MINIMIZING PERIODIC TRENDS BY APPLYING LAPLACE TRANSFORM

Fractals ◽  
2011 ◽  
Vol 19 (02) ◽  
pp. 203-211 ◽  
Author(s):  
AIJING LIN ◽  
PENGJIAN SHANG
Keyword(s):  
Time Series ◽  
Laplace Transform ◽  
Moving Average ◽  
Stationary Time Series ◽  
Fluctuation Analysis ◽  
Range Analysis ◽  
Long Range Correlations ◽  
Cross Correlation Analysis ◽  
Rescaled Range Analysis ◽  
Cross Correlations

Rescaled range analysis (R/S analysis), detrended fluctuation analysis (DFA) and detrended moving average (DMA) are widely-used methods for detection of long-range correlations in time series. Detrended cross-correlation analysis (DCCA) is a recently developed method to quantify the cross-correlations of two non-stationary time series. Another method for studying auto-correlations and cross-correlations was presented by Sergio Arianos and Anna Carbone in 2009. Recent studies have reported the susceptibility of this methods to periodic trends, which can result in spurious crossovers. In this paper, we propose the modified methods base on Laplace transform to minimizing the effect of periodic trends. The effectiveness of our techniques are demonstrated on stock data corrupted with periodic trends.

Measuring long-range correlations in news flow intensity time series

2017 ◽  
Vol 28 (08) ◽  
pp. 1750103 ◽  
Author(s):  
Sergei Sidorov ◽  
Alexey Faizliev ◽  
Vladimir Balash
Keyword(s):  
Time Series ◽  
Fourier Transform ◽  
Long Range ◽  
Fluctuation Analysis ◽  
Range Analysis ◽  
Crossover Effect ◽  
Transform Method ◽  
Long Range Correlations ◽  
Rescaled Range Analysis ◽  
Flow Intensity

We consider the flow intensity of economic and financial news taken from a nine-month period of 2015. This data is found to be well approximated by a persistent self-affine walk. It is characterized by a Hurst exponent of [Formula: see text] over three orders of magnitude in time ranging from minutes to several days. In this paper, we use the Detrended Fluctuation Analysis (DFA) of order 1, Rescaled Range Analysis (R/S) and Fourier Transform Method (FTM) to examine long-range auto-correlation and self-similarity of time series of news flow intensity. DFA method allowed us to reveal a strong scaling behavior as well as to detect a distinct crossover effect. On the other hand, it turns out that for the classic R/S analysis and Fourier transform techniques, the scaling regimes and/or positions of cross-overs are hard to define.

MODELING CROSS-CORRELATIONS OF TRAFFIC FLOW

2010 ◽  
Vol 20 (10) ◽  
pp. 3323-3328 ◽  
Author(s):  
PENGJIAN SHANG ◽  
KEQIANG DONG ◽  
SANTI KAMAE
Keyword(s):  
Time Series ◽  
Traffic Flow ◽  
Power Law ◽  
Cross Correlation ◽  
Heavy Tails ◽  
Fluctuation Analysis ◽  
Cross Correlation Analysis ◽  
Cross Correlations ◽  
Large Increment ◽  
Active Research

The study of diverse natural and nonstationary signals has recently become an area of active research for physicists. This is because these signals exhibit interesting dynamical properties such as scale invariance, volatility correlation, heavy tails and fractality. The focus of the present paper is on the intriguing power-law autocorrelations and cross-correlations in traffic series. Detrended Cross-Correlation Analysis (DCCA) is used to study the traffic flow fluctuations. It is demonstrated that the time series, observed on the Anhua-Bridge highway in the Beijing Third Ring Road (BTRR), may exhibit power-law cross-correlations when they come from two adjacent sections or lanes. This indicates that a large increment in one traffic variable is more likely to be followed by large increment in the other traffic variable. However, for traffic time series derived from nonadjacent sections or lanes, we find that even though they are power-law autocorrelated, there is no cross-correlation between them with a unique exponent. Our results show that DCCA techniques based on Detrended Fluctuation Analysis (DFA) can be used to analyze and interpret the traffic flow.

scholarly journals Multifractal Detrended Cross-Correlation Analysis of Global Methane and Temperature

2020 ◽  
Vol 12 (3) ◽  
pp. 557 ◽  
Author(s):  
Chris G. Tzanis ◽  
Ioannis Koutsogiannis ◽  
Kostas Philippopoulos ◽  
Nikolaos Kalamaras
Keyword(s):  
Time Series ◽  
Correlation Analysis ◽  
Cross Correlation ◽  
Lower Troposphere ◽  
Fluctuation Analysis ◽  
Tropospheric Temperature ◽  
Long Range Correlations ◽  
Temperature Anomalies ◽  
Cross Correlation Analysis ◽  
The Cross

Multifractal Detrended Cross-Correlation Analysis (MF-DCCA) was applied to time series of global methane concentrations and remotely-sensed temperature anomalies of the global lower and mid-troposphere, with the purpose of investigating the multifractal characteristics of their cross-correlated time series and examining their interaction in terms of nonlinear analysis. The findings revealed the multifractal nature of the cross-correlated time series and the existence of positive persistence. It was also found that the cross-correlation in the lower troposphere displayed more abundant multifractal characteristics when compared to the mid-troposphere. The source of multifractality in both cases was found to be mainly the dependence of long-range correlations on different fluctuation magnitudes. Multifractal Detrended Fluctuation Analysis (MF-DFA) was also applied to the time series of global methane and global lower and mid-tropospheric temperature anomalies to separately study their multifractal properties. From the results, it was found that the cross-correlated time series exhibit similar multifractal characteristics to the component time series. This could be another sign of the dynamic interaction between the two climate variables.

FORECASTING SMOOTHED NON-STATIONARY TIME SERIES USING GENETIC ALGORITHMS

2007 ◽  
Vol 18 (06) ◽  
pp. 1071-1086 ◽  
Author(s):  
P. NOROUZZADEH ◽  
B. RAHMANI ◽  
M. S. NOROUZZADEH
Keyword(s):  
Genetic Algorithm ◽  
Time Series ◽  
Kernel Smoothing ◽  
Financial Time Series ◽  
Stationary Time Series ◽  
Time Variability ◽  
Fluctuation Analysis ◽  
Multifractal Detrended Fluctuation Analysis ◽  
Long Range Correlations ◽  
Smoothing Methods

We introduce kernel smoothing method to extract the global trend of a time series and remove short time scales variations and fluctuations from it. A multifractal detrended fluctuation analysis (MF-DFA) shows that the multifractality nature of TEPIX returns time series is due to both fatness of the probability density function of returns and long range correlations between them. MF-DFA results help us to understand how genetic algorithm and kernel smoothing methods act. Then we utilize a recently developed genetic algorithm for carrying out successful forecasts of the trend in financial time series and deriving a functional form of Tehran price index (TEPIX) that best approximates the time variability of it. The final model is mainly dominated by a linear relationship with the most recent past value, while contributions from nonlinear terms to the total forecasting performance are rather small.

scholarly journals Assessment of long-range cross-correlations in cardiorespiratory and cardiovascular interactions

2021 ◽  
Vol 379 (2212) ◽  
Author(s):  
Akio Nakata ◽  
Miki Kaneko ◽  
Chinami Taki ◽  
Naoko Evans ◽  
Taiki Shigematsu ◽  
...  
Keyword(s):  
Time Series ◽  
Long Range ◽  
Moving Average ◽  
Time Lag ◽  
Higher Order ◽  
Cross Correlation Analysis ◽  
Challenges And Opportunities ◽  
Cross Correlations ◽  
Different Order

We propose higher-order detrending moving-average cross-correlation analysis (DMCA) to assess the long-range cross-correlations in cardiorespiratory and cardiovascular interactions. Although the original (zeroth-order) DMCA employs a simple moving-average detrending filter to remove non-stationary trends embedded in the observed time series, our approach incorporates a Savitzky–Golay filter as a higher-order detrending method. Because the non-stationary trends can adversely affect the long-range correlation assessment, the higher-order detrending serves to improve accuracy. To achieve a more reliable characterization of the long-range cross-correlations, we demonstrate the importance of the following steps: correcting the time scale, confirming the consistency of different order DMCAs, and estimating the time lag between time series. We applied this methodological framework to cardiorespiratory and cardiovascular time series analysis. In the cardiorespiratory interaction, respiratory and heart rate variability (HRV) showed long-range auto-correlations; however, no factor was shared between them. In the cardiovascular interaction, beat-to-beat systolic blood pressure and HRV showed long-range auto-correlations and shared a common long-range, cross-correlated factor. This article is part of the theme issue ‘Advanced computation in cardiovascular physiology: new challenges and opportunities’.

MULTIFRACTAL CROSS-CORRELATION ANALYSIS BASED ON STATISTICAL MOMENTS

Fractals ◽  
2012 ◽  
Vol 20 (03n04) ◽  
pp. 271-279 ◽  
Author(s):  
JING WANG ◽  
PENGJIAN SHANG ◽  
WEIJIE GE
Keyword(s):  
Time Series ◽  
Correlation Analysis ◽  
Cross Correlation ◽  
Moving Average ◽  
Statistical Moments ◽  
Comparative Performance ◽  
Cross Correlation Analysis ◽  
Cross Correlations ◽  
Better Than

We introduce a new method, multifractal cross-correlation analysis based on statistical moments (MFSMXA), to investigate the long-term cross-correlations and cross-multifractality between time series generated from complex system. Efficiency of this method is shown on multifractal series, comparing with the well-known multifractal detrended cross-correlation analysis (MFXDFA) and multifractal detrending moving average cross-correlation analysis (MFXDMA). We further apply this method on volatility time series of DJIA and NASDAQ indices, and find some interesting results. The MFSMXA has comparative performance with MFXDMA and sometimes perform slightly better than MFXDFA. Multifractal nature exists in volatility series. In addition, we find that the cross-multifractality of volatility series is mainly due to their cross-correlations, via comparing the MFSMXA results for original series with those for shuffled series.

THE ROBUST FRACTAL ANALYSIS OF TIME SERIES: CONCERNING SIGNAL CLASS AND DATA LENGTH

Fractals ◽  
2011 ◽  
Vol 19 (01) ◽  
pp. 29-49 ◽  
Author(s):  
M. H. FATTAHI ◽  
N. TALEBBEYDOKHTI ◽  
G. R. RAKHSHANDEHROO ◽  
A. SHAMSAI ◽  
E. NIKOOEE
Keyword(s):  
Time Series ◽  
Fractal Analysis ◽  
Variation Method ◽  
Fluctuation Analysis ◽  
Analysis Method ◽  
Range Analysis ◽  
Rescaled Range Analysis ◽  
Data Points ◽  
Data Length ◽  
Analysis Of Time Series

In the present paper, the influence of the signal class (fBm/fGn) and the data length of time series on choosing the robust fractal analysis method have been studied. More than 1000 fBm/fGn generated time series in short, intermediate and long ranges have been analyzed using common fractal analysis methods. The chosen techniques were power spectral density, detrended fluctuation analysis, rescaled range analysis, box counting, average wavelet coefficients, and the variation method. Numerous graphs indicating the suitability of each method in terms of biases in calculating the fundamental fractal feature of time series, Hurst coefficient, were employed. The results strongly emphasized the crucial influence of the signal class as well as the data length when choosing the appropriate fractal analysis method. Furthermore, as a step forward, a study on the number of data points present in a classified class/length was performed. The effect of the number of data points could not be neglected either. Based on the results, a strategy flowchart for fractal analysis of time series has been proposed. Finally, as an empirical example, the monthly, weekly and daily scaled flow time series of Ghar-e-Aghaj River have been analyzed within the framework of the strategy flowchart.

CROSS-CORRELATIONS BETWEEN BACTERIAL FOODBORNE DISEASES AND METEOROLOGICAL FACTORS BASED ON MF-DCCA: A CASE IN SOUTH KOREA

Fractals ◽  
2020 ◽  
Vol 28 (03) ◽  
pp. 2050046 ◽  
Author(s):  
JIAN WANG ◽  
WEI SHAO ◽  
JUNSEOK KIM
Keyword(s):  
Time Series ◽  
South Korea ◽  
Long Range ◽  
Cross Correlation ◽  
Meteorological Factors ◽  
Foodborne Diseases ◽  
Long Range Correlations ◽  
Cross Correlation Analysis ◽  
Cross Correlations ◽  
Series Pair

In this study, we apply multifractal detrended cross-correlation analysis (MF-DCCA) to examine the nonlinear cross-correlations between bacterial foodborne diseases (FBDs) and meteorological factors in South Korea. The results demonstrate that power-law cross-correlations between bacterial FBD and meteorological factors exist; and that multifractal characteristics are significant. In addition, the cross-correlation between bacterial FBD and temperature is more persistent than that between bacterial FBD and humidity. Comparison of the strengths of multifractal spectra showed that the degree of multifractality of the Humidity/FBD time series pair is greater than that of Temperature/FBD pair; this indicates that the monthly number of outpatient FBD cases is more sensitive to humidity. Furthermore, to document the major source of multifractality, we shuffle the original series. We conclude that both the long-range correlations and fat-tail distribution contribute to the multifractality of the Temperature/FBD time series pair. The long-range correlations are also an important source that contributes to the multifractality between bacterial FBD and humidity time series.

Return Intervals Analysis of the Sunspot Time Series

2010 ◽  
Vol 29-32 ◽  
pp. 1144-1149
Author(s):  
Jie Fan ◽  
Wan Qing Li ◽  
Hong Zhang ◽  
Ke Qiang Dong
Keyword(s):  
Time Series ◽  
Long Range ◽  
Threshold Values ◽  
Range Analysis ◽  
Scaling Method ◽  
Long Range Correlations ◽  
Rescaled Range ◽  
Rescaled Range Analysis

Rescaled range analysis (R/S) method is a scaling method commonly used for detecting the long-range correlations in many time series. The aim of this paper is to show that, using the rescaled range analysis on sunspot time series, how the threshold values q affects the correlations of the return intervals for events above a certain threshold q. We find that both the original records and the return intervals are long-range correlated.

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