Cautionary Remarks on the Auto-Correlation Analysis of Self-Similar Time Series

2017 ◽  
pp. 207-212
Author(s):  
Sung Yong Kim
Keyword(s):  
Time Series ◽  
Correlation Analysis ◽  
Similar Time ◽  
Auto Correlation ◽  
Self Similar

scholarly journals A NOVEL R/S FRACTAL ANALYSIS AND WAVELET ENTROPY CHARACTERIZATION APPROACH FOR ROBUST FORECASTING BASED ON SELF-SIMILAR TIME SERIES MODELING

Fractals ◽  
2020 ◽  
Vol 28 (08) ◽  
pp. 2040032
Author(s):  
YELIZ KARACA ◽  
DUMITRU BALEANU
Keyword(s):  
Decision Making ◽  
Time Series ◽  
Fractal Analysis ◽  
Back Propagation ◽  
Long Term Memory ◽  
Similar Time ◽  
Wavelet Entropy ◽  
Feed Forward Back Propagation ◽  
Self Similar

It has become vital to effectively characterize the self-similar and regular patterns in time series marked by short-term and long-term memory in various fields in the ever-changing and complex global landscape. Within this framework, attempting to find solutions with adaptive mathematical models emerges as a major endeavor in economics whose complex systems and structures are generally volatile, vulnerable and vague. Thus, analysis of the dynamics of occurrence of time section accurately, efficiently and timely is at the forefront to perform forecasting of volatile states of an economic environment which is a complex system in itself since it includes interrelated elements interacting with one another. To manage data selection effectively and attain robust prediction, characterizing complexity and self-similarity is critical in financial decision-making. Our study aims to obtain analyzes based on two main approaches proposed related to seven recognized indexes belonging to prominent countries (DJI, FCHI, GDAXI, GSPC, GSTPE, N225 and Bitcoin index). The first approach includes the employment of Hurst exponent (HE) as calculated by Rescaled Range ([Formula: see text]) fractal analysis and Wavelet Entropy (WE) in order to enhance the prediction accuracy in the long-term trend in the financial markets. The second approach includes Artificial Neural Network (ANN) algorithms application Feed forward back propagation (FFBP), Cascade Forward Back Propagation (CFBP) and Learning Vector Quantization (LVQ) algorithm for forecasting purposes. The following steps have been administered for the two aforementioned approaches: (i) HE and WE were applied. Consequently, new indicators were calculated for each index. By obtaining the indicators, the new dataset was formed and normalized by min-max normalization method’ (ii) to form the forecasting model, ANN algorithms were applied on the datasets. Based on the experimental results, it has been demonstrated that the new dataset comprised of the HE and WE indicators had a critical and determining direction with a more accurate level of forecasting modeling by the ANN algorithms. Consequently, the proposed novel method with multifarious methodology illustrates a new frontier, which could be employed in the broad field of various applied sciences to analyze pressing real-world problems and propose optimal solutions for critical decision-making processes in nonlinear, complex and dynamic environments.

scholarly journals GENERALIZED APPROACH TO HURST EXPONENT ESTIMATING BY TIME SERIES

2018 ◽  
Vol 8 (1) ◽  
pp. 28-31 ◽  
Author(s):  
Lyudmyla Kirichenko ◽  
Tamara Radivilova ◽  
Vitalii Bulakh
Keyword(s):  
Time Series ◽  
Fractal Analysis ◽  
Hurst Exponent ◽  
Hypothesis Test ◽  
Interval Estimation ◽  
Stationary Time Series ◽  
Similar Time ◽  
Self Similar ◽  
Short Time

This paper presents a generalized approach to the fractal analysis of self-similar random processes by short time series. Several stages of the fractal analysis are proposed. Preliminary time series analysis includes the removal of short-term dependence, the identification of true long-term dependence and hypothesis test on the existence of a self-similarity property. Methods of unbiased interval estimation of the Hurst exponent in cases of stationary and non-stationary time series are discussed. Methods of estimate refinement are proposed. This approach is applicable to the study of self-similar time series of different nature.

Properties of wavelet coefficients of self-similar time series

2015 ◽  
Vol 6 (1) ◽  
pp. 1492-1499 ◽  
Author(s):  
Vyacheslav V. Lyashenko ◽  
Zh. V. Deineko ◽  
M. Ayaz Ahmad
Keyword(s):  
Time Series ◽  
Wavelet Coefficients ◽  
Similar Time ◽  
Self Similar

scholarly journals Effective temperature of self-similar time series

2005 ◽  
Vol 8 (4) ◽  
pp. 761
Author(s):  
Olemskoi ◽  
Kokhan
Keyword(s):  
Time Series ◽  
Effective Temperature ◽  
Similar Time ◽  
Self Similar

scholarly journals A Study of Wavelet Analysis and Data Extraction from Second-Order Self-Similar Time Series

2013 ◽  
Vol 2013 ◽  
pp. 1-14 ◽  
Author(s):  
Leopoldo Estrada Vargas ◽  
Deni Torres Roman ◽  
Homero Toral Cruz
Keyword(s):  
Time Series ◽  
Discrete Time ◽  
Close Association ◽  
Second Order ◽  
Basis Functions ◽  
Hurst Index ◽  
Similar Time ◽  
Sample Mean ◽  
Discrete Time Series ◽  
Self Similar

Statistical analysis and synthesis of self-similar discrete time signals are presented. The analysis equation is formally defined through a special family of basis functions of which the simplest case matches the Haar wavelet. The original discrete time series is synthesized without loss by a linear combination of the basis functions after some scaling, displacement, and phase shift. The decomposition is then used to synthesize a new second-order self-similar signal with a different Hurst index than the original. The components are also used to describe the behavior of the estimated mean and variance of self-similar discrete time series. It is shown that the sample mean, although it is unbiased, provides less information about the process mean as its Hurst index is higher. It is also demonstrated that the classical variance estimator is biased and that the widely accepted aggregated variance-based estimator of the Hurst index results biased not due to its nature (which is being unbiased and has minimal variance) but to flaws in its implementation. Using the proposed decomposition, the correct estimation of theVariance Plotis described, as well as its close association with the popularLogscale Diagram.

scholarly journals A Novel Time-Sensitive Composite Similarity Model for Multivariate Time-Series Correlation Analysis

Entropy ◽  
2021 ◽  
Vol 23 (6) ◽  
pp. 731
Author(s):  
Mengxia Liang ◽  
Xiaolong Wang ◽  
Shaocong Wu
Keyword(s):  
Time Series ◽  
Correlation Analysis ◽  
Stock Price ◽  
Multivariate Time Series ◽  
Temporal Features ◽  
Proposed Model ◽  
Time Series Segmentation ◽  
Similarity Model ◽  
Dynamic Time ◽  
Investment Portfolios

Finding the correlation between stocks is an effective method for screening and adjusting investment portfolios for investors. One single temporal feature or static nontemporal features are generally used in most studies to measure the similarity between stocks. However, these features are not sufficient to explore phenomena such as price fluctuations similar in shape but unequal in length which may be caused by multiple temporal features. To research stock price volatilities entirely, mining the correlation between stocks should be considered from the point view of multiple features described as time series, including closing price, etc. In this paper, a time-sensitive composite similarity model designed for multivariate time-series correlation analysis based on dynamic time warping is proposed. First, a stock is chosen as the benchmark, and the multivariate time series are segmented by the peaks and troughs time-series segmentation (PTS) algorithm. Second, similar stocks are screened out by similarity. Finally, the rate of rising or falling together between stock pairs is used to verify the proposed model’s effectiveness. Compared with other models, the composite similarity model brings in multiple temporal features and is generalizable for numerical multivariate time series in different fields. The results show that the proposed model is very promising.

Sign in / Sign up

Export Citation Format

Share Document