analysis of Gearbox Fault Diagnosis Research Based on the EMD and Hilbert Envelope Demodulation

2014 ◽  
Vol 926-930 ◽  
pp. 1800-1805 ◽  
Author(s):  
Guo Dong Han ◽  
Shu Ting Wan ◽  
Zhan Jie Lv ◽  
Rong Hai Liu ◽  
Jin Wang ◽  
...  
Keyword(s):  
Fourier Transform ◽  
Fault Diagnosis ◽  
Power Spectrum ◽  
Fast Fourier Transform ◽  
Empirical Mode Decomposition ◽  
Hilbert Transform ◽  
Mode Decomposition ◽  
Signal Characteristics ◽  
The Hilbert Transform ◽  
Fault Characteristic

This paper puts forward a kind of gearbox fault diagnosis methods which based on empirical mode decomposition (EMD), Hilbert transform, Fast Fourier Transform (FFT) and spectrum refined techniques. This method is applicable to the analysis of the nonlinear unsteady signal. First of all used wavelet denoising to the acquisition of gearbox vibrate signal, again carries on the empirical mode decomposition (EMD), than get a certain number of intrinsic mode function (imf); Choose the specific imf, based on kurtosis value, after the Hilbert transform and Fast Fourier Transform is done, the corresponding power spectrum can be obtained; To refine the power spectrum and extract the gearbox fault characteristic frequency; Then in pattern recognition and diagnosis of the gearbox fault, and compared with the normal signal characteristics. The analysis results show that the proposed method can effectively detect the gearbox fault characteristics.

scholarly journals Analysis of Natural and Artificial Phenomena Using Signal Processing and Fractional Calculus

2015 ◽  
Vol 18 (2) ◽  
Author(s):  
J. A. Tenreiro Machado ◽  
António M. Lopes
Keyword(s):  
Time Series ◽  
Fourier Transform ◽  
Vector Field ◽  
System Dynamics ◽  
Power Law ◽  
System Behavior ◽  
Amplitude Spectra ◽  
The Fourier Transform ◽  
Complex Phenomena ◽  
Power Law Parameters

AbstractIn this paper we study several natural and man-made complex phenomena in the perspective of dynamical systems. For each class of phenomena, the system outputs are time-series records obtained in identical conditions. The time-series are viewed as manifestations of the system behavior and are processed for analyzing the system dynamics. First, we use the Fourier transform to process the data and we approximate the amplitude spectra by means of power law functions. We interpret the power law parameters as a phenomenological signature of the system dynamics. Second, we adopt the techniques of non-hierarchical clustering and multidimensional scaling to visualize hidden relationships between the complex phenomena. Third, we propose a vector field based analogy to interpret the patterns unveiled by the PL parameters.

Recent Developments in Chaotic Time Series Analysis

2003 ◽  
Vol 13 (06) ◽  
pp. 1383-1422 ◽  
Author(s):  
Ying-Cheng Lai ◽  
Nong Ye
Keyword(s):  
Time Series ◽  
Time Series Analysis ◽  
Hilbert Transform ◽  
Chaotic Time Series ◽  
Unstable Periodic Orbits ◽  
Series Analysis ◽  
Delay Coordinate Embedding ◽  
The Hilbert Transform ◽  
Chaotic Time Series Analysis ◽  
Coordinate Embedding

In this paper, two issues are addressed: (1) the applicability of the delay-coordinate embedding method to transient chaotic time series analysis, and (2) the Hilbert transform methodology for chaotic signal processing.A common practice in chaotic time series analysis has been to reconstruct the phase space by utilizing the delay-coordinate embedding technique, and then to compute dynamical invariant quantities of interest such as unstable periodic orbits, the fractal dimension of the underlying chaotic set, and its Lyapunov spectrum. As a large body of literature exists on applying the technique to time series from chaotic attractors, a relatively unexplored issue is its applicability to dynamical systems that exhibit transient chaos. Our focus will be on the analysis of transient chaotic time series. We will argue and provide numerical support that the current delay-coordinate embedding techniques for extracting unstable periodic orbits, for estimating the fractal dimension, and for computing the Lyapunov exponents can be readily adapted to transient chaotic time series.A technique that is gaining an increasing attention is the Hilbert transform method for signal processing in nonlinear systems. The general goal of the Hilbert method is to assess the spectrum of the instantaneous frequency associated with the underlying dynamical process. To obtain physically meaningful results, it is necessary for the signal to possess a proper rotational structure in the complex plane of the analytic signal constructed by the original signal and its Hilbert transform. We will describe a recent decomposition procedure for this task and apply the technique to chaotic signals. We will also provide an example to demonstrate that the methodology can be useful for addressing some fundamental problems in chaotic dynamics.

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