scholarly journals Towards Understanding the Interconnection between Celestial Pole Motion and Earth’s Magnetic Field Using Space Geodetic Techniques

Sensors ◽  
2021 ◽  
Vol 21 (22) ◽  
pp. 7555
Author(s):  
Sadegh Modiri ◽  
Robert Heinkelmann ◽  
Santiago Belda ◽  
Zinovy Malkin ◽  
Mostafa Hoseini ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Time Series ◽  
Geomagnetic Field ◽  
Stationary Time Series ◽  
Wavelet Coherence ◽  
Time Lags ◽  
Time Frequency ◽  
Pole Motion ◽  
Celestial Pole ◽  
Wavelet Coherence Analysis

The understanding of forced temporal variations in celestial pole motion (CPM) could bring us significantly closer to meeting the accuracy goals pursued by the Global Geodetic Observing System (GGOS) of the International Association of Geodesy (IAG), i.e., 1 mm accuracy and 0.1 mm/year stability on global scales in terms of the Earth orientation parameters. Besides astronomical forcing, CPM excitation depends on the processes in the fluid core and the core–mantle boundary. The same processes are responsible for the variations in the geomagnetic field (GMF). Several investigations were conducted during the last decade to find a possible interconnection of GMF changes with the length of day (LOD) variations. However, less attention was paid to the interdependence of the GMF changes and the CPM variations. This study uses the celestial pole offsets (CPO) time series obtained from very long baseline interferometry (VLBI) observations and data such as spherical harmonic coefficients, geomagnetic jerk, and magnetic field dipole moment from a state-of-the-art geomagnetic field model to explore the correlation between them. In this study, we use wavelet coherence analysis to compute the correspondence between the two non-stationary time series in the time–frequency domain. Our preliminary results reveal interesting common features in the CPM and GMF variations, which show the potential to improve the understanding of the GMF’s contribution to the Earth’s rotation. Special attention is given to the corresponding signal between FCN and GMF and potential time lags between geomagnetic jerks and rotational variations.

Modeling and forecasting multifractal wavelet scale: Western market versus eastern market

2018 ◽  
Vol 29 (11) ◽  
pp. 1850109 ◽  
Author(s):  
Emrah Oral ◽  
Gazanfer Unal
Keyword(s):  
Time Series ◽  
Time Series Data ◽  
Moving Average ◽  
Price Change ◽  
Wavelet Coherence ◽  
Series Data ◽  
Primary Study ◽  
Fluctuation Analysis ◽  
Multifractal Detrended Fluctuation Analysis ◽  
Time Frequency

This leading primary study is about modeling multifractal wavelet scale time series data using multiple wavelet coherence (MWC), continuous wavelet transform (CWT) and multifractal detrended fluctuation analysis (MFDFA) and forecasting with vector autoregressive fractionally integrated moving average (VARFIMA) model. The data is acquired from Yahoo Finances!, which is composed of 1671 daily stock market of eastern (NIKKEI, TAIEX, KOPSI) and western (SP500, FTSE, DAX) markets. Once the co-movement dependencies on time-frequency space are determined with MWC, the coherent data is extracted out of raw data at a certain scale by using CWT. The multifractal behavior of the extracted series is verified by MFDFA and its local Hurst exponents have been calculated obtaining root mean square of residuals at each scale. This inter-calculated fluctuation function time series has been re-scaled and used to estimate the process with VARFIMA model and forecasted accordingly. The results have shown that the direction of price change is determined without difficulty and the efficiency of forecasting has been substantially increased using highly correlated multifractal wavelet scale time series data.

scholarly journals Application of the cross wavelet transform and wavelet coherence to geophysical time series

2004 ◽  
Vol 11 (5/6) ◽  
pp. 561-566 ◽  
Author(s):  
A. Grinsted ◽  
J. C. Moore ◽  
S. Jevrejeva
Keyword(s):  
Time Series ◽  
Wavelet Transform ◽  
Statistical Significance ◽  
Wavelet Coherence ◽  
The Arctic ◽  
Arctic Oscillation Index ◽  
Time Frequency ◽  
Cross Wavelet Transform ◽  
The Cross ◽  
Cross Wavelet

Abstract. Many scientists have made use of the wavelet method in analyzing time series, often using popular free software. However, at present there are no similar easy to use wavelet packages for analyzing two time series together. We discuss the cross wavelet transform and wavelet coherence for examining relationships in time frequency space between two time series. We demonstrate how phase angle statistics can be used to gain confidence in causal relationships and test mechanistic models of physical relationships between the time series. As an example of typical data where such analyses have proven useful, we apply the methods to the Arctic Oscillation index and the Baltic maximum sea ice extent record. Monte Carlo methods are used to assess the statistical significance against red noise backgrounds. A software package has been developed that allows users to perform the cross wavelet transform and wavelet coherence (www.pol.ac.uk/home/research/waveletcoherence/).

Dynamic correlation of Eastern and Western markets and forecasting: Scale-by-scale wavelet-based approach

2017 ◽  
Vol 04 (04) ◽  
pp. 1750040 ◽  
Author(s):  
Emrah Oral ◽  
Gazanfer Unal
Keyword(s):  
Time Series ◽  
Wavelet Transform ◽  
Moving Average ◽  
Wavelet Coherence ◽  
Vector Autoregressive ◽  
Frequency Space ◽  
Time Frequency ◽  
Dynamic Correlation ◽  
Frequency Scale ◽  
Highly Correlated

In this paper, dynamic four-dimensional (4D) correlation of eastern and western markets is analyzed. A wavelet-based scale-by-scale analysis method has been introduced to model and forecast stock market data for strongly correlated time intervals. The daily data of stock markets of SP500, FTSE and DAX (western markets) and NIKKEI, TAIEX and KOSPI (eastern markets) are obtained from 2009 to the end of 2016 and their co-movement dependencies on time–frequency space using 4D multiple wavelet coherence (MWC) are determined. Once the data is detached into levels of different frequencies using scale-by-scale continuous wavelet transform, all of the time series possessing the same frequency scale are selected, inversed and forecasted using multivariate model, vector autoregressive moving average (VARMA). It is concluded that the efficiency of forecasting is increased substantially using the same-frequency highly correlated time series obtained by scale-by-scale wavelet transform. Moreover, the increasing or decreasing trend of prospected price shift is foreseen fairly well.

Time-Local Spectral Analysis for Non-Stationary Time Series: The S-Transform for Noisy Signals

2003 ◽  
Vol 03 (03) ◽  
pp. L357-L364 ◽  
Author(s):  
C. R. Pinnegar ◽  
L. Mansinha
Keyword(s):  
Time Series ◽  
Spectral Analysis ◽  
Wavelet Transforms ◽  
Gaussian White Noise ◽  
Stationary Time Series ◽  
Time Frequency ◽  
S Transform ◽  
Undesirable Characteristic ◽  
Noisy Signals ◽  
Short Time

The S-transform is a method of time-local spectral analysis (also known as time-frequency analysis), a modified short-time Fourier Transform, in which the width of the analyzing window scales inversely with frequency, in analogy with continuous wavelet transforms. If the time series is non-stationary and consists of a mix of Gaussian white noise and a deterministic signal, though, this type of scaling leads to larger apparent noise amplitudes at higher frequencies. In this paper, we introduce a modified S-transform window with a different scaling function that addresses this undesirable characteristic.

scholarly journals Analysis of spatiotemporal variations of drought and its correlations with remote sensing-based indices via wavelet analysis and clustering methods

2021 ◽  
Author(s):  
Roghayeh Ghasempour ◽  
Kiyoumars Roushangar ◽  
V. S. Ozgur Kirca ◽  
Mehmet Cüneyd Demirel
Keyword(s):  
Time Series ◽  
Vegetation Index ◽  
Standardized Precipitation Index ◽  
Condition Index ◽  
Stationary Time Series ◽  
Sensor Data ◽  
Wavelet Coherence ◽  
Spatiotemporal Pattern ◽  
Discrete Wavelet ◽  
Clustering Methods

Abstract Beside in situ observations, satellite-based products can provide an ideal data source for spatiotemporal monitoring of drought. In this study, the spatiotemporal pattern of drought was investigated for the northwest part of Iran using ground- and satellite-based datasets. First, the Standardized Precipitation Index series were calculated via precipitation data of 29 sites located in the selected area and the CPC Merged Analysis of Precipitation satellite. The Maximal Overlap Discrete Wavelet Transform (MODWT) was used for obtaining the temporal features of time series, and further decomposition was performed using Ensemble Empirical Mode Decomposition (EEMD) to have more stationary time series. Then, multiscale zoning was done based on subseries energy values via two clustering methods, namely the self-organizing map and K-means. The results showed that the MODWT–EEMD–K-means method successfully identified homogenous drought areas. On the other hand, correlation between the satellite sensor data (i.e. the Normalized Difference Vegetation Index, the Vegetation Condition Index, the Vegetation Healthy Index, and the Temperature Condition Index) was evaluated. The possible links between central stations of clusters and satellite-based indices were assessed via the wavelet coherence method. The results revealed that all applied satellite-based indices had significant statistical correlations with the ground-based drought index within a certain period.

scholarly journals The Empirical Adaptive Wavelet Decomposition (EAWD): An adaptive decomposition for the variability analysis of observation time series in atmospheric science

2022 ◽  
Author(s):  
Olivier Delage ◽  
Thierry Portafaix ◽  
Hassan Bencherif ◽  
Alain Bourdier ◽  
Emma Lagracie
Keyword(s):  
Time Series ◽  
Time Scales ◽  
Observation Time ◽  
Stationary Time Series ◽  
Original Time Series ◽  
Adaptive Wavelet ◽  
Time Frequency ◽  
Variability Analysis ◽  
Original Time ◽  
Different Time Scales

Abstract. Most observational data sequences in geophysics can be interpreted as resulting from the interaction of several physical processes at several time and space scales. As a consequence, measurements time series have often characteristics of non-linearity and non-stationarity and thereby exhibit strong fluctuations at different time-scales. The variability analysis of a time series consists in decomposing it into several mode of variability, each mode representing the fluctuations of the original time series at a specific time-scale. Such a decomposition enables to obtain a time-frequency representation of the original time series and turns out to be very useful to estimate the dimensionality of the underlying dynamics. Decomposition techniques very well suited to non-linear and non-stationary time series have recently been developed in the literature. Among the most widely used of these technics are the empirical mode decomposition (EMD) and the empirical wavelet transformation (EWT). The purpose of this paper is to present a new adaptive filtering method that combines the advantages of the EMD and EWT technics, while remaining close to the dynamics of the original signal made of atmospheric observations, which means reconstructing as close as possible to the original time series, while preserving its variability at different time scales.

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.

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