Time Series Analysis

Applied Time Series Analysis and Innovative Computing contains the applied time series analysis and innovative computing paradigms, with frontier application studies for the time series problems based on the recent works at the Oxford University Computing Laboratory, University of Oxford, the University of Hong Kong, and the Chinese University of Hong Kong. The monograph was drafted when the author was a post-doctoral fellow in Harvard School of Engineering and Applied Sciences, Harvard University. It provides a systematic introduction to the use of innovative computing paradigms as an investigative tool for applications in time series analysis. Applied Time Series Analysis and Innovative Computing offers the state of art of tremendous advances in applied time series analysis and innovative computing paradigms and also serves as an excellent reference work for researchers and graduate students working on applied time series analysis and innovative computing paradigms.

Since the 2008 global economic crisis, the detection of financial instabilities has garnered extensive research attention, particularly through the application of time-series analysis. In this study, a novel time-series analysis method, integrating the Kullback-Leibler Divergence (KLD) metric with a sliding window technique, is proposed to detect instabilities in time-series data, especially in financial markets. Global financial time series from 2004 to 2022 were analyzed. The raw time series were preprocessed into return rate series and transformed into complex networks using the directed horizontal visibility graph (DHVG) algorithm, effectively preserving temporal variabilities in network topologies. The KLD method was evaluated through both retrospective analysis and real-time monitoring. It successfully identified idiosyncratic incidents in the financial market, correlating them with specific economic events. Compared to traditional metrics (e.g., moments) and econometric methods, KLD demonstrated superior performance in capturing sequence information and detecting anomalies without requiring linear regression models. Although initially designed for financial data, the KLD method is versatile and can be applied to other types of time series as well.

The application of time series analysis to describe the dynamic movements of suspension bridges

The application of machine learning (ML) for use in generating insights and making predictions on new records continues to expand within the medical community. Despite this progress to date, the application of time series analysis has remained underexplored due to complexity of the underlying techniques. In this study, we have deployed a novel ML, called automated time series (AutoTS) machine learning, to automate data processing and the application of a multitude of models to assess which best forecasts future values. This rapid experimentation allows for and enables the selection of the most accurate model in order to perform time series predictions. By using the nation-wide ICD-10 (International Classification of Diseases, Tenth Revision) dataset of hospitalized patients of Romania, we have generated time series datasets over the period of 2008–2018 and performed highly accurate AutoTS predictions for the ten deadliest diseases. Forecast results for the years 2019 and 2020 were generated on a NUTS 2 (Nomenclature of Territorial Units for Statistics) regional level. This is the first study to our knowledge to perform time series forecasting of multiple diseases at a regional level using automated time series machine learning on a national ICD-10 dataset. The deployment of AutoTS technology can help decision makers in implementing targeted national health policies more efficiently.

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.

TSERIES is a computer program which was written to perform Box-Jenkins type analyses for univariate time series data. The program is capable of performing the analyses described in the first nine chapters of Box and Jenkins (1976) and it follows the general outline given there. TSERIES is both versatile and easy to use. Input is accomplished through a series of simple, compact commands, only a small number of which are needed for standard analyses. However, there are a large number of additional commands that can be used to modify standard assumptions and invoke special options. It is easy to learn to use the program. As a result, it has been very useful in practical applications as well as for giving students hands-on experience in courses on applied time series analysis. One of the important features of TSERIES is its easy-to-use free field command structure which was patterned after two other popular statistical packages, OMNITAB and MINITAB. For example, the following commands would be sufficient to produce outputs for identification of a time series model for a stationary time series of length 200:

Aquifers in mountain areas are a strategic resource for the people who live there. To optimise future management, it is vital to understand hydrogeological systems from both geological and hydrogeological perspectives. Historically, methods such as hydrograph and time series analyses have been applied to characterise large karst systems. The aim of this paper was to apply these methods to small mountain springs supplied by porous and shallow aquifers. Specifically were made: (1) a comparison to understand which method better fits the depletion curve of the aquifers and (2) an application of time series analysis both by auto-correlation (analysis of individual series) and by cross-correlation methods (analysis of interrelationships between time series) on all the three parameters monitored from the probe (discharge Q, temperature T, electrical conductivity EC). These techniques were applied on four mountain springs located in the Italy North-Western Alps in the Aosta Valley Region. The results suggested that spring hydrograph and time series analyses on Q, T and EC parameters are useful tools for understanding the hydrodynamic behaviour of porous and shallow aquifers and how to make a proper management of the resource.

Thyroid cancer, a prevalent and potentially life-threatening disease, demands early detection for effective treatment. This study proposes a novel approach for the early detection of thyroid cancer by employing Time Series Analysis (TSA) and Quadratic Discriminant Analysis (QDA). The integration of these techniques aims to enhance diagnostic accuracy and reliability, providing a valuable tool for clinicians to detect the disease in its early stages. In our approach, TSA was used to extract meaningful patterns and trends from temporal data, offering valuable insights into the evolving health status of the thyroid. Subsequently, QDA was applied to build a robust classification model, using the identified time series features to distinguish between cancerous and non-cancerous cases. The application of TSA and QDA yielded promising results, demonstrating high sensitivity and specificity, and outperforming traditional diagnostic methods. Our model achieved an accuracy of 97.72%, precision of 90.91%, sensitivity of 94.01%, and specificity of 98.2%. The incorporation of temporal dynamics through TSA provided a nuanced understanding of the evolving pathology, contributing to the enhanced accuracy of the diagnostic model. In conclusion, this study introduces a novel methodology for early thyroid cancer detection, combining the strengths of TSA and QDA. The results highlight the effectiveness of this integrated approach in improving diagnostic accuracy, particularly in identifying subtle temporal changes indicative of thyroid cancer. The proposed TSA-QDA model shows superior performance in terms of sensitivity, specificity, and classification accuracy for multi-class TIRADS classification.

There are many reasons to analyze the time series data, for example, to understand the underlying generating mechanism better, to achieve optimal control of the system, or to obtain better forecasting of future values. Applied time series analysis consists of empirical models for analyzing time series in order to extract meaningful statistics and other properties of the time series data. Time series models have various forms and represent different stochastic processes. Time series analysis model is usually classified as either time domain model or frequency domain model. Time domain models include the auto-correlation and cross-correlation analysis. In a time domain model, mathematical functions are usually used to study the data with respect to time. The three broad classes for modeling the variations of time series process are the autoregressive models, the integrated models, and the moving average models. The autoregressive integrated moving average models are the general class of these models for forecasting a time series that can be stationarized by transformations such as differencing. In a frequency domain model, the analysis of mathematical functions or signals is conducted with respect to frequency rather than time. Mathematical models can be used to convert the time series data between the time and frequency domains. The parameters and features in the frequency domain can be used as inputs for the mathematical models like discrimination analysis and improved results can be obtained.KeywordsTime series analysisBasic characteristicsEstimation of correlationAutoregressionMathematical models

With the diversification of applications and the diversity of users, the era of big data is always producing various new types of data, such as graph data, time series data, and spatial data. When predicting the future trend of the system, we always need to learn from the historical working state, and time series data plays a huge value in this aspect. Hardware resources are becoming cheaper, computing power has made major breakthroughs, and multi-machine and multi-core scenarios have become commonplace. At present, the focus of large-scale time series data processing is either focused on data collection and storage, or on single-machine processing, which has been unable to meet the existing needs. In response to this problem, this paper designs and implements a distributed large-scale time series processing and analysis system based on the Spark platform. The system framework is mainly divided into storage layer, operator layer and algorithm layer. At the storage layer, the system completes the organization and indexing of large-scale time series data based on HDFS and Hive. At the operator layer, the system provides users with basic operations commonly used for time series data on the Spark platform, and allows users to directly use these operators to implement custom time series related processing algorithms. At the algorithm level, the system implements some commonly used time series analysis algorithms in the Spark platform, including time series similarity query, clustering and prediction, so that users can directly use these algorithms to analyze time series. Finally, the feasibility and practicability of this system are verified by testing the performance and function of the system.

Virtually any random process developing chronologically can be viewed as a time series. In economics closing prices of stocks, the cost of money, the jobless rate, and retail sales are just a few examples of many. Developed from course notes and extensively classroom-tested, Applied Time Series Analysis with R, Second Edition includes examples across a variety of fields, develops theory, and provides an R-based software package to aid in addressing time series problems in a broad spectrum of fields. The material is organized in an optimal format for graduate students in statistics as well as in the natural and social sciences to learn to use and understand the tools of applied time series analysis. Features Gives readers the ability to actually solve significant real-world problems Addresses many types of nonstationary time series and cutting-edge methodologies Promotes understanding of the data and associated models rather than viewing it as the output of a black box Provides the R package tswge available on CRAN which contains functions and over 100 real and simulated data sets to accompany the book. Extensive help regarding the use of tswge functions is provided in appendices and on an associated website. Over 150 exercises and extensive support for instructors The second edition includes additional real-data examples, uses R-based code that helps students easily analyze data, generate realizations from models, and explore the associated characteristics. It also adds discussion of new advances in the analysis of long memory data and data with time-varying frequencies (TVF).

BSMART: a Matlab/C toolbox for analysis of multichannel neural time series.

Singular spectral and control chart analysis of soil radon and thoron time series for forecasting seismic activities

Daily time series of microwave radiometer data obtained in one-orbit direction are full of observation gaps due to satellite configuration and errors from spatial sampling. Such time series carry information about the surface signal including surface emittance and vegetation attenuation, and the atmospheric signal including atmosphere emittance and atmospheric attenuation. To extract the surface signal from this noisy time series, the Time Series Analysis Procedure (TSAP) was developed, based on the properties of the Discrete Fourier Transform (DFT). TSAP includes two stages: (1) identify the spectral features of observation gaps and errors and remove them with a modified boxcar filter; and (2) identify the spectral features of the surface signal and reconstruct it with the Harmonic Analysis of Time Series (HANTS) algorithm. Polarization Difference Brightness Temperature (PDBT) at 37 GHz data were used to illustrate the problems, to explain the implementation of TSAP and to validate this method, due to the PDBT sensitivity to the water content both at the land surface and in the atmosphere. We carried out a case study on a limited heterogeneous crop land and lake area, where the power spectrum of the PDBT time series showed that the harmonic components associated with observation gaps and errors have periods ≤8 days. After applying the modified boxcar filter with a length of 10 days, the RMSD between raw and filtered time series was above 11 K, mainly related to the power reduction in the frequency range associated with observation gaps and errors. Noise reduction is beneficial when applying PDBT observations to monitor wet areas and open water, since the PDBT range between dryland and open water is about 20 K. The spectral features of the atmospheric signal can be revealed by time series analysis of rain-gauge data, since the PDBT at 37 GHz is mainly attenuated by hydrometeors that yield precipitation. Thus, the spectral features of the surface signal were identified in the PDBT time series with the help of the rain-gauge data. HANTS reconstructed the upper envelope of the signal, i.e., correcting for atmospheric influence, while retaining the spectral features of the surface signal. To evaluate the impact of TSAP on retrieval accuracy, the fraction of Water Saturated Surface (WSS) in the region of Poyang Lake was retrieved with 37 GHz observations. The retrievals were evaluated against estimations of the lake area obtained with MODerate-resolution Imaging Spectroradiometer (MODIS) and Advanced Synthetic Aperture Radar (ASAR) data. The Relative RMSE on WSS was 39.5% with unfiltered data and 23% after applying TSAP, i.e., using the estimated surface signal only.

In tropical and subtropical regions of eastern and South-eastern Asia, dengue fever (DF) and dengue hemorrhagic fever (DHF) outbreaks occur frequently. Previous studies indicate an association between meteorological variables and dengue incidence using time series analyses. The impacts of meteorological changes can affect dengue outbreak. However, difficulties in collecting detailed time series data in developing countries have led to common use of monthly data in most previous studies. In addition, time series analyses are often limited to one area because of the difficulty in collecting meteorological and dengue incidence data in multiple areas. To gain better understanding, we examined the effects of meteorological factors on dengue incidence in three geographically distinct areas (Ratnapura, Colombo, and Anuradhapura) of Sri Lanka by time series analysis of weekly data. The weekly average maximum temperature and total rainfall and the total number of dengue cases from 2005 to 2011 (7 years) were used as time series data in this study. Subsequently, time series analyses were performed on the basis of ordinary least squares regression analysis followed by the vector autoregressive model (VAR). In conclusion, weekly average maximum temperatures and the weekly total rainfall did not significantly affect dengue incidence in three geographically different areas of Sri Lanka. However, the weekly total rainfall slightly influenced dengue incidence in the cities of Colombo and Anuradhapura.