Prediction of dynamic trends of landslides in fault zone areas based on time series analysis

Editorial: Special issue on time series analysis in the biological sciences

Making sense of antimicrobial use and resistance surveillance data: application of ARIMA and transfer function models

Time series analysis is the most commonly used technique for assessing the association between counts of health events over time and exposure to ambient air pollution. Recently, case-crossover analysis has been proposed as an alternative analytical approach. While each technique has its own advantages and disadvantages, there remains considerable uncertainty as to which statistical methodology is preferable for evaluating data of this type. The objective of this paper is to evaluate the performance of different variations of these two procedures using computer simulation. Hospital admission data were generated under realistic models with known parameters permitting estimates based on time series and case-crossover analyses to be compared with these known values. While accurate estimates can be achieved with both methods, both methods require some decisions to be made by the researcher during the course of the analysis. With time series analysis, it is necessary to choose the time span in the LOESS smoothing process, or degrees of freedom when using natural cubic splines. For case-crossover studies using either uni- or bi-directional control selection strategies, the choice of time intervals needs to be made. We prefer the times series approach because the best estimates of risk that can be obtained with time series analysis are more precise than the best estimates based on case-crossover analysis.

BackgroundBiomechanical changes and neuromuscular adaptations have been suggested as risk factors of secondary injury in individuals after anterior cruciate ligament reconstruction (ACLr). To achieve a better understanding of preventive mechanisms, movement quality is an important factor of consideration. Few studies have explored time-series analysis during landing alongside clinical performance in injured and non-injured individuals. The purpose of the study was to investigate the biomechanical risks of recurrent injury by comparing clinical and jump-landing performance assessments between athletes with ACLr and healthy controls.MethodThis study was observational study. Sixteen athletes with and without ACLr voluntarily participated in clinical and laboratory measurements. Single-leg hop distance, isokinetic tests, landing error score, and limb symmetry index (LSI) were included in clinical report. Lower limb movements were recorded to measure joint biomechanics during multi-directional landings in motion analysis laboratory. Hip-knee angle and angular velocity were explored using discrete time-point analysis, and a two-way mixed analysis of variance (2 × 4, group × jump-landing direction) was used for statistical analysis. Time series and hip-knee coordination analyses were performed using statistical parametric mapping and descriptive techniques.ResultsSignificantly lower single-leg hop distance was noted in ACLr group (158.10 cm) compared to control group (178.38 cm). Although the hip and knee moments showed significant differences between four directions (p < 0.01), no group effect was observed (p > 0.05). Statistical parametric mapping showed significant differences (p ≤ 0.05) between groups for hip abduction and coordinate plot of hip and knee joints. Athletes with ACLr demonstrated a higher velocity of hip adduction. Time-series analysis revealed differences in coordination between groups for frontal hip and knee motion.ConclusionsAthletes with ACLr landed with poor hip adduction control and stiffer knee on the involved side. Multi-directions landing should be considered over the entire time series, which may facilitate improved movement quality and return to sports in athletes with ACLr.

Most research on time series analysis and forecasting is normally based on the assumption of no structural change, which implies that the mean and the variance of the parameter in the time series model are constant over time. However, when structural change occurs in the data, the time series analysis methods based on the assumption of no structural change will no longer be appropriate; and thus there emerges another approach to solving the problem of structural change. Almost all time series analysis or forecasting methods always assume that the structure is consistent and stable over time, and all available data will be used for the time series prediction and analysis. When any structural change occurs in the middle of time series data, any analysis result and forecasting drawn from full data set will be misleading. Structural change is quite common in the real world. In the study of a very large set of macroeconomic time series that represent the ‘fundamentals’ of the US economy, Stock and Watson (1996) has found evidence of structural instability in the majority of the series. Besides, ignoring structural change reduces the prediction accuracy. Persaran and Timmermann (2003), Hansen (2001) and Clement and Hendry (1998, 1999) showed that structural change is pervasive in time series data, ignoring structural breaks which often occur in time series significantly reduces the accuracy of the forecast, and results in misleading or wrong conclusions. This chapter mainly focuses on introducing the most common time series methods. The author highlights the problems when applying to most real situations with structural changes, briefly introduce some existing structural change methods, and demonstrate how to apply structural change detection in time series decomposition.

The process of collecting and organizing sets of observations represents a common theme throughout the history of science. However, despite the ubiquity of scientists measuring, recording and analysing the dynamics of different processes, an extensive organization of scientific time-series data and analysis methods has never been performed. Addressing this, annotated collections of over 35 000 real-world and model-generated time series, and over 9000 time-series analysis algorithms are analysed in this work. We introduce reduced representations of both time series, in terms of their properties measured by diverse scientific methods, and of time-series analysis methods, in terms of their behaviour on empirical time series, and use them to organize these interdisciplinary resources. This new approach to comparing across diverse scientific data and methods allows us to organize time-series datasets automatically according to their properties, retrieve alternatives to particular analysis methods developed in other scientific disciplines and automate the selection of useful methods for time-series classification and regression tasks. The broad scientific utility of these tools is demonstrated on datasets of electroencephalograms, self-affine time series, heartbeat intervals, speech signals and others, in each case contributing novel analysis techniques to the existing literature. Highly comparative techniques that compare across an interdisciplinary literature can thus be used to guide more focused research in time-series analysis for applications across the scientific disciplines.

In this article we discuss some of the consequences of the mixed membership perspective on time series analysis. In its most abstract form, a mixed membership model aims to associate an individual entity with some set of attributes based on a collection of observed data. Although much of the literature on mixed membership models considers the setting in which exchangeable collections of data are associated with each member of a set of entities, it is equally natural to consider problems in which an entire time series is viewed as an entity and the goal is to characterize the time series in terms of a set of underlying dynamic attributes or dynamic regimes. Indeed, this perspective is already present in the classical hidden Markov model, where the dynamic regimes are referred to as “states,” and the collection of states realized in a sample path of the underlying process can be viewed as a mixed membership characterization of the observed time series. Our goal here is to review some of the richer modeling possibilities for time series that are provided by recent developments in the mixed membership framework. 1. Introduction. In this article we discuss some of the consequences of the mixed membership perspective on time series analysis. In its most

Errors in measurement can be categorized into two types: systematic errors that are predictable, and random errors that are inherently unpredictable and have null expected value. Random error is always present in a measurement. More often than not, readings in time series may contain inherent random errors due to causes like dynamic error, drift, noise, hysteresis, digitalization error and limited sampling frequency. Random errors may affect the quality of time series analysis substantially. Unfortunately, most of the existing time series mining and analysis methods, such as similarity search, clustering, and classification tasks, do not address random errors, possibly because random error in a time series, which can be modeled as a random variable of unknown distribution, is hard to handle. In this paper, we tackle this challenging problem. Taking similarity search as an example, which is an essential task in time series analysis, we develop MISQ, a statistical approach for random error reduction in time series analysis. The major intuition in our method is to use only the readings at different time instants in a time series to reduce random errors. We achieve a highly desirable property in MISQ: it can ensure that the recall is above a user-specified threshold. An extensive empirical study on 20 benchmark real data sets clearly shows that our method can lead to better performance than the baseline method without random error reduction in real applications such as classification. Moreover, MISQ achieves good quality in similarity search.

Short-term geodynamic displacements of the Earth's surface are studied insufficiently because the unambiguous identification of such geodynamic processes is quite a difficult task. Short-term geodynamic processes can be observed by considering GNSS time series lasting up to 2 months. The coordinate displacements are visually almost unnoticeable comparing annual time series. In this work, an algorithm based on the results of statistical analysis of time series of several GNSS stations on purpose to find simultaneous displacements of the Earth's surface is developed. Authors propose a method for detecting short-term displacements based on sliding correlation and covariance interrelationships between the time series of two GNSS stations for short periods, which are shifted along with the entire time series. The approach allows showing the characteristic of the displacements throughout the study area based on the selection of anomalous displacements of selected GNSS stations. The high correlation coefficient between the periods of stations indicates the presence of simultaneous and identical in absolute value offsets. The high value of covariance indicates the synchronicity and unidirectionality of such displacements. As a result, the time series of 8 GNSS stations of the Geoterrace network for the period from the end of 2017 to the beginning of 2021 are studied according to the presented method. The anomalous altitude displacements in the region for the epoch of 185th day of 2018 and 20 days period is investigated. Based on the processing, maps of the spatial distribution of correlation and covariance coefficients are constructed. The proposed method could be improved and applied to the study of kinematic processes in areas with a dense network of GNSS stations with long time series similarly GNSS networks for monitoring of large electricity produced objects such as HPPs and PSPs.

The article will present the methodology for holistic time series analysis, based on time series transformation model REFII (REFII is an acronym for Raise-Equal-Fall and the model version is II or 2) Patel et al. (Mining motifs in massive time series databases, 2002) [1], Perng and Parker (SQL/LPP: a time series extension of SQL based on limited patience patterns, 1999) [2], Popivanov and Miller (Similarity search over time series data using wavelets, 2002) [3]. The main purpose of REFII model is to automate time series analysis through a unique transformation model of time series. The advantage of this approach to a time series analysis is the linkage of different methods for time series analysis linking traditional data mining tools in time series, and constructing new algorithms for analyzing time series. REFII model is not a closed system, which means that there is a finite set of methods. This is primarily a model used for transformation of values of time series, which prepares data used by different sets of methods based on the same model of transformation in the domain of problem space. REFII model gives a new approach in time series analysis based on a unique model of transformation, which is a base for all kind of time series analyses. In combination with elements of other methods, such as self-organizing maps or frequent-pattern trees, REFII models can make new hybrid methods for efficient time temporal data mining. Similar principle of hybridization could be used as a tool for time series temporal pattern recognition. The article describes real case study illustrating practical application of described methodology.

In current time series prediction tasks, many methods transform time series into the frequency domain for analysis. Analyzing time series in the frequency domain reveals the spectral characteristics and energy distribution across different frequencies, providing a clearer understanding of the contributions of various frequency components. However, existing methods using frequency domain analysis often overlook the characteristic information contained within the amplitude and phase in the same frequency range. Additionally, many frequency domain analysis models paired with transformers result in significant time complexity. Therefore, we designed a parallel dual-channel network that processes frequencies categorically and then decomposes the complex values in the frequency domain to obtain amplitude and phase information within the same frequency range. This allows for capturing the intensity and relative position of corresponding frequency components in the entire time series. To capture the variations of amplitude and phase within the same frequency range in the time series, a frequency domain complex decomposition module was designed for refined feature extraction. Finally, the extracted amplitude-phase features are recombined into a complex number, providing a more accurate description of the distribution characteristics of frequency components in the time series. This method helps the model better understand frequency variations within the time series, thus improving prediction accuracy. Experiments show that, compared to the current state-of-the-art models, the proposed model achieves an average mean squared error (MSE) reduction of 6.29% to 18.90% across seven datasets including ETT and Weather, with significantly lower temporal and spatial complexity.

Time series modeling and analysis is central to most financial and econometric data modeling. With increased globalization in trade, commerce and finance, national variables like gross domestic productivity (GDP) and unemployment rate, market variables like indices and stock prices and global variables like commodity prices are more tightly coupled than ever before. This translates to the use of multivariate or vector time series models and algorithms in analyzing and understanding the relationships that these variables share with each other. Autocorrelation is one of the fundamental aspects of time series modeling. However, traditional linear models, that arise from a strong observed autocorrelation in many financial and econometric time series data, are at times unable to capture the rather nonlinear relationship that characterizes many time series data. This necessitates the study of nonlinear models in analyzing such time series. The class of bilinear models is one of the simplest nonlinear models. These models are able to capture temporary erratic fluctuations that are common in many financial returns series and thus, are of tremendous interest in financial time series analysis. Another aspect of time series analysis is homoscedasticity versus heteroscedasticity. Many time series data, even after differencing, exhibit heteroscedasticity. Thus, it becomes important to incorporate this feature in the associated models. The class of conditional heteroscedastic autoregressive (ARCH) models and its variants form the primary backbone of conditional heteroscedastic time series models. Robustness is a highly underrated feature of most time series applications and models that are presently in use in the industry. With an ever increasing amount of information available for modeling, it is not uncommon for the data to have some aberrations within itself in terms of level shifts and the occasional large fluctuations. Conventional methods like the maximum likelihood and least squares are well known to be highly sensitive to such contaminations. Hence, it becomes important to use robust methods, especially in this age with high amounts of computing power readily available, to take into account such aberrations. While robustness and time series modeling have been vastly researched individually in the past, application of robust methods to estimate time series models is still quite open. The central goal of this thesis is the study of robust parameter estimation of some simple vector and nonlinear time series models. More precisely, we will briefly study some prominent linear and nonlinear models in the time series literature and apply the robust S-estimator in estimating parameters of some simple models like the vector autoregressive (VAR) model, the (0, 0, 1, 1) bilinear model and a simple conditional heteroscedastic bilinear model. In each case, we will look at the important aspect of stationarity of the model and analyze the asymptotic behavior of the S-estimator.

Neural Networks are one of many data mining analytical tools that can be utilized to make predictions for demographic sequences. In this paper, we presented the application of a hybrid model that integrates Long-Short Term Memory-Recurrent Neural Network (LSTM-RNN), time series analysis and clustering techniques where time series analysis and clustering methods provide augmentation of sequences data for the training of RNN. Comprehensive characteristics of nations from UN database are used as input to the hybrid model to predict the nations future population. The results prove that, RNN combined with time series and clustering methods has outperformed mere RNN approach without time series and clustering analysis. In addition, the hybrid Time Series and Clustering-RNN with relevant inputs lead to 20% higher predictive accuracy, measured by Root-Mean-Squared Error, compared to results produced by RNN alone.

The analyses of trends in vegetation dynamics require a profound knowledge of its seasonality. For the determination of the seasonality conventional methods of time series analyses often use a simple averaging of measured values of the identical time in different cycle of the whole time series (e.g. bfast). Then it is assumed that the resulting seasonal portion of a time series is constant and stable for the entire time series. However, analyses of vegetation time series show that trends in vegetation dynamics do not always run steadily, but show structural breaks, especially in regions with high potential for possible landscape changes. For such conversion areas, the assumption of a constant seasonality is not always ensured. The dynamic or variability of the seasonality can have temporal effects by a shift of the start of the season (SOS) or the end of the season (EOS) and therefore also on the length of the vegetation period. To show whether seasonal dynamics can be detected in vegetation time series, two requirements must be fulfilled. (1) High-temporal resolution vegetation information provided for example as MODIS-NDVI. (2) Indicators are needed which allows the description of the variability of seasonality. As a result these metrics allow a better modeling of long-term vegetation dynamics in the trend, taking into account the variability of the seasonality. But at the same time the metrics itself serve as indicators for long term vegetation dynamics. The aim of the present study is to analyse phenological and greenness metrics for the modelling of vegetation dynamics in the nature reserve Konigsbrucker Heide. Detailed analyses of key metrics like SOS and EOS using different metric approaches and interpolation methods are applied and compared. The results show that it is difficult to determine consistent information for example for the trend of single phenology metrics.

Discussion of the Paper by Bruce and Martin