Clustering complex time-series databases by using periodic components

2017 ◽  
Vol 10 (2) ◽  
pp. 89-106 ◽  
Author(s):  
Francesco Giordano ◽  
Michele La Rocca ◽  
Maria Lucia Parrella
Keyword(s):  
Time Series ◽  
Complex Time ◽  
Periodic Components

scholarly journals Analysis of Ocean Bottom Pressure Anomalies and Seismic Activities in the MedRidge Zone

2021 ◽  
Vol 13 (7) ◽  
pp. 1242
Author(s):  
Hakan S. Kutoglu ◽  
Kazimierz Becek
Keyword(s):  
Time Series ◽  
Mass Change ◽  
Ocean Bottom ◽  
Bottom Pressure ◽  
Vertical Movements ◽  
Ocean Bottom Pressure ◽  
Continuous Mass ◽  
Mediterranean Ridge Accretionary Complex ◽  
Gravity Recovery ◽  
Periodic Components

The Mediterranean Ridge accretionary complex (MAC) is a product of the convergence of Africa–Europe–Aegean plates. As a result, the region exhibits a continuous mass change (horizontal/vertical movements) that generates earthquakes. Over the last 50 years, approximately 430 earthquakes with M ≥ 5, including 36 M ≥ 6 earthquakes, have been recorded in the region. This study aims to link the ocean bottom deformations manifested through ocean bottom pressure variations with the earthquakes’ time series. To this end, we investigated the time series of the ocean bottom pressure (OBP) anomalies derived from the Gravity Recovery and Climate Experiment (GRACE) and GRACE Follow-On (GRACE-FO) satellite missions. The OBP time series comprises a decreasing trend in addition to 1.02, 1.52, 4.27, and 10.66-year periodic components, which can be explained by atmosphere, oceans, and hydrosphere (AOH) processes, the Earth’s pole movement, solar activity, and core–mantle coupling. It can be inferred from the results that the OBP anomalies time series/mass change is linked to a rising trend and periods in the earthquakes’ energy time series. Based on this preliminary work, ocean-bottom pressure variation appears to be a promising lead for further research.

scholarly journals Scale-dependent intrinsic entropies of complex time series

2016 ◽  
Vol 374 (2065) ◽  
pp. 20150204 ◽  
Author(s):  
Jia-Rong Yeh ◽  
Chung-Kang Peng ◽  
Norden E. Huang
Keyword(s):  
Time Series ◽  
Time Scales ◽  
Spatial Scales ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
Complex Time ◽  
Multi Scale ◽  
Mode Decomposition ◽  
Simulated Time ◽  
Simulated Time Series

Multi-scale entropy (MSE) was developed as a measure of complexity for complex time series, and it has been applied widely in recent years. The MSE algorithm is based on the assumption that biological systems possess the ability to adapt and function in an ever-changing environment, and these systems need to operate across multiple temporal and spatial scales, such that their complexity is also multi-scale and hierarchical. Here, we present a systematic approach to apply the empirical mode decomposition algorithm, which can detrend time series on various time scales, prior to analysing a signal’s complexity by measuring the irregularity of its dynamics on multiple time scales. Simulated time series of fractal Gaussian noise and human heartbeat time series were used to study the performance of this new approach. We show that our method can successfully quantify the fractal properties of the simulated time series and can accurately distinguish modulations in human heartbeat time series in health and disease.

scholarly journals An Empirical Mode-Spatial Model for Environmental Data Imputation

Hydrology ◽  
2018 ◽  
Vol 5 (4) ◽  
pp. 63 ◽  
Author(s):  
Benjamin Nelsen ◽  
D. Williams ◽  
Gustavious Williams ◽  
Candace Berrett
Keyword(s):  
Time Series ◽  
Spatial Data ◽  
Missing Values ◽  
Time Series Data ◽  
Environmental Data ◽  
Series Data ◽  
Data Imputation ◽  
Accurate Data ◽  
Target Station ◽  
Periodic Components

Complete and accurate data are necessary for analyzing and understanding trends in time-series datasets; however, many of the available time-series datasets have gaps that affect the analysis, especially in the earth sciences. As most available data have missing values, researchers use various interpolation methods or ad hoc approaches to data imputation. Since the analysis based on inaccurate data can lead to inaccurate conclusions, more accurate data imputation methods can provide accurate analysis. We present a spatial-temporal data imputation method using Empirical Mode Decomposition (EMD) based on spatial correlations. We call this method EMD-spatial data imputation or EMD-SDI. Though this method is applicable to other time-series data sets, here we demonstrate the method using temperature data. The EMD algorithm decomposes data into periodic components called intrinsic mode functions (IMF) and exactly reconstructs the original signal by summing these IMFs. EMD-SDI initially decomposes the data from the target station and other stations in the region into IMFs. EMD-SDI evaluates each IMF from the target station in turn and selects the IMF from other stations in the region with periodic behavior most correlated to target IMF. EMD-SDI then replaces a section of missing data in the target station IMF with the section from the most closely correlated IMF from the regional stations. We found that EMD-SDI selects the IMFs used for reconstruction from different stations throughout the region, not necessarily the station closest in the geographic sense. EMD-SDI accurately filled data gaps from 3 months to 5 years in length in our tests and favorably compares to a simple temporal method. EMD-SDI leverages regional correlation and the fact that different stations can be subject to different periodic behaviors. In addition to data imputation, the EMD-SDI method provides IMFs that can be used to better understand regional correlations and processes.

scholarly journals Disentangling the stochastic behavior of complex time series

2016 ◽  
Vol 6 (1) ◽  
Author(s):  
Mehrnaz Anvari ◽  
M. Reza Rahimi Tabar ◽  
Joachim Peinke ◽  
Klaus Lehnertz
Keyword(s):  
Time Series ◽  
Stochastic Behavior ◽  
Complex Time

Time series analysis of Holocene climate data

1990 ◽  
Vol 330 (1615) ◽  
pp. 601-616 ◽  
Keyword(s):  
Time Series ◽  
Time Series Analysis ◽  
Time Domain ◽  
Small Sample ◽  
Climate Data ◽  
Holocene Climate ◽  
Series Analysis ◽  
Window Method ◽  
Band Limited ◽  
Periodic Components

Holocene climate records are imperfect proxies for processes containing complicated mixtures of periodic and random signals. I summarize time series analysis methods for such data with emphasis on the multiple-data-window technique. This method differs from conventional approaches to time series analysis in that a set of data tapers is applied to the data in the time domain before Fourier transforming. The tapers, or data windows, are discrete prolate spheroidal sequences characterized as being the most nearly band-limited functions possible among functions defined on a finite time domain. The multiple-window method is a small-sample theory and essentially an inverse method applied to the finite Fourier transform. For climate data it has the major advantage of providing a narrowband F -test for the presence and significance of periodic components and of being able to separate them from the non-deterministic part of the process. Confidence intervals for the estimated quantities are found by jackknifing across windows. Applied to 14 C records, this method confirms the presence of the ‘Suess wiggles’ and give an estimated period of 208.2 years. Analysis of the thickness variations of bristlecone pine growth rings shows a general absence of direct periodic components but a variation in the structure of the time series with a 2360-year period.

scholarly journals Analysis of the time series of waste water quality at the inflow of the wastewater treatment plant and transfer functions

2014 ◽  
Vol 62 (1) ◽  
pp. 55-59 ◽  
Author(s):  
Ivan Nesmerak ◽  
Sarka D. Blazkova
Keyword(s):  
Time Series ◽  
Wastewater Treatment ◽  
Wastewater Treatment Plant ◽  
Transfer Functions ◽  
Treatment Plant ◽  
Total Precipitation ◽  
Periodic Components ◽  
The Relationship ◽  
Pollution Loads ◽  
Daily Total

Abstract Time series of the daily total precipitation, daily wastewater discharges and daily concentrations and pollution loads of BOD5, COD, SS, N-NH4, Ntot and Ptot were analyzed at the inflow to the wastewater treatment plant (WWTP) for a larger city in 2004-2009 (WWTP is loaded by pollution from 435,000 equivalent inhabitants). The time series of the outflow from a WWTP was also available for 2007. The time series of daily total precipitation, daily wastewater discharges, concentrations and pollution loads at the inflow and outflow from the WWTP were standardized year by year to exclude a long-term trend, and periodic components with a period of 7 days and 365 days (and potentially also 186.5 days) were excluded from the standardized series. However, these two operations eliminated only a small part of the variance; there was a substantial reduction in the variance only for ammonium nitrogen and total nitrogen at the inflow and outflow from a WWTP. The relationship between the inflow into a WWTP and the outflow from a WWTP for the concentrations and pollution loads was described by simple transfer functions (SISO models) and more complicated transfer functions (MISO models). A simple transfer function (SISO model) was employed to describe the relationship between the daily total precipitation and the wastewater discharge.

Analysis of Time Series Based on a New Entropy Plane by Using Weighted Dispersion Pattern

2021 ◽  
Vol 31 (09) ◽  
pp. 2150128
Author(s):  
Guyue Qin ◽  
Pengjian Shang
Keyword(s):  
Time Series ◽  
Financial Markets ◽  
Stock Markets ◽  
Simulated Data ◽  
Tsallis Entropy ◽  
Dispersion Pattern ◽  
Complex Time ◽  
Plane Method ◽  
Stock Indexes ◽  
Analysis Of Time Series

Complexity is an important feature of complex time series. In this paper, we construct a weighted dispersion pattern and propose a new entropy plane using past Tsallis entropy and past Rényi entropy by using weighted dispersion pattern (PTEWD and PREWD, respectively), to quantify the complexity of time series. Through analyzing simulated data and actual data, we have verified the reliability of the entropy plane method. This entropy plane successfully distinguishes American and Chinese stock indexes, as well as developed and emergent stock markets. We introduce PTEWD and PREWD into multiscale settings, which could also well distinguish different stock markets. The results show that the new entropy plane could be used as an effective tool to distinguish financial markets.

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