Time Series Analysis Tools Research Articles

Real-Time Monitoring of Non-linear Suicidal Dynamics: Methodology and a Demonstrative Case Report.

In recent years, a number of different authors have stressed the usefulness of non-linear dynamic systems approach in suicide research and suicide prevention. This approach applies specific methods of time series analysis and, consequently, it requires a continuous and fine-meshed assessment of the processes under consideration. The technical means for this kind of process assessment and process analysis are now available. This paper outlines how suicidal dynamics can be monitored in high-risk patients by an Internet-based application for continuous self-assessment with integrated tools of non-linear time series analysis: the Synergetic Navigation System. This procedure is illustrated by data from a patient who attempted suicide at the end of a 90-day monitoring period. Additionally, future research topics and clinical applications of a non-linear dynamic systems approach in suicidology are discussed.

Unveiling Temporal Correlations Characteristic of a Phase Transition in the Output Intensity of a Fiber Laser.

We use advanced statistical tools of time-series analysis to characterize the dynamical complexity of the transition to optical wave turbulence in a fiber laser. Ordinal analysis and the horizontal visibility graph applied to the experimentally measured laser output intensity reveal the presence of temporal correlations during the transition from the laminar to the turbulent lasing regimes. Both methods unveil coherent structures with well-defined time scales and strong correlations both, in the timing of the laser pulses and in their peak intensities. Our approach is generic and may be used in other complex systems that undergo similar transitions involving the generation of extreme fluctuations.

Statistical Inference for Partially Observed Markov Processes via theRPackagepomp

Partially observed Markov process (POMP) models, also known as hidden Markov models or state space models, are ubiquitous tools for time series analysis. The R package pomp provides a very flexible framework for Monte Carlo statistical investigations using nonlinear, non-Gaussian POMP models. A range of modern statistical methods for POMP models have been implemented in this framework including sequential Monte Carlo, iterated filtering, particle Markov chain Monte Carlo, approximate Bayesian computation, maximum synthetic likelihood estimation, nonlinear forecasting, and trajectory matching. In this paper, we demonstrate the application of these methodologies using some simple toy problems. We also illustrate the specification of more complex POMP models, using a nonlinear epidemiological model with a discrete population, seasonality, and extra-demographic stochasticity. We discuss the specification of user-defined models and the development of additional methods within the programming environment provided by pomp.

Introduction to Symposium on Time Series Error Correction Methods in Political Science

In recent years, political science has seen a boom in the use of sophisticated methodological tools for time series analysis. One such tool is the general error correction model (GECM), originally introduced to political scientists in the pages of this journal over 20 years ago (Durr 1992; Ostrom and Smith 1992) and re-introduced by De Boef and Keele (2008), who advocate its use for a wider set of time series data than previously considered appropriate. Their article has proven quite influential, with numerous papers justifying their methodological choices with reference to De Boef and Keele's contribution.Grant and Lebo (2016) take issue with the increasing use of the GECM in political science and argue that the methodology is widely misused and abused by practitioners. Given the recent surge of research conducted using error correction methods, there is every reason to take their suggestions seriously and provide a fuller discussion of the points they raise in their paper. The present symposium serves such a role. It consists of Grant and Lebo's critique, a detailed response by Keele, Linn, and Webb (2016b), and shorter comments by Esarey (2016), Freeman (2016), and Helgason (2016). Finally, Lebo and Grant (2016) and Keele, Linn, and Webb (2016a) reflect on the contributions made in the symposium, as well as discuss outstanding issues.

Photometry of the long period dwarf nova MU Centauri

Even among the brighter cataclysmic variables an appreciable number of objects exist about which not much is known. One of them, MU Cen, was observed as part of a small project to better characterize these neglected systems. The temporal variations of the brightness of MU Cen during quiescence were studied in order to find clues to the structure of the system and its behavior on time scales of hours and shorter. Light curves observed in white light at a time resolution of a few seconds and with a duration of several hours, obtained in six nights and spanning a total time base of five months, were investigated using different time series analysis tools, as well as model fits. The light curve of MU Cen is dominated by ellipsoidal variations of the secondary star. The refined orbital period is Porb=0.341883 days. Model fits permit to constrain the temperature of the secondary star to ∼5000 K and the orbital inclination to 50° ≤ i ≤ 65°. The latter result permits estimates of the component masses which are probably somewhat smaller that derived in previous publications. A second persistent period of P2=0.178692 days was also identified. Its origin remains unclear. As all cataclysmic variables, MU Cen exhibits flickering, however, on a rather low level. Its frequency behavior is normal for quiescent dwarf novae. There are indications that the individual flickering events are not always independent but can lead to effects reminiscent of quasi-periodic oscillations.

Spatiotemporal analysis of GPS time series in vertical direction using independent component analysis

GPS has been widely used in the field of geodesy and geodynamics thanks to its technology development and the improvement of positioning accuracy. A time series observed by GPS in vertical direction usually contains tectonic signals, non-tectonic signals, residual atmospheric delay, measurement noise, etc. Analyzing these information is the basis of crustal deformation research. Furthermore, analyzing the GPS time series and extracting the non-tectonic information are helpful to study the effect of various geophysical events. Principal component analysis (PCA) is an effective tool for spatiotemporal filtering and GPS time series analysis. But as it is unable to extract statistically independent components, PCA is unfavorable for achieving the implicit information in time series. Independent component analysis (ICA) is a statistical method of blind source separation (BSS) and can separate original signals from mixed observations. In this paper, ICA is used as a spatiotemporal filtering method to analyze the spatial and temporal features of vertical GPS coordinate time series in the UK and Sichuan-Yunnan region in China. Meanwhile, the contributions from atmospheric and soil moisture mass loading are evaluated. The analysis of the relevance between the independent components and mass loading with their spatial distribution shows that the signals extracted by ICA have a strong correlation with the non-tectonic deformation, indicating that ICA has a better performance in spatiotemporal analysis.

Energy Performance Assessment of Buildings and Building Components. Guidelines for Data Analysis from Dynamic Experimental Campaigns Part 1: Physical Aspects

This document describes guidelines for using time series analysis methods and tools for estimating the thermal performance of buildings and building components. This is integrated in a more comprehensive work. This first part is mainly dealing with physical aspects. A second part focused on statistical aspects has been also elaborated. Both documents must be considered as complementary. Minimum steps to carry out data analysis are reported and different alternative analysis approaches are outlined. This document is mainly focused on the most critical aspects particularly regarding energy performance assessment of buildings and building components. More general techniques also required to carry out data analysis are briefly presented in this document including references for more comprehensive information. Case studies that help to understand the different aspects discussed are included along this text and references are given for further information.

Time-Dependent Gene Network Modelling by Sequential Monte Carlo.

Most existing methods used for gene regulatory network modeling are dedicated to inference of steady state networks, which are prevalent over all time instants. However, gene interactions evolve over time. Information about the gene interactions in different stages of the life cycle of a cell or an organism is of high importance for biology. In the statistical graphical models literature, one can find a number of methods for studying steady-state network structures while the study of time varying networks is rather recent. A sequential Monte Carlo method, namely particle filtering (PF), provides a powerful tool for dynamic time series analysis. In this work, the PF technique is proposed for dynamic network inference and its potentials in time varying gene expression data tracking are demonstrated. The data used for validation are synthetic time series data available from the DREAM4 challenge, generated from known network topologies and obtained from transcriptional regulatory networks of S. cerevisiae. We model the gene interactions over the course of time with multivariate linear regressions where the parameters of the regressive process are changing over time.

Lake-level variations and tides in Lago Argentino, Patagonia: insights from pressure tide gauge records

Based on precise pressure tide gauge observations lake-level records are derived for two sites in Lago Argentino, southern Patagonia, of 2.5 and 1 years of duration. Applying the tools of time series analysis, the principal processes affecting the lake level are identified and quantified. Lake-level changes reflecting variations in lake volume are dominated by a seasonal cycle of 1.2 m in amplitude. Lake-volume changes occur in addition with a daily period in response to melt water influx from surrounding glaciers. Sporadic lake-volume jumps are caused by bursting of the ice dam of Perito Moreno glacier. Water movements in Lago Argentino are dominated by surface seiches reaching 20 cm in amplitude. Lake tides reach a maximum amplitude of 3 mm. The comparison of the tidal signal extracted from the lake-level observations with a model composed of the contributions of body tide and ocean tidal loading indicates a phase shift of 23° which is most likely explained by an 1 hour phase lag of global ocean tide models in the region of the highly fragmented Pacific coast. The comparison of the obtained results with those of a previous study of Lago Fagnano, Tierra del Fuego, allows to relate differences in the hydrological and hydrodynamic processes between both lakes to morphological properties. This leads to a tentative prediction of the lake-level variability to be expected from other great Patagonian lakes. The presented geodetic results shall serve as a starting point for a detailed limnological investigation of these aquatic ecosystems.

Human photoplethysmogram: new insight into chaotic characteristics

The photoplethysmogram is widely used in medical settings and sports equipment to measure biological signals. The photoplethysmogram, which is measured noninvasively, can provide valuable information about cardiovascular system performance. The present study sought to investigate the underlying dynamics of photoplethysmographic signals from healthy young human subjects. In previous studies the photoplethysmogram was claimed to be driven by deterministic chaos [Tsuda 1992, Sumida 2000]; however, the methods applied for chaos detection were noise sensitive and inconclusive. Therefore, to reach a consistent conclusion it is important to employ additional nonlinear time series analysis tools that can test different features of the signal's underlying dynamics. In this paper, methods of nonlinear time series analysis, including time delay embedding, largest Lyapunov exponent, deterministic nonlinear prediction, Poincaré section, the Wayland test and method of surrogate data were applied to photoplethysmogram time series to identify the unique characteristics of the photoplethysmogram as a dynamical system. Results demonstrated that photoplethysmogram dynamics is consistent with the definition of chaotic movement, and its chaotic properties showed some similarity to Rossler's single band chaos with induced dynamical noise. Additionally it was found that deterministic nonlinear prediction, Poincaré section and the Wayland test can reveal important characteristics of photoplethysmographic signals that will be important tools for theoretical and applied studies on the photoplethysmogram.

Robust estimation of (partial) autocorrelation

AbstractThe autocorrelation function (acf) and the partial autocorrelation function (pacf) are elementary tools of linear time series analysis. The sensitivity of the conventional sample acf and pacf to outliers is well known. We review robust estimators and evaluate their performances in different data situations considering Gaussian scenarios with and without outliers as well as times series with heavy tails in a simulation study.WIREs Comput Stat2015, 7:205–222. doi: 10.1002/wics.1351This article is categorized under:Statistical and Graphical Methods of Data Analysis > Robust MethodsData: Types and Structure > Time Series, Stochastic Processes, and Functional Data

Optimal Estimation of Multivariate ARMA Models

Autoregressive moving average (ARMA) models are a fundamental tool in timeseries analysis that offer intuitive modeling capability and efficient predictors. Unfortunately, the lack of globally optimal parameter estimation strategies for these models remains a problem:application studies often adopt the simpler autoregressive model that can be easily estimated by maximizing (a posteriori) likelihood. We develop a (regularized, imputed) maximum likelihood criterion that admits efficient global estimation via structured matrix norm optimization methods. An empirical evaluation demonstrates the benefits of globally optimal parameter estimation over local and moment matching approaches.

New Robust Estimators of Correlation and Weighted Basis Pursuit

The autocorrelation function is a commonly used tool in statistical time series analysis. In this paper we examine the robustness of two estimators of correlation based on memoryless nonlinear functions of the observations, the Median-of-Ratios Estimator (MRE) and the Phase-Phase Correlator (PPC), which are applicable to complex-valued Gaussian random processes. We show that they are robust to impulsive noise from a bias perspective at the expense of statistical efficiency at the Gaussian distribution. Additionally, we develop iterative versions of these estimators named the IMRE and IPPC, realizing an improved bias performance over their non-iterative counterparts and the well-known robust Schweppe-type Generalized M-estimator utilizing a Huber cost function (SHGM). We use robust Mahalanobis distances generated by the IMRE and IPPC to improve the performance of impulsive noise suppression through the use of weighted basis pursuit methods. These estimation and data-cleaning techniques are applied to both synthetic and actual collected data using an Ettus Research USRP to perform robust spectral estimation on signals from the digital television band in the presence of additive impulsive noise. Finally, the analysis reveals that if the time series is highly correlated and the contamination rate is low, the MRE outperforms the PPC estimator from a variance and bias perspective. However, the PPC is the estimator of choice when the correlation is lower and is better suited to time critical applications due to lower computation costs.

Time Series Analysis of Booking Data of a Free-Floating Carsharing System in Berlin

The most rapidly growing carsharing system in North America and Europe is the free-floating one (FFCS). In a FFCS system customers can book and return vehicles of the fleet in every place of a defined operating area. While first studies tried to characterize the user of such a system and explain the booking behavior this work focuses on the short times prediction of FFCS bookings.Booking data of the FFCS operator DriveNow in Berlin are the basis for the forecast. They enable modeling time series for vehicle bookings by hour. The forecast provides predictions for every hour of a future week. To include spatial differences of FFCS bookings forecasts are calculated for every zip code area. Two methods of time series analysis are used to compare their performance for the present data: A seasonal ARIMA model and exponential smoothing with Holt-Winters-Filter.These two models are realized each with four settings. They are based upon data of a whole year, a half-year, a quarter or just a month and compared regarding their precision and practicability. Preliminary analyses such as the spectral analysis show that FFCS booking frequencies have weekly recurring trends. Additionally, it is visible that in areas with a high booking density this level lasts for the whole time. By this, spectral analysis can be applied as a spatial clustering method.The comparison of the two tools of time series analysis yields to the Holt-Winters Filtering (HWF) as the favorite method. Finding the optimal parameters for the ARIMA models is computationally intensive and results in just equally good or even worse forecasts than with exponential smoothing.The best prediction is performed with Holt-Filters-Filtering using three months of booking data. The forecast predicts bookings with an average error of only 0.84 vehicles per hour. The largest average absolute error of all compared forecast models is around 20% higher but makes the model still useful in practice though.

Price Discovery and Market Efficiency of Commodities Futures Market in India- A Cointegration and Causality Analysis

The paper studies the Indian commodity futures market in order to determine the price discovery, long run market efficiency and short run dynamics in futures market using by time series analysis tools. To test the market efficiency and long run equilibrium, tools like Engle and Granger co-integration test (1987) and Johansen co-integration test (1988) have been applied. The Granger Causality (1969) test is used test the market efficiency to infer cause and affect relationship between spot and futures market in India. To examine efficiency of commodity futures and spot market the MCXs1 four spot and futures commodity indices data are used. The paper observes that the role of commodity futures is very significant in price discovery, and improving efficiency of the market.

Disappearing Paradigms in Shareholder Protection: Leximetric Evidence for 30 Countries, 1990-2013

Scholars frequently claim that path dependency of the law, the influence of the US model of corporate governance, and the role of legal origin and the stage of legal development are key for a comparative understanding of shareholder protection. This article, however, suggests that these paradigms of comparative company law gradually seem to disappear. The basis for our assessment is an original leximetric dataset that measures the development of shareholder protection for 30 countries over the last 24 years. Using tools of descriptive statistics, time series and cluster analysis, our main findings are that all legal origins have now in average about the same level of shareholder protection, that paternalistic tools have overtaken enabling tools of protection, and that after the global financial crisis this area has become a less frequent object of law reforms.

Disappearing Paradigms in Shareholder Protection: Leximetric Evidence for 30 Countries, 1990–2013

Scholars frequently claim that the path dependency of the law, the influence of the US model of corporate governance, and the role of legal origin and the stage of legal development are key for a comparative understanding of shareholder protection. This article, however, suggests that these paradigms of comparative company law gradually seem to be disappearing. The basis for our assessment is an original leximetric dataset that measures the development of shareholder protection for 30 countries over the last 24 years. Using tools of descriptive statistics, time series and cluster analysis, our main findings are that all legal origins now have on average about the same level of shareholder protection, that paternalistic tools have overtaken enabling tools of protection, and that, after the global financial crisis, this area has become a less frequent object of law reforms.

Long-term changes in the north–south asymmetry of solar activity: a nonlinear dynamics characterization using visibility graphs

Abstract. Solar activity is characterized by complex dynamics superimposed onto an almost periodic, approximately 11-year cycle. One of its main features is the presence of a marked, time-varying hemispheric asymmetry, the deeper reasons for which have not yet been completely uncovered. Traditionally, this asymmetry has been studied by considering amplitude and phase differences. Here, we use visibility graphs, a novel tool of nonlinear time series analysis, to obtain complementary information on hemispheric asymmetries in dynamical properties. Our analysis provides deep insights into the potential and limitations of this method, revealing a complex interplay between factors relating to statistical and dynamical properties, i.e., effects due to the probability distribution and the regularity of observed fluctuations. We demonstrate that temporal changes in the hemispheric predominance of the graph properties lag those directly associated with the total hemispheric sunspot areas. Our findings open a new dynamical perspective on studying the north–south sunspot asymmetry, which is to be further explored in future work.

Applying Distributed Lag Models to Individual Data in Environmental Studies

Distributed lag models, either for linear (DLM) or non-linear (DLNM) associations, represent an established methodological tool in time series analysis of environmental factors. Recent developments of this modelling framework allows extensions beyond time series data, for instance in study designs based on individual data. In this contribution, we illustrate an example of application in a case-crossover study of the effect of air pollution and temperature on respiratory mortality. Data include 410,728 deaths for respiratory causes occurring in England and Wales in 2001-2006. Control days were selected following a time-stratified design. Daily measures of ozone and mean temperature were assigned individually to each subject using modelled data on a 5-km grid. Odds ratios (OR) for the two exposures were estimated by conditional logistic regression including a DLM and a DLNM based on spline functions with lag periods up to 10 and 21 days, respectively. We also tested interactions with individual variables such as sex or socio-economic status. All analyses was performed in R with the package dlnm. The lag-response for ozone showed significant effects up to 8 days, with an overall cumulative linear OR of 1.010 (95%CI:1.005-1.014) for 10 ug/m3. The overall cumulative exposure-response of temperature displayed the classical U-shape, with OR of 1.94 (95%CI: 1.81-2.07) for 0°C and 7.80 (95%CI:3.65-16.67) for 28°C, compared to the minimum mortality temperature of 19°C. Neither sex nor socio-economic status show significant effect modifications. Information at the individual level, now more readily available for environmental studies, provides the opportunity to extend and improve epidemiological investigations. In this application we illustrate how the flexibility of DLM-DLNM can be extended to study designs based on individual data. Advantages and limitations if compared to the standard time series approach are discussed, together with statistical and computational aspects.

KIC 10526294: a slowly rotating B star with rotationally split, quasi-equally spaced gravity modes

Massive stars are important for the chemical enrichment of the universe. Since internal mixing processes influence their lives, it is very important to place constraints on the corresponding physical parameters, such as core overshooting and the internal rotation profile, so as to calibrate their stellar structure and evolution models. Although asteroseismology has been shown to be able to deliver the most precise constraints so far, the number of detailed seismic studies delivering quantitative results is limited. Our goal is to extend this limited sample with an in-depth case study and provide a well-constrained set of asteroseismic parameters, contributing to the ongoing mapping efforts of the instability strips of the beta Cep and SPB stars. We derived fundamental parameters from high-resolution spectra using spectral synthesis techniques. We used custom masks to obtain optimal light curves from the original pixel level data from the Kepler satellite. We used standard time-series analysis tools to construct a set of significant pulsation modes that provide the basis for the seismic analysis carried out afterwards. We find that KIC 10526294 is a cool SPB star, one of the slowest rotators ever found. Despite this, the length of Kepler observations is sufficient to resolve narrow rotationally split multiplets for each of its 19 quasi-equally spaced dipole modes. The number of detected consecutive (in radial order) dipole modes in this series is higher than ever before. The observed amount of splitting shows an increasing trend towards longer periods, which - largely independent of the seismically calibrated stellar models - points towards a non-rigid internal rotation profile. From the average splitting we deduce a rotation period of ~188 d. From seismic modelling, we find that the star is young with a central hydrogen mass fraction X_c>0.64; it has a core overshooting alpha_ov<=0.15.