Identification and analysis of nonlinear trends in InSAR displacement time series

2021 ◽  
Author(s):  
Fabio Bovenga ◽  
Alberto Refice ◽  
Guido Pasquariello ◽  
Raffaele Nutricato ◽  
Davide Nitti
Keyword(s):  
Time Series ◽  
Nonlinear Trends

Multiscaled Neural Autoregressive Distributed Lag: A New Empirical Mode Decomposition Model for Nonlinear Time Series Forecasting

2020 ◽  
Vol 30 (08) ◽  
pp. 2050039 ◽  
Author(s):  
Foued Saâdaoui ◽  
Othman Ben Messaoud
Keyword(s):  
Neural Networks ◽  
Time Series ◽  
Empirical Mode Decomposition ◽  
Multivariate Time Series ◽  
Seasonal Effects ◽  
Real World Data ◽  
Distributed Lag ◽  
Autoregressive Distributed Lag ◽  
Mode Decomposition ◽  
Nonlinear Trends

Forecasting has always been the cornerstone of machine learning and statistics. Despite the great evolution of the time series theory, forecasters are still in the hunt for better models to make more accurate decisions. The huge advances in neural networks over the last years has led to the emergence of a new generation of effective models replacing classic econometric models. It is in this direction that we propose, in this paper, a new multiscaled Feedforward Neural Network (FNN), with the aim of forecasting multivariate time series. This new model, called Empirical Mode Decomposition (EMD)-based Neural ARDL, is inspired from the well-known Autoregressive Distributed Lag (ARDL) model being our proposal founded upon the concepts of nonlinearity, EMD-multiresolution and neural networks. These features give the model the ability to effectively capture many nonlinear patterns like the ones often present in econophysical time series, such as nonlinear trends, seasonal effects, long-range dependency, etc. The proposed algorithm can be summarized into the following four basic tasks: (i) EMD breaking-down multivariate time series into different resolution levels, (ii) feeding EMD components from the same levels into a number of feedforward neural ARDL models, (iii) from one level to the next, extrapolating the component corresponding to the response variable (scalar output) a number of steps ahead, and finally, (iv) recombining level-by-level forecasts into a single output. An optimal learning scheme is rigorously designed for efficiently training the new proposed architecture. The approach is finally tested and compared to a number of powerful benchmark models, where experiments are conducted on real-world data.

scholarly journals Multi-scale analysis of teleconnection indices: climate noise and nonlinear trend analysis

2009 ◽  
Vol 16 (1) ◽  
pp. 65-76 ◽  
Author(s):  
C. Franzke
Keyword(s):  
Time Series ◽  
Decadal Variability ◽  
Statistical Significance ◽  
Stationary Time Series ◽  
Intrinsic Mode Functions ◽  
Multi Scale ◽  
The North ◽  
Teleconnection Indices ◽  
Nonlinear Trends ◽  
Climate Noise

Abstract. The multi-scale nature and climate noise properties of teleconnection indices are examined by using the Empirical Mode Decomposition (EMD) procedure. The EMD procedure allows for the analysis of non-stationary time series to extract physically meaningful intrinsic mode functions (IMF) and nonlinear trends. The climatologically relevant monthly mean teleconnection indices of the North Atlantic Oscillation (NAO), the North Pacific index (NP) and the Southern Annular Mode (SAM) are analyzed. The significance of IMFs and trends are tested against the null hypothesis of climate noise. The analysis of surrogate monthly mean time series from a red noise process shows that the EMD procedure is effectively a dyadic filter bank and the IMFs (except the first IMF) are nearly Gaussian distributed. The distribution of the variance contained in IMFs of an ensemble of AR(1) simulations is nearly χ2 distributed. To test the statistical significance of the IMFs of the teleconnection indices and their nonlinear trends we utilize an ensemble of corresponding monthly averaged AR(1) processes, which we refer to as climate noise. Our results indicate that most of the interannual and decadal variability of the analysed teleconnection indices cannot be distinguished from climate noise. The NP and SAM indices have significant nonlinear trends, while the NAO has no significant trend when tested against a climate noise hypothesis.

scholarly journals Nonlinear Trends, Long-Range Dependence, and Climate Noise Properties of Surface Temperature

2012 ◽  
Vol 25 (12) ◽  
pp. 4172-4183 ◽  
Author(s):  
Christian Franzke
Keyword(s):  
Time Series ◽  
Climate Variability ◽  
Null Model ◽  
Warming Trend ◽  
Temperature Time Series ◽  
Trend Detection ◽  
Detection Methods ◽  
Nonlinear Trends ◽  
Temperature Time ◽  
Climate Noise

Abstract This study investigates the significance of trends of four temperature time series—Central England Temperature (CET), Stockholm, Faraday-Vernadsky, and Alert. First the robustness and accuracy of various trend detection methods are examined: ordinary least squares, robust and generalized linear model regression, Ensemble Empirical Mode Decomposition (EEMD), and wavelets. It is found in tests with surrogate data that these trend detection methods are robust for nonlinear trends, superposed autocorrelated fluctuations, and non-Gaussian fluctuations. An analysis of the four temperature time series reveals evidence of long-range dependence (LRD) and nonlinear warming trends. The significance of these trends is tested against climate noise. Three different methods are used to generate climate noise: (i) a short-range-dependent autoregressive process of first order [AR(1)], (ii) an LRD model, and (iii) phase scrambling. It is found that the ability to distinguish the observed warming trend from stochastic trends depends on the model representing the background climate variability. Strong evidence is found of a significant warming trend at Faraday-Vernadsky that cannot be explained by any of the three null models. The authors find moderate evidence of warming trends for the Stockholm and CET time series that are significant against AR(1) and phase scrambling but not the LRD model. This suggests that the degree of significance of climate trends depends on the null model used to represent intrinsic climate variability. This study highlights that in statistical trend tests, more than just one simple null model of intrinsic climate variability should be used. This allows one to better gauge the degree of confidence to have in the significance of trends.

scholarly journals Observed drought and wetness trends in Europe: an update

2009 ◽  
Vol 13 (8) ◽  
pp. 1519-1530 ◽  
Author(s):  
I. Bordi ◽  
K. Fraedrich ◽  
A. Sutera
Keyword(s):  
Time Series ◽  
Time Scale ◽  
Linear Trend ◽  
Singular Spectrum Analysis ◽  
Standardized Precipitation Index ◽  
Principal Component ◽  
Monthly Precipitation ◽  
Nonlinear Trend ◽  
Nonlinear Trends ◽  
Grid Points

Abstract. Linear and nonlinear trends of drought and wetness are analysed in terms of the gridded Standardized Precipitation Index (SPI) determined from monthly precipitation in Europe (NCEP/NCAR). In characterizing the meteorological and hydrological aspects, the index is computed on a seasonal and on a bi-annual time scale. Two datasets are compared: one from 1949 to 1997 and the other one includes the update of the last decade (to February 2009). The following results are noted: (i) time series of drought and wetness area coverage (number of grid points above/below the severity threshold) show a remarkable linear trend until about the end of the last century, which is reversed in the last (update) decade. This recent trend reversal is an indication of a nonlinear trend, which is more pronounced on the hydrological time scale. (ii) A nonlinear trend analysis is performed based on the time series of the principal component (PC) associated to the first spatial SPI-eigenvector after embedding it in a time delay coordinate system using a sliding window of 70 months (singular spectrum analysis). Nonlinearity appears as a clear feature on the hydrological time scale. (iii) The first spatial EOF-patterns of the shorter and the longer (updated) SPI time series fields show similar structure. An inspection of the SPI time behaviour at selected grid points illustrates the spatial variability of the detected trends.

scholarly journals Multi-annual changes of NO<sub>x</sub> emissions in megacity regions: nonlinear trend analysis of satellite measurement based estimates

2010 ◽  
Vol 10 (17) ◽  
pp. 8481-8498 ◽  
Author(s):  
I. B. Konovalov ◽  
M. Beekmann ◽  
A. Richter ◽  
J. P. Burrows ◽  
A. Hilboll
Keyword(s):  
Time Series ◽  
Probabilistic Approach ◽  
Air Pollutant ◽  
Nox Emission ◽  
Pollutant Emissions ◽  
Satellite Measurement ◽  
Near Surface ◽  
Nonlinear Trend ◽  
Nonlinear Trends ◽  
Linear Trends

Abstract. Hazardous impact of air pollutant emissions from megacities on atmospheric composition on regional and global scales is currently an important issue in atmospheric research. However, the quantification of emissions and related effects is frequently a difficult task, especially in the case of developing countries, due to the lack of reliable data and information. This study examines possibilities to retrieve multi-annual NOx emissions changes in megacity regions from satellite measurements of nitrogen dioxide and to quantify them in terms of linear and nonlinear trends. By combining the retrievals of the GOME and SCIAMACHY satellite instrument data with simulations performed by the CHIMERE chemistry transport model, we obtain the time series of NOx emission estimates for the 12 largest urban agglomerations in Europe and the Middle East in the period from 1996 to 2008. We employ then a novel method allowing estimation of a nonlinear trend in a noisy time series of an observed variable. The method is based on the probabilistic approach and the use of artificial neural networks; it does not involve any quantitative a priori assumptions. As a result, statistically significant nonlinearities in the estimated NOx emission trends are detected in 5 megacities (Bagdad, Madrid, Milan, Moscow and Paris). Statistically significant upward linear trends are detected in Istanbul and Tehran, while downward linear trends are revealed in Berlin, London and the Ruhr agglomeration. The presence of nonlinearities in NOx emission changes in Milan, Paris and Madrid is confirmed by comparison of simulated NOx concentrations with independent air quality monitoring data. A good quantitative agreement between the linear trends in the simulated and measured near surface NOx concentrations is found in London.

scholarly journals Multi-annual changes of NO<sub>x</sub> emissions in megacity regions: nonlinear trend analysis of satellite measurement based estimates

2010 ◽  
Vol 10 (4) ◽  
pp. 10925-10968 ◽  
Author(s):  
I. B. Konovalov ◽  
M. Beekmann ◽  
A. Richter ◽  
J. P. Burrows ◽  
A. Hilboll
Keyword(s):  
Time Series ◽  
Probabilistic Approach ◽  
Air Pollutant ◽  
Nox Emission ◽  
Pollutant Emissions ◽  
Satellite Measurement ◽  
Near Surface ◽  
Nonlinear Trend ◽  
Nonlinear Trends ◽  
Linear Trends

Abstract. Hazardous impact of air pollutant emissions from megacities on atmospheric composition on regional and global scales is currently an important issue in atmospheric research. However, the quantification of emissions and related effects is frequently a difficult task, especially in the case of developing countries, due to the lack of reliable data and information. This study examines possibilities to retrieve multi-annual NOx emissions changes in megacity regions from satellite measurements of nitrogen dioxide and to quantify them in terms of linear and nonlinear trends. By combining the retrievals of the GOME and SCIAMACHY satellite instrument data with simulations performed by the CHIMERE chemistry transport model, we obtain the time series of NOx emission estimates for the 12 largest urban agglomerations in Europe and the Middle East in the period from 1996 to 2008. We employ then a novel method allowing estimation of a nonlinear trend in a noisy time series of an observed variable. The method is based on the probabilistic approach and the use of artificial neural networks; it does not involve any quantitative a priori assumptions. As a result, statistically significant nonlinearities in the estimated NOx emission trends are detected in 5 megacities (Bagdad, Madrid, Milan, Moscow and Paris). Statistically significant upward linear trends are detected in Istanbul and Tehran, while downward linear trends are revealed in Berlin, London and the Ruhr agglomeration. The presence of nonlinearities in NOx emission changes in Milan, Paris and Madrid is confirmed by comparison of simulated NOx concentrations with independent air quality monitoring data. A good quantitative agreement between the linear trends in the simulated and measured near surface NOx concentrations is found in London.

scholarly journals Long-Range Dependence and Climate Noise Characteristics of Antarctic Temperature Data

2010 ◽  
Vol 23 (22) ◽  
pp. 6074-6081 ◽  
Author(s):  
Christian Franzke
Keyword(s):  
Time Series ◽  
Long Range ◽  
Short Range ◽  
Null Model ◽  
Null Models ◽  
Environmental Research ◽  
Noise Characteristics ◽  
Dependent Process ◽  
Nonlinear Trends ◽  
Climate Noise

Abstract This study examines the long-range dependency, climate noise characteristics, and nonlinear temperature trends of eight Antarctic stations from the Reference Antarctic Data for Environmental Research (READER) dataset. Evidence is shown that Antarctic temperatures are long-range dependent. To identify possible nonlinear trends, the ensemble empirical mode decomposition (EEMD) method is used, and then the question of whether the observed trends can arise from internal atmospheric fluctuations is examined. To answer this question, surrogate data are generated from two paradigmatic null models: a standard first-order autoregressive process representing a short-range dependent process and a fractional integrated process representing a long-range dependent process. It is found that three of the eight stations show statistically significant trends when tested against the short-range dependent process while only the Faraday–Vernadsky station temperature time series shows a significant trend when tested against the long-range dependent null model. All other considered stations show no trends that are statistically significant against the two null models, and thus they can be explained by internal atmospheric variability. These results imply that more attention should be given to assessing the correlation structure of climate time series.

scholarly journals Observed drought and wetness trends in Europe: an update

2009 ◽  
Vol 6 (3) ◽  
pp. 3891-3915 ◽  
Author(s):  
I. Bordi ◽  
K. Fraedrich ◽  
A. Sutera
Keyword(s):  
Time Series ◽  
Time Scale ◽  
Linear Trend ◽  
Singular Spectrum Analysis ◽  
Standardized Precipitation Index ◽  
Principal Component ◽  
Monthly Precipitation ◽  
Nonlinear Trend ◽  
Nonlinear Trends ◽  
Grid Points

Abstract. Linear and nonlinear trends of drought and wetness are analysed in terms of the gridded Standardized Precipitation Index (SPI) determined from monthly precipitation in Europe (NCEP/NCAR), which characterizes the meteorological and hydrological aspects on a seasonal and on a bi-annual time scale, respectively. Two datasets are compared: one from 1949 to 1997 and the other one includes the update of the last decade (to February 2009). The following results are noted: (I) Time series of drought and wetness area coverage (number of grid points above/below the severity threshold) show a remarkable linear trend until about the end of the last century, which is reversed in the last (update) decade. This recent trend reversal is an indication of a nonlinear trend, which is more pronounced on the hydrological time scale. (II) A nonlinear trend analysis is performed based on the time series of the principal component (PC) associated to the first spatial SPI-eigenvector after embedding it in a time delay coordinate system using a sliding window of 70 months (singular spectrum analysis). Nonlinearity appears as a clear feature on the hydrological time scale. (III) The first spatial EOF-patterns of the shorter and the longer (updated) SPI time series fields show similar structure. An inspection of the SPI time behaviour at selected grid points illustrates the spatial variability of the detected trends.

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