Time Series Analysis Tools Research Articles

Identifying quasi-periodic variability using multivariate empirical mode decomposition: a case of the tropical Pacific

Abstract. A variety of statistical tools have been used in climate science to gain a better understanding of the climate system's variability on various temporal and spatial scales. However, these tools are mostly linear, stationary, or both. In this study, we use a recently developed nonlinear and nonstationary multivariate time series analysis tool – multivariate empirical mode decomposition (MEMD). MEMD is a powerful tool for objectively identifying (intrinsic) timescales of variability within a given spatio-temporal system without any timescale pre-selection. Additionally, a red noise significance test is developed to robustly extract quasi-periodic modes of variability. We apply these tools to reanalysis and observational data of the tropical Pacific. This reveals a quasi-periodic variability in the tropical Pacific on timescales ∼ 1.5–4.5 years, which is consistent with El Niño–Southern Oscillation (ENSO) – one of the most prominent quasi-periodic modes of variability in the Earth’s climate system. The approach successfully confirms the well-known out-of-phase relationship of the tropical Pacific mean thermocline depth with sea surface temperature in the eastern tropical Pacific (recharge–discharge process). Furthermore, we find a co-variability between zonal wind stress in the western tropical Pacific and the tropical Pacific mean thermocline depth, which only occurs on the quasi-periodic timescale. MEMD coupled with a red noise test can therefore successfully extract (nonstationary) quasi-periodic variability from the spatio-temporal data and could be used in the future for identifying potential (new) relationships between different variables in the climate system.

Nationwide urban ground deformation in Japan for 15 years detected by ALOS and Sentinel-1

InSAR time series analysis has become a major tool for nationwide land deformation monitoring. Sentinel-1 SAR data have enabled us to measure and monitor ground deformation globally with high accuracy and resolution through InSAR time series analysis, due to its constant and frequent global coverage and open data policy since 2014. Although several datasets from previous SAR satellites were available before Sentinel-1, such comprehensive deformation monitoring was not performed due to several limitations such as data quality, analysis technique, data policy, and processing capacity at that time. However, since a large amount of ALOS InSAR products and an open-source InSAR time series analysis tool LiCSBAS have become openly and freely available, we can easily derive the deformation from 2006 to 2011 by using them. In this study, we detected the deformation time series and velocity in all major urban areas in Japan from 2006 to 2011 and compared the results with the deformation from 2014 to 2020 detected by Sentinel-1 data. The two deformation datasets with different time periods revealed various 15-year deformation histories, such as long-term constant subsidence in Tomakomai and Niigata, changes in deformation areas and/or velocities in Hirosaki, Kujyukuri, Kanazawa, and Matsushiro, and appearance or disappearance of deformation in Joso, Yoyogi, and Kyoto. Future abundant and continuous SAR data acquisitions will reveal more long-term deformation transitions and help to understand the details of the mechanisms.

Stock Price Forecasting with LSTM: A Brief Analysis of Mathematics Behind LSTM

Stock marketing prediction is really important in this digital world and for this reason, its forecasting tools are highly desired. This research examines the influence of Long Short-Term Memory (LSTM) in stock market prediction. The basic genetic algorithm behind the time series analysis tool is described with the help of a structure diagram, and its mathematical structure is explained. We also described the application of LSTM in the field of finance. LSTM is playing a vital role in prediction in several applications. Experiments on the proposed method have been conducted on stock market data. The results show that LSTM predicts the price quite fairly accurately. It outperformed other prediction models due to long-term dependency and due to its accuracy. The research demonstrates the LSTM tool’s impact on finance, particularly stock market prediction.

(Structural) VAR models with ignored changes in mean and volatility

The paper discusses how standard forecasting tools in multivariate time series analysis are affected when ignoring possible changes in the mean and the (co)variance. We study the estimation, forecasts, and estimated impulse responses of so-called long vector autoregressions, for which the complexity of the model increases with the sample size. We prove that, in spite of structural change in the data generating process, coefficient estimates and out-of-sample forecasts based on such long vector autoregressions are consistent. The sampling behaviour of estimated impulse responses depends primarily on the residual covariance matrix, which converges to an “average” covariance matrix in the case of varying (co)variances. Localised estimators (also obtained by means of a suitable long vector autoregression) may be more suitable in this case. Monte Carlo simulations support our theoretical findings. The empirical relevance of the theory is illustrated in two applications: (i) the international dynamics of inflation, and (ii) uncertainty and economic activity.

Nonparametric Bayesian Networks as a Tool of Multiscale Time Series Analysis and Remote Sensing Data Integration

Introduction. Nonparametric Bayesian networks are a promising tool for analyzing, visualizing, interpreting and predicting the structural and dynamic characteristics of complex systems. Modern interdisciplinary research involves the complex processing of heterogeneous data obtained using sensors of various physical nature. In the study of the forest fund, both methods of direct dendrological measurements and methods of remote observation using unmanned aerial vehicles are widely used. Information obtained using these methods must be analyzed in conjunction with hydrometeorological monitoring data.Aim. Investigation of the possibility of automating the monitoring of the well-being of the forest fund based on the integration of ground survey data, remote multispectral measurements and hydrometeorological observations using the mathematical apparatus of nonparametric Bayesian networks.Materials and methods. To assess the long-term joint dynamics of natural and climatic indicators and the radial growth of trees, a modified method of multiscale cross-correlation analysis was used with the removal of the background trend described by the moving average model. Relationships between various indicators were estimated based on the unconditional and conditional nonparametric Spearman correlation coefficients, which were used to reconstruct and parameterize the nonparametric Bayesian network.Results. A multiscale nonparametric Bayesian network was constructed to characterize both unconditional and conditional statistical relationships between parameters obtained from remote sensing, hydroclimatic and dendrological measurements. The proposed model showed a good quality of the plant fund state forecasting. The correlation coefficients between the observed and predicted indicators exceed 0.6, with the correlation coefficient comprising 0.77 when predicting the growth trend of annual tree rings.Conclusion. The proposed nonparametric Bayesian network model reflects the relationship between various factors that affect the forest ecosystem. The Bayesian network can be used to assess risks and improve environmental management planning.

A time-series COVID-19 policy outcome analysis tool to measure human behavior from a herd instinct perspective.

There are 47 municipalities and prefectures in Japan that operate similar COVID-19 policies in a unified manner. There are significant differences regarding their policy outcomes. In order to investigate when the outcomes are different, we made a COVID-19 policy outcome analysis tool, jpcovid for evaluating time-series scores of individual prefectures, not a policy analysis tool. Scoring policies is based on a single population mortality metric: the number of COVID-19 deaths divided by the population in millions from a demographic perspective. Although uniformed policies have been adopted by the 47 prefectures in Japan, there are significant differences in the calculated scores among the 47 prefectures. This difference can be caused by differences in the herding instincts of the community with COVID-19 variants. The herd instinct is an inherent tendency to associate with others and follow the group's behavior or a behavior wherein people tend to react to the actions of others without considering the reason. The snapshot scoring tool, jpscore showed that Niigata has the best score of 67.9 while Osaka has the worst score of 727.9. jpcovid allows users to identify when herd instincts made changes in time-series scores. This is the world's first large-scale measurement on the herd instinct of prefectures in Japan. The proposed method can be applied to other countries in general. The online version contains supplementary material available at 10.1007/s12553-023-00759-x.

Challenges and perspectives in recurrence analyses of event time series

The analysis of event time series is in general challenging. Most time series analysis tools are limited for the analysis of this kind of data. Recurrence analysis, a powerful concept from nonlinear time series analysis, provides several opportunities to work with event data and even for the most challenging task of comparing event time series with continuous time series. Here, the basic concept is introduced, the challenges are discussed, and the future perspectives are summarized.

SARClust—A New Tool to Analyze InSAR Displacement Time Series for Structure Monitoring

Interferometric Synthetic Aperture Radar (InSAR) has proved its efficiency for displacement monitoring in urban areas. However, the large volume of data generated by this technology turns the retrieval of information useful for structure monitoring into a big data problem. In this study, a new tool (SARClust) to analyze InSAR displacement time series is proposed. The tool performs the clustering of persistent scatterers (PSs) based on dissimilarities between their displacement time series evaluated through dynamic time warping. This strategy leads to the formation of clusters containing PSs with similar displacements, which can be analyzed together, reducing data dimensionality, and facilitating the identification of displacement patterns potentially related to structural damage. A proof of concept was performed for downtown Lisbon, Portugal, where ten distinct displacement patterns were identified. A relationship between clusters presenting centimeter-level displacements and buildings located on steep slopes was observed. The results were validated through visual inspections and comparison with another tool for time series analysis. Agreement was found in both cases. The innovation in this study is the attention brought to SARClust’s ability to (i) analyze vertical and horizontal displacements simultaneously, using an unsupervised procedure, and (ii) characterize PSs assisting the displacement interpretation. The main finding is the strategy to identify signs of structure damage, even on isolated buildings, in a large amount of InSAR data. In conclusion, SARClust is of the utmost importance to detect potential signs of structural damage in InSAR displacement time series, supporting structure safety experts in more efficient and sustainable monitoring tasks.

Entropy-Based Tests for Complex Dependence in Economic and Financial Time Series with the R Package tseriesEntropy

Testing for complex serial dependence in economic and financial time series is a crucial task that bears many practical implications. However, the linear paradigm remains pervasive among practitioners as the autocorrelation function, because, despite its known shortcomings, it is still one of the most used tools in time series analysis. We propose a solution to the problem, by introducing the R package tseriesEntropy, dedicated to testing for serial/cross dependence and nonlinear serial dependence in time series, based on the entropy metric Sρ. The package implements tests for both continuous and categorical data. The nonparametric tests, based on Sρ, rely on minimal assumptions and have also been shown to be powerful for small sample sizes. The measure can be used as a nonlinear auto/cross-dependence function, both as an exploratory tool, or as a diagnostic measure, if computed on the residuals from a fitted model. Different null hypotheses of either independence or linear dependence can be tested by means of resampling methods, backed up by a sound theoretical background. We showcase our methods on a panel of commodity price time series. The results hint at the presence of a complex dependence in the conditional mean, together with conditional heteroskedasticity, and indicate the need for an appropriate nonlinear specification.

Machine learning in environmental radon science

Temporal dynamic as well as spatial variability of environmental radon are controlled by factors such as meteorology, lithology, soil properties, hydrogeology, tectonics, and seismicity. In addition, indoor radon concentration is subject to anthropogenic factors, such as physical characteristics of a building and usage pattern.New tools for spatial and time series analysis and prediction belong to what is commonly called machine learning (ML). The ML algorithms presented here build models based on sample and predictor data to extract information and to make predictions. We give a short overview on ML methods and discuss their respective merits, their application, and ways of validating results. We show examples of 1) geogenic radon mapping in Germany involving a number of predictors, and of 2) time series analysis of a long-term experiment being carried out in Chiba, Japan, involving indoor radon concentrations and meteorological predictors.Finally, we identified the main weakness of the techniques, and we suggest actions to overcome their limitations.

Machine learning and optimal transport: some statistical and algorithmic tools

In this paper, we focus on the analysis of data that can be described by probability measures supported on a Euclidean space, by way of optimal transport. Our main objective is to present a first and second order statistical analyses in the space of distributions in a concise manner, as a first approach to understand the general modes of variation of a set of observations. In the context of optimal transport, these studies correspond to the barycenter and the decomposition into geodesic principal components in theWasserstein space. In particular, we aim attention at a regularised estimator of the barycenter, in order to handle the noise coming from the observations. Additionally, we leverage these tools for time series analysis, whose spectral informations are compared using optimal transport.

COVID-19 policy analysis for 10 European countries.

The goal of this paper is to analyze the COVID-19 policies of 10 European countries, including Sweden, Finland, Norway, Italy, France, Germany, Poland, Belgium, the Netherlands, and Hungary, with a time-series policy analysis tool. The results of the COVID-19 policy analysis are based on a single time-series indicator, or daily population mortality rate: the number of COVID-19 daily cumulative deaths divided by the population in millions. The lower the score, the better the policy. Although many experts believe that the COVID-19 policy outcome analysis is premature, time series analysis is an excellent analysis that can provide information on the progress and transition of policy outcomes. In other words, the proposed time series analysis tool allows policymakers to identify and quantify when mistakes were made during the on-going COVID-19 pandemic. The COVID-19 policy analysis discovered many useful facts. Sweden failed due to the herd immunity approach. Hungary made a fundamental mistake in COVID-19 tactics. Countries such as Sweden, Hungary, Belgium, and Poland showed time-series changes that differed from the others. Public health interventions can play a key role in mitigating the COVID-19 pandemic. The proposed policy analysis tool, hiscovid demonstrated the effectiveness of the time-series score behavior for discovering when policymakers made mistakes.

IMPACT OF ENTREPRENEURSHIP ON EMPLOYMENT: AN ECONOMETRIC INVESTIGATION FOR TURKEY

As is the case in the past, one of the main problems faced by economic administrators and political decision makers is increasing employment and struggling with unemployment. Turkey is a country that has had to deal with the high unemployment rates seen in almost every period since 1960’s. Especially after the 1980s, unemployment which started to increase due to globalization and technological progress reached high levels in the 1990s in terms of global measures.
 Besides financial and monetary policies, there are various social tools that governments can use for this purpose. Subsidies for the private sector, assistance to self-employed people, investment incentives and facilities can be regarded in this framework. It can, therefore, be expected that these policies to support entrepreneurial activities will contribute positively, both indirectly and indirectly, through employment and growth.
 In this study, reflections of the increase in entrepreneurship onto employment and unemployment are empirically investigated for the case of Turkey. According to the empirical findings obtained from the analysis carried out using modern time series analysis tools, while the increase in entrepreneurial activities in Turkey has a positive effect on employment in the long run, it does not have the expected effect on unemployment. This seemingly contradictory result can be explained partly by the weakness of entrepreneurial skills and partly by analyses of unsuccessful and inadequate investment.

Financial Speculation Impact on Agricultural and Other Commodity Return Volatility: Implications for Sustainable Development and Food Security

Global commodity markets, due to major health crises, political tension, sanctions, growing demand, and other global supply and demand factors, are currently particularly unstable. In addition to the macro-environmental factors that drive the prices, agricultural and other commodity markets are becoming more susceptible to the continuously-growing speculation on major commodity exchanges. Therefore, the purpose of this study is to analyze the influence of financial speculation on agricultural and other commodity prices and return volatility. In our study, we use daily returns on wheat, soybean, corn, and oats futures from the Chicago Mercantile Exchange as well as two additional commodities (crude oil and gold) to compare the extent of this effect. To measure this impact, we, besides traditional tools for time-series analysis, apply the threshold autoregressive conditional heteroskedasticity (TGARCH) technique. We also provide a model using dummy variables for the season to determine whether or not financial speculation’s impact on return volatility differs among seasons, as seasonality plays an important role in return dynamics for agriculture. Our study’s findings show that financial speculation, except for the oats market, either has no impact or makes the underlying futures returns less volatile. Therefore, we draw the conclusion that either there is no relationship between the rise in short-run speculation and the volatility of agricultural commodity prices, or the link is at best questionable. Research results provide important implications for the sustainable development of commodity markets, as passive legislation measurers can be seen as more effective ones compared to more strict active ones in order to maintain these markets liquid and capable of distributing price risks for agricultural producers and manufacturers in a challenging economic and geopolitical environment.

Effects of shady environments on fish collective behavior

Despite significant efforts devoted to understanding the underlying complexity and emergence of collective movement in animal groups, the role of different external settings on this type of movement remains largely unexplored. Here, by combining time series analysis and complex network tools, we present an extensive investigation of the effects of shady environments on the behavior of a fish species (Silver Carp Hypophthalmichthys molitrix) within earthen ponds. We find that shade encourages fish residence during daylight hours, but the degree of preference for shade varies substantially among trials and ponds. Silver Carp are much slower and exhibit lower persistence in their speeds when under shade than out of it during daytime and nighttime, with fish displaying the highest persistence degree and speeds at night. Furthermore, our research shows that shade affects fish schooling behavior by reducing their polarization, number of interactions among individuals, and the stability among local neighbors; however, fish keep a higher local degree of order when under shade compared to nighttime positions.

Helheim Glacier ice velocity variability responds to runoff and terminus position change at different timescales

The Greenland Ice Sheet discharges ice to the ocean through hundreds of outlet glaciers. Recent acceleration of Greenland outlet glaciers has been linked to both oceanic and atmospheric drivers. Here, we leverage temporally dense observations, regional climate model output, and newly developed time series analysis tools to assess the most important forcings causing ice flow variability at one of the largest Greenland outlet glaciers, Helheim Glacier, from 2009 to 2017. We find that ice speed correlates most strongly with catchment-integrated runoff at seasonal to interannual scales, while multi-annual flow variability correlates most strongly with multi-annual terminus variability. The disparate time scales and the influence of subglacial topography on Helheim Glacier’s dynamics highlight different regimes that can inform modeling and forecasting of its future. Notably, our results suggest that the recent terminus history observed at Helheim is a response to, rather than the cause of, upstream changes.

Multiscale online-horizontal-visibility-graph correlation analysis of financial market

In this study, we introduce an analogous multiscale online-horizontal-visibility-graph correlation analysis (MOHVGCA) method to quantify the association strength between pairwise nonlinear time series. The new method is based on complex network approaches and proved to be a powerful and efficient tool for large-scale time series analysis. The versatility and robustness of this new method are illustrated through synthetic series. Results obtained allow us to be optimistic about its efficiency in correlation analysis of complex time series. Furthermore, we employ the new method to characterize the association between WTI Crude Oil futures and representative traded currencies on 5 min intra-day recordings in the period January 2013–December 2015. The results reveal that there exist positive associations between WTI Crude Oil and the considered traded currencies, and the association degree between WTI Crude Oil and currencies from oil-exporting and oil-importing countries is significantly different over different scales. The oil crisis weakens the association between oil and the currencies from the oil-importing currencies and the information exchange between oil and currencies from oil-exporting countries strengthened dramatically after the oil crisis. Even more, we detect that the Russian ruble always has the strongest ties with oil in different periods. These findings shed new light on the correlation analysis from the perspective of multiscale network analysis.

Poincaré Plot Nonextensive Distribution Entropy: A New Method for Electroencephalography (EEG) Time Series.

As a novel form of visual analysis technique, the Poincaré plot has been used to identify correlation patterns in time series that cannot be detected using traditional analysis methods. In this work, based on the nonextensive of EEG, Poincaré plot nonextensive distribution entropy (NDE) is proposed to solve the problem of insufficient discrimination ability of Poincaré plot distribution entropy (DE) in analyzing fractional Brownian motion time series with different Hurst indices. More specifically, firstly, the reasons for the failure of Poincaré plot DE in the analysis of fractional Brownian motion are analyzed; secondly, in view of the nonextensive of EEG, a nonextensive parameter, the distance between sector ring subintervals from the original point, is introduced to highlight the different roles of each sector ring subinterval in the system. To demonstrate the usefulness of this method, the simulated time series of the fractional Brownian motion with different Hurst indices were analyzed using Poincaré plot NDE, and the process of determining the relevant parameters was further explained. Furthermore, the published sleep EEG dataset was analyzed, and the results showed that the Poincaré plot NDE can effectively reflect different sleep stages. The obtained results for the two classes of time series demonstrate that the Poincaré plot NDE provides a prospective tool for single-channel EEG time series analysis.

Multi-scale transition network approaches for nonlinear time series analysis

Complex networks are powerful tools for nonlinear time series analysis, which are undergoing fast development in the recent decade. Here we propose a novel way to construct multi-scale transition networks from time series, which are based on coarse-graining partitions of phase space. Using time series from both discrete Hénon map and continuous Rössler systems, we demonstrate that the multi-scale transition entropy values of the resulting networks show the same power as the Lyapunov exponents, identifying chaotic transitions successfully. The advantage is that our method works successfully when only a small number of 3–5 bins is used for the partition generation, while the traditional static node entropy measures work poorly. Further experimental examples in fMRI and ECG analysis show that these entropy measures are able to characterizing different rhythmic states of subjects, showing high potential for time series analysis from complex systems.

Permutation Jensen-Shannon distance: A versatile and fast symbolic tool for complex time-series analysis.

The main motivation of this paper is to introduce the permutation Jensen-Shannon distance, a symbolic tool able to quantify the degree of similarity between two arbitrary time series. This quantifier results from the fusion of two concepts, the Jensen-Shannon divergence and the encoding scheme based on the sequential ordering of the elements in the data series. The versatility and robustness of this ordinal symbolic distance for characterizing and discriminating different dynamics are illustrated through several numerical and experimental applications. Results obtained allow us to be optimistic about its usefulness in the field of complex time-series analysis. Moreover, thanks to its simplicity, low computational cost, wide applicability, and less susceptibility to outliers and artifacts, this ordinal measure can efficiently handle large amounts of data and help to tackle the current big data challenges.