Detrended Correlogram Method for Non-Stationary Time-Series Analysis

2021 ◽  
pp. 2250012
Author(s):  
G. F. Zebende ◽  
E. F. Guedes
Keyword(s):  
Time Series ◽  
Time Series Analysis ◽  
Correlation Coefficient ◽  
Memory Effect ◽  
Cross Correlation ◽  
Time Lag ◽  
Stationary Time Series ◽  
Time Lags ◽  
Statistical Tool ◽  
Auto Correlation

A correlogram is a statistical tool that is used to check time-series memory by computing the auto-correlation coefficient as a function of the time lag. If the time-series has no memory, then the auto-correlation must be close to zero for any time lag, otherwise if there is a memory, then the auto-correlations must be significantly different from zero. Therefore, based on the robust detrended cross-correlation coefficient, [Formula: see text], we propose the detrended correlogram method in this paper, which will be tested for some time-series (simulated and empirical). This new statistical tool is able to visualize a complete map of the auto-correlation for many time lags and time-scales, and can therefore analyze the memory effect for any time-series.

scholarly journals GRACE-Derived Time Lag of Mekong Estuarine Freshwater Transport in the Western South China Sea Validated by Isotopic Tracer Age

2021 ◽  
Vol 13 (6) ◽  
pp. 1193
Author(s):  
Zhongtian Ma ◽  
Hok Sum Fok ◽  
Linghao Zhou
Keyword(s):  
Time Series ◽  
South China Sea ◽  
South China ◽  
Cross Correlation ◽  
Time Lag ◽  
Time Lags ◽  
Substantial Impact ◽  
China Sea ◽  
Freshwater Transport ◽  
Western South China Sea

Estuarine freshwater transport has a substantial impact on the near-shore ecosystem and coastal ocean environment away from the estuary. This paper introduces two independent methods to track the Mekong freshwater-induced mass transport by calculating the time lag (or equivalently, the phase) between in situ Mekong basin runoff and the equivalent water height (EWH) time series over the western South China Sea from a gravity recovery and climate experiment (GRACE). The first method is the harmonic analysis that determines the phase difference between annual components of the two time series (called the P-method), and the other is the cross-correlation analysis that directly obtains the time lag by shifting the lagged time series forward to attain the highest cross-correlation between the two time series (called the C-method). Using a three-year rolling window, the time lag variations in three versions of GRACE between 2005 and 2012 are computed for demonstrating the consistency of the results. We found that the time lag derived from the P-method is, on average, slightly larger and more variable than that from the C-method. A comparison of our gridded time lag against the age determined via radium isotopes in September, 2007 by Chen et al. (2010) revealed that our gridded time lag results were in good agreement with most isotope-derived ages, with the largest difference less than 6 days. Among the three versions of the GRACE time series, CSR Release 05 performed the best. The lowest standard deviation of time lag was ~1.6 days, calculated by the C-method, whereas the mean difference for all the time lags from the isotope-derived ages is ~1 day by P-method. This study demonstrates the potential of monitoring Mekong estuarine freshwater transport over the western South China Sea by GRACE.

SEVERAL FUNDAMENTAL PROPERTIES OF DCCA CROSS-CORRELATION COEFFICIENT

Fractals ◽  
2017 ◽  
Vol 25 (02) ◽  
pp. 1750017 ◽  
Author(s):  
XIAOJUN ZHAO ◽  
PENGJIAN SHANG ◽  
JINGJING HUANG
Keyword(s):  
Time Series ◽  
Correlation Coefficient ◽  
Cross Correlation ◽  
Stationary Time Series ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
Linear Measure ◽  
Fundamental Properties ◽  
Cross Correlation Analysis ◽  
Synthetic Time Series

The (detrended cross-correlation analysis) DCCA cross-correlation coefficient was proposed to measure the level of long-range cross-correlations between two non-stationary time series on multiple time scales. It has been applied to diverse areas of interest, although many properties of this method are not clear. In this paper, we theoretically study several fundamental properties of the DCCA cross-correlation coefficient, which contributes to acquiring more statistical characteristics of this measure. We resort to a synthetic time series that is followed by the integration and the detrending procedures of the DCCA cross-correlation coefficient, which divide the steps to estimate the coefficient into two portions. The former portion, including the integration and the detrending, is proved to be a linear transformation. The second portion is devoted to measuring Pearson’s [Formula: see text] between two synthetic time series. We confirm that the DCCA cross-correlation coefficient is also a linear measure by definition. The simulations including the ARFIMA processes and the multifractal binomial measures are numerically analyzed, which confirm the theoretical analysis.

scholarly journals Dependency Structures in Differentially Coded Cardiovascular Time Series

2017 ◽  
Vol 2017 ◽  
pp. 1-17 ◽  
Author(s):  
Tatjana Tasic ◽  
Sladjana Jovanovic ◽  
Omer Mohamoud ◽  
Tamara Skoric ◽  
Nina Japundzic-Zigon ◽  
...  
Keyword(s):  
Blood Pressure ◽  
Time Series ◽  
Systolic Blood Pressure ◽  
Dynamic Range ◽  
Time Lag ◽  
Conditional Entropy ◽  
Pulse Interval ◽  
Time Lags ◽  
Aging Rats ◽  
Male Wistar Rats

Objectives. This paper analyses temporal dependency in the time series recorded from aging rats, the healthy ones and those with early developed hypertension. The aim is to explore effects of age and hypertension on mutual sample relationship along the time axis.Methods. A copula method is applied to raw and to differentially coded signals. The latter ones were additionally binary encoded for a joint conditional entropy application. The signals were recorded from freely moving male Wistar rats and from spontaneous hypertensive rats, aged 3 months and 12 months.Results. The highest level of comonotonic behavior of pulse interval with respect to systolic blood pressure is observed at time lagsτ=0, 3, and 4, while a strong counter-monotonic behavior occurs at time lagsτ=1and 2.Conclusion. Dynamic range of aging rats is considerably reduced in hypertensive groups. Conditional entropy of systolic blood pressure signal, compared to unconditional, shows an increased level of discrepancy, except for a time lag 1, where the equality is preserved in spite of the memory of differential coder. The antiparallel streams play an important role at single beat time lag.

Provincial Level Time Series Analysis : Community Mobility and COVID-19 Daily Cases in Turin, Italy (Preprint)

2021 ◽  
Author(s):  
Dayana Benny
Keyword(s):  
Time Series ◽  
Time Series Analysis ◽  
Cross Correlation ◽  
Provincial Level ◽  
Epidemic Curve ◽  
The Past ◽  
Series Analysis ◽  
Community Mobility ◽  
Cross Correlation Analysis ◽  
Restrictive Measures

BACKGROUND Turin, a province in the Piedmont region sees second highest new COVID-19 infections in Northern part of Italy as of March 31, 2021. During the first wave of pandemic, many restrictive measures were introduced in this province. There are many studies that conducted time series analysis of various regions in Italy, but studies that are analysing the data in province level are limited. Also, no applications of Cross Correlation Function(CCF) have been proposed to analyse relationships between COVID-19 new cases and community mobility at the provincial level in Italy. OBJECTIVE The goal of this time series analysis is to find how the restrictive measures in Turin province, Italy impacted community mobility and helped in flattening the epidemic curve during the first wave of the pandemic. METHODS A simple time series analysis is conducted in this study to analyse whether there is an association between COVID-19 daily cases and community mobility. In this study, we analysed whether the time series of the parameter that estimates the reproduction of infection in the outbreak is related to the past lags of community mobility time series by performing cross-correlation analysis. RESULTS Multiple regression is carried out in which the R0 variable is a linear function of past lags 6, 7, 8, and 1 of the community mobility variable and all coefficients are statistically significant where P = 0.024043, 2.69e-05, 0.045350 and 0.000117 respectively. The cross-correlation between data fitted from the significant past lags of community mobility and transformed basic reproduction number (R0) time-series is obtained in such a manner that the R0 of a day is related to the past lags of community mobility in Turin province. CONCLUSIONS Our analysis shows that the restrictive measures are having an impact on community mobility during the first wave of COVID-19 and it can be related to the reported secondary cases of COVID-19 in Turin province at that time. Through further improvement, this simple model could serve as preliminary research for developing right preventive methods during the early stages of an epidemic.

Provincial Level Time Series Analysis : Community Mobility and COVID-19 Daily Cases in Turin, Italy (Preprint)

2021 ◽  
Author(s):  
Dayana Benny
Keyword(s):  
Time Series ◽  
Time Series Analysis ◽  
Cross Correlation ◽  
Provincial Level ◽  
Epidemic Curve ◽  
The Past ◽  
Series Analysis ◽  
Community Mobility ◽  
Cross Correlation Analysis ◽  
Restrictive Measures

BACKGROUND Turin, a province in the Piedmont region sees second highest new COVID-19 infections in Northern part of Italy as of March 31, 2021. During the first wave of pandemic, many restrictive measures were introduced in this province. There are many studies that conducted time series analysis of various regions in Italy, but studies that are analysing the data in province level are limited. Also, no applications of Cross Correlation Function(CCF) have been proposed to analyse relationships between COVID-19 new cases and community mobility at the provincial level in Italy. OBJECTIVE The goal of this time series analysis is to find how the restrictive measures in Turin province, Italy impacted community mobility and helped in flattening the epidemic curve during the first wave of the pandemic. METHODS A simple time series analysis is conducted in this study to analyse whether there is an association between COVID-19 daily cases and community mobility. In this study, we analysed whether the time series of the parameter that estimates the reproduction of infection in the outbreak is related to the past lags of community mobility time series by performing cross-correlation analysis. RESULTS Multiple regression is carried out in which the R0 variable is a linear function of past lags 6, 7, 8, and 1 of the community mobility variable and all coefficients are statistically significant where P = 0.024043, 2.69e-05, 0.045350 and 0.000117 respectively. The cross-correlation between data fitted from the significant past lags of community mobility and transformed basic reproduction number (R0) time-series is obtained in such a manner that the R0 of a day is related to the past lags of community mobility in Turin province. CONCLUSIONS Our analysis shows that the restrictive measures are having an impact on community mobility during the first wave of COVID-19 and it can be related to the reported secondary cases of COVID-19 in Turin province at that time. Through further improvement, this simple model could serve as preliminary research for developing right preventive methods during the early stages of an epidemic.

scholarly journals Modeling Complex System Correlation Using Detrended Cross-Correlation Coefficient

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Keqiang Dong ◽  
Hong Zhang ◽  
You Gao
Keyword(s):  
Complex System ◽  
Time Series ◽  
Correlation Coefficient ◽  
Cross Correlation ◽  
Heavy Tails ◽  
Correlation Property ◽  
Traffic Time Series ◽  
Cross Correlations ◽  
The Cross ◽  
Active Research

The understanding of complex systems has become an area of active research for physicists because such systems exhibit interesting dynamical properties such as scale invariance, volatility correlation, heavy tails, and fractality. We here focus on traffic dynamic as an example of a complex system. By applying the detrended cross-correlation coefficient method to traffic time series, we find that the traffic fluctuation time series may exhibit cross-correlation characteristic. Further, we show that two traffic speed time series derived from adjacent sections exhibit much stronger cross-correlations than the two speed series derived from adjacent lanes. Similarly, we also demonstrate that the cross-correlation property between the traffic volume variables from two adjacent sections is stronger than the cross-correlation property between the volume variables of adjacent lanes.

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