Search results for: geophysical time series

Authors: Maria C. Mariani, Md Al Masum Bhuiyan, Osei K. Tweneboah, Hector G. Huizar

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This work is devoted to the study of modeling geophysical time series. A stochastic technique with time-varying parameters is used to forecast the volatility of data arising in geophysics. In this study, the volatility is defined as a logarithmic first-order autoregressive process. We observe that the inclusion of log-volatility into the time-varying parameter estimation significantly improves forecasting which is facilitated via maximum likelihood estimation. This allows us to conclude that the estimation algorithm for the corresponding one-step-ahead suggested volatility (with ±2 standard prediction errors) is very feasible since it possesses good convergence properties.

Keywords: Augmented Dickey Fuller Test, geophysical time series, maximum likelihood estimation, stochastic volatility model

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Authors: Tak-Chung Fu, Ying-Kit Hung, Fu-Lai Chung

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In the field of time series data mining, the concept of the Perceptually Important Point (PIP) identification process is first introduced in 2001. This process originally works for financial time series pattern matching and it is then found suitable for time series dimensionality reduction and representation. Its strength is on preserving the overall shape of the time series by identifying the salient points in it. With the rise of Big Data, time series data contributes a major proportion, especially on the data which generates by sensors in the Internet of Things (IoT) environment. According to the nature of PIP identification and the successful cases, it is worth to further explore the opportunity to apply PIP in time series ‘Big Data’. However, the performance of PIP identification is always considered as the limitation when dealing with ‘Big’ time series data. In this paper, two distributed versions of PIP identification based on the Specialized Binary (SB) Tree are proposed. The proposed approaches solve the bottleneck when running the PIP identification process in a standalone computer. Improvement in term of speed is obtained by the distributed versions.

Keywords: distributed computing, performance analysis, Perceptually Important Point identification, time series data mining

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Authors: Ognjen Vukovic

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Chern-Simons equation represents the cornerstone of quantum physics. The question that is often asked is if the aforementioned equation can be successfully applied to the interaction in international financial markets. By analysing the time series in financial theory, it is proved that Chern-Simons equation can be successfully applied to financial time-series. The aforementioned statement is based on one important premise and that is that the financial time series follow the fractional Brownian motion. All variants of Chern-Simons equation and theory are applied and analysed. Financial theory time series movement is, firstly, topologically analysed. The main idea is that exchange rate represents two-dimensional projections of three-dimensional Brownian motion movement. Main principles of knot theory and topology are applied to financial time series and setting is created so the Chern-Simons equation can be applied. As Chern-Simons equation is based on small particles, it is multiplied by the magnifying factor to mimic the real world movement. Afterwards, the following equation is optimised using Solver. The equation is applied to n financial time series in order to see if it can capture the interaction between financial time series and consequently explain it. The aforementioned equation represents a novel approach to financial time series analysis and hopefully it will direct further research.

Keywords: Brownian motion, Chern-Simons theory, financial time series, econophysics

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Authors: Farhad Asadi, Mohammad Javad Mollakazemi

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In this paper, Bayesian online inference in models of data series are constructed by change-points algorithm, which separated the observed time series into independent series and study the change and variation of the regime of the data with related statistical characteristics. variation of statistical characteristics of time series data often represent separated phenomena in the some dynamical system, like a change in state of brain dynamical reflected in EEG signal data measurement or a change in important regime of data in many dynamical system. In this paper, prediction algorithm for studying change point location in some time series data is simulated. It is verified that pattern of proposed distribution of data has important factor on simpler and smother fluctuation of hazard rate parameter and also for better identification of change point locations. Finally, the conditions of how the time series distribution effect on factors in this approach are explained and validated with different time series databases for some dynamical system.

Keywords: time series, fluctuation in statistical characteristics, optimal learning, change-point algorithm

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Authors: C. Slim

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Traditional techniques for analyzing time series are based on the notion of stationarity of phenomena under study, but in reality most economic and financial series do not verify this hypothesis, which implies the implementation of specific tools for the detection of such behavior. In this paper, we study nonstationary non-seasonal time series tests in a non-exhaustive manner. We formalize the problem of nonstationary processes with numerical simulations and take stock of their statistical characteristics. The theoretical aspects of some of the most common unit root tests will be discussed. We detail the specification of the tests, showing the advantages and disadvantages of each. The empirical study focuses on the application of these tests to the exchange rate (USD/TND) and the Consumer Price Index (CPI) in Tunisia, in order to compare the Power of these tests with the characteristics of the series.

Keywords: stationarity, unit root tests, economic time series, ADF tests

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Authors: Vineetha Bettaiah, Heggere S. Ranganath

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This paper presents a Hierarchical Piecewise Linear Approximation (HPLA) for the representation of time series data in which the time series is treated as a curve in the time-amplitude image space. The curve is partitioned into segments by choosing perceptually important points as break points. Each segment between adjacent break points is recursively partitioned into two segments at the best point or midpoint until the error between the approximating line and the original curve becomes less than a pre-specified threshold. The HPLA representation achieves dimensionality reduction while preserving prominent local features and general shape of time series. The representation permits course-fine processing at different levels of details, allows flexible definition of similarity based on mathematical measures or general time series shape, and supports time series data mining operations including query by content, clustering and classification based on whole or subsequence similarity.

Keywords: data mining, dimensionality reduction, piecewise linear representation, time series representation

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Authors: Ioannis Andrianakis, Vasileios Gkatas, Nikos Eleftheriadis, Alexios Ellinidis, Ermioni Avramidou

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pscmsForecasting is an open-source web service that implements a variety of time series forecasting algorithms and exposes them to the user via the ubiquitous HTTP protocol. It allows developers to enhance their applications by adding time series forecasting functionalities through an intuitive and easy-to-use interface. This paper provides some background on time series forecasting and gives details about the implemented algorithms, aiming to enhance the end user’s understanding of the underlying methods before incorporating them into their applications. A detailed description of the web service’s interface and its various parameterizations is also provided. Being an open-source project, pcsmsForecasting can also be easily modified and tailored to the specific needs of each application.

Keywords: time series, forecasting, web service, open source

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Authors: Muhammad Tariq, Hammad Tahir, Fawwad Mahmood Butt

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Purpose: This study attempts to examine the best forecasting methodologies in the time series. The time series forecasting models such as VAR, ARCH and the ARMA are considered for the analysis. Methodology: The Bench Marks or the parameters such as Adjusted R square, F-stats, Durban Watson, and Direction of the roots have been critically and empirically analyzed. The empirical analysis consists of time series data of Consumer Price Index and Closing Stock Price. Findings: The results show that the VAR model performed better in comparison to other models. Both the reliability and significance of VAR model is highly appreciable. In contrary to it, the ARCH model showed very poor results for forecasting. However, the results of ARMA model appeared double standards i.e. the AR roots showed that model is stationary and that of MA roots showed that the model is invertible. Therefore, the forecasting would remain doubtful if it made on the bases of ARMA model. It has been concluded that VAR model provides best forecasting results. Practical Implications: This paper provides empirical evidences for the application of time series forecasting model. This paper therefore provides the base for the application of best time series forecasting model.

Keywords: forecasting, time series, auto regression, ARCH, ARMA

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Authors: O. Delage, H. Bencherif, T. Portafaix, A. Bourdier

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The main purpose of time series analysis is to learn about the dynamics behind some time ordered measurement data. Two approaches are used in the literature to get a better knowledge of the dynamics contained in observation data sequences. The first of these approaches concerns time series decomposition, which is an important analysis step allowing patterns and behaviors to be extracted as components providing insight into the mechanisms producing the time series. As in many cases, time series are short, noisy, and non-stationary. To provide components which are physically meaningful, methods such as Empirical Mode Decomposition (EMD), Empirical Wavelet Transform (EWT) or, more recently, Empirical Adaptive Wavelet Decomposition (EAWD) have been proposed. The second approach is to reconstruct the dynamics underlying the time series as a trajectory in state space by mapping a time series into a set of Rᵐ lag vectors by using the method of delays (MOD). Takens has proved that the trajectory obtained with the MOD technic is equivalent to the trajectory representing the dynamics behind the original time series. This work introduces the singular spectrum decomposition (SSD), which is a new adaptive method for decomposing non-linear and non-stationary time series in narrow-banded components. This method takes its origin from singular spectrum analysis (SSA), a nonparametric spectral estimation method used for the analysis and prediction of time series. As the first step of SSD is to constitute a trajectory matrix by embedding a one-dimensional time series into a set of lagged vectors, SSD can also be seen as a reconstruction method like MOD. We will first give a brief overview of the existing decomposition methods (EMD-EWT-EAWD). The SSD method will then be described in detail and applied to experimental time series of observations resulting from total columns of ozone measurements. The results obtained will be compared with those provided by the previously mentioned decomposition methods. We will also compare the reconstruction qualities of the observed dynamics obtained from the SSD and MOD methods.

Keywords: time series analysis, adaptive time series decomposition, wavelet, phase space reconstruction, singular spectrum analysis

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Authors: Mohammad H. Fattahi

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Chaotic analysis has been performed on the river flow time series before and after applying the wavelet based de-noising techniques in order to investigate the noise content effects on chaotic nature of flow series. In this study, 38 years of monthly runoff data of three gauging stations were used. Gauging stations were located in Ghar-e-Aghaj river basin, Fars province, Iran. The noise level of time series was estimated with the aid of Gaussian kernel algorithm. This step was found to be crucial in preventing removal of the vital data such as memory, correlation and trend from the time series in addition to the noise during de-noising process.

Keywords: chaotic behavior, wavelet, noise reduction, river flow

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Authors: Valeria Bondarenko

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We proposed algorithms for: estimation of parameters fBm (volatility and Hurst exponent) and for the approximation of random time series by functional of fBm. We proved the consistency of the estimators, which constitute the above algorithms, and proved the optimal forecast of approximated time series. The adequacy of estimation algorithms, approximation, and forecasting is proved by numerical experiment. During the process of creating software, the system has been created, which is displayed by the hierarchical structure. The comparative analysis of proposed algorithms with the other methods gives evidence of the advantage of approximation method. The results can be used to develop methods for the analysis and modeling of time series describing the economic, physical, biological and other processes.

Keywords: mathematical model, random process, Wiener process, fractional Brownian motion

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Authors: Plessen Mogens Graf

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Within the context of multivariate time series segmentation, this paper proposes a method inspired by a posteriori optimal trading. After a normalization step, time series are treated channelwise as surrogate stock prices that can be traded optimally a posteriori in a virtual portfolio holding either stock or cash. Linear transaction costs are interpreted as hyperparameters for noise filtering. Trading signals, as well as trading signals obtained on the reversed time series, are used for unsupervised channelwise labeling before a consensus over all channels is reached that determines the final segmentation time instants. The method is model-free such that no model prescriptions for segments are made. Benefits of proposed approach include simplicity, computational efficiency, and adaptability to a wide range of different shapes of time series. Performance is demonstrated on synthetic and real-world data, including a large-scale dataset comprising a multivariate time series of dimension 1000 and length 2709. Proposed method is compared to a popular model-based bottom-up approach fitting piecewise affine models and to a recent model-based top-down approach fitting Gaussian models and found to be consistently faster while producing more intuitive results in the sense of segmenting time series at peaks and valleys.

Keywords: time series segmentation, model-free, trading-inspired, multivariate data

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Authors: Jisun Lee, Jay Hyoun Kwon

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As an alternative way to compensate the INS (inertial navigation system) error in non-GNSS (Global Navigation Satellite System) environment, geophysical database referenced navigation is being studied. In this study, both gravity gradient and terrain data were combined to complement the weakness of sole geophysical data as well as to improve the stability of the positioning. The main process to compensate the INS error using geophysical database was constructed on the basis of the EKF (Extended Kalman Filter). In detail, two type of combination method, centralized and decentralized filter, were applied to check the pros and cons of its algorithm and to find more robust results. The performance of each navigation algorithm was evaluated based on the simulation by supposing that the aircraft flies with precise geophysical DB and sensors above nine different trajectories. Especially, the results were compared to the ones from sole geophysical database referenced navigation to check the improvement due to a combination of the heterogeneous geophysical database. It was found that the overall navigation performance was improved, but not all trajectories generated better navigation result by the combination of gravity gradient with terrain data. Also, it was found that the centralized filter generally showed more stable results. It is because that the way to allocate the weight for the decentralized filter could not be optimized due to the local inconsistency of geophysical data. In the future, switching of geophysical data or combining different navigation algorithm are necessary to obtain more robust navigation results.

Keywords: Extended Kalman Filter, geophysical database referenced navigation, gravity gradient, terrain

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Authors: Anita Setianingrum, Oki S. Jaya, Zuherman Rustam

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Forecasting stock price is a challenging task due to the complex time series of the data. The complexity arises from many variables that affect the stock market. Many time series models have been proposed before, but those previous models still have some problems: 1) put the subjectivity of choosing the technical indicators, and 2) rely upon some assumptions about the variables, so it is limited to be applied to all datasets. Therefore, this paper studied a novel Adaptive Neuro-Fuzzy Inference System (ANFIS) time series model based on Support Vector Regression (SVR) for forecasting the stock market. In order to evaluate the performance of proposed models, stock market transaction data of TAIEX and HIS from January to December 2015 is collected as experimental datasets. As a result, the method has outperformed its counterparts in terms of accuracy.

Keywords: ANFIS, fuzzy time series, stock forecasting, SVR

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Authors: Sumit Sen, Sohan Khedekar, Umang Shinde, Shivam Bhargava

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This study has been undertaken to investigate whether the deep learning models are able to predict the future stock prices by training the model with the historical stock price data. Since this work required time series analysis, various models are present today to perform time series analysis such as Recurrent Neural Network LSTM, ARIMA and Facebook Prophet. Applying these models the movement of stock price of stocks are predicted and also tried to provide the future prediction of the stock price of a stock. Final product will be a stock price prediction web application that is developed for providing the user the ease of analysis of the stocks and will also provide the predicted stock price for the next seven days.

Keywords: Autoregressive Integrated Moving Average, Deep Learning, Long Short Term Memory, Time-series

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Authors: Tushnik Sarkar, Mofazzal H. Khondekar, Subrata Banerjee

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This paper investigates the nature of the fluctuation of the daily average Solar wind speed time series collected over a period of 2492 days, from 1^st January, 1997 to 28^th October, 2003. The degree of self-similarity and scalability of the Solar Wind Speed signal has been explored to characterise the signal fluctuation. Multi-fractal Detrended Fluctuation Analysis (MFDFA) method has been implemented on the signal which is under investigation to perform this task. Furthermore, the singularity spectra of the signals have been also obtained to gauge the extent of the multifractality of the time series signal.

Keywords: detrended fluctuation analysis, generalized hurst exponent, holder exponents, multifractal exponent, multifractal spectrum, singularity spectrum, time series analysis

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Authors: Valeria Bondarenko

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In this paper, we propose two problems related to fractal Brownian motion. First problem is simultaneous estimation of two parameters, Hurst exponent and the volatility, that describe this random process. Numerical tests for the simulated fBm provided an efficient method. Second problem is approximation of the increments of the observed time series by a power function by increments from the fractional Brownian motion. Approximation and estimation are shown on the example of real data, daily deposit interest rates.

Keywords: fractional Brownian motion, Gausssian processes, approximation, time series, estimation of properties of the model

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Authors: Wen Liang Chang, Mei Wei Wang, Ruey Huei Yeh

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This paper studies the comparisons of individual and group replacement policies for a series connection system with two machines. Suppose that manufacturer’s production system is a series connection system which is combined by two machines. For two machines, when machines fail within the operating time, minimal repair is performed for machines by the manufacturer. The manufacturer plans to a preventive replacement for machines at a pre-specified time to maintain system normal operation. Under these maintenance policies, the maintenance cost rate models of individual and group replacement for a series connection system with two machines is derived and further, optimal preventive replacement time is obtained such that the expected total maintenance cost rate is minimized. Finally, some numerical examples are given to illustrate the influences of individual and group replacement policies to the maintenance cost rate.

Keywords: individual replacement, group replacement, replacement time, two machines, series connection system

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Authors: Ying Su, Morgan C. Wang

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Long-term time series forecasting is an important research area for automated machine learning (AutoML). Currently, forecasting based on either machine learning or statistical learning is usually built by experts, and it requires significant manual effort, from model construction, feature engineering, and hyper-parameter tuning to the construction of the time series model. Automation is not possible since there are too many human interventions. To overcome these limitations, this article proposed to use recurrent neural networks (RNN) through the memory state of RNN to perform long-term time series prediction. We have shown that this proposed approach is better than the traditional Autoregressive Integrated Moving Average (ARIMA). In addition, we also found it is better than other network systems, including Fully Connected Neural Networks (FNN), Convolutional Neural Networks (CNN), and Nonpooling Convolutional Neural Networks (NPCNN).

Keywords: automated machines learning, autoregressive integrated moving average, neural networks, time series analysis

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Authors: Nor Zila Abd Hamid, Mohd Salmi M. Noorani

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This study is focused on the development of prediction models of the Ozone concentration time series. Prediction model is built based on chaotic approach. Firstly, the chaotic nature of the time series is detected by means of phase space plot and the Cao method. Then, the prediction model is built and the local linear approximation method is used for the forecasting purposes. Traditional prediction of autoregressive linear model is also built. Moreover, an improvement in local linear approximation method is also performed. Prediction models are applied to the hourly ozone time series observed at the benchmark station in Malaysia. Comparison of all models through the calculation of mean absolute error, root mean squared error and correlation coefficient shows that the one with improved prediction method is the best. Thus, chaotic approach is a good approach to be used to develop a prediction model for the Ozone concentration time series.

Keywords: chaotic approach, phase space, Cao method, local linear approximation method

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Authors: Olivier Delage, Hassan Bencherif, Alain Bourdier

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Signal decomposition approaches represent an important step in time series analysis, providing useful knowledge and insight into the data and underlying dynamics characteristics while also facilitating tasks such as noise removal and feature extraction. As most of observational time series are nonlinear and nonstationary, resulting of several physical processes interaction at different time scales, experimental time series have fluctuations at all time scales and requires the development of specific signal decomposition techniques. Most commonly used techniques are data driven, enabling to obtain well-behaved signal components without making any prior-assumptions on input data. Among the most popular time series decomposition techniques, most cited in the literature, are the empirical mode decomposition and its variants, the empirical wavelet transform and singular spectrum analysis. With increasing popularity and utility of these methods in wide ranging applications, it is imperative to gain a good understanding and insight into the operation of these algorithms. In this work, we describe all of the techniques mentioned above as well as their ability to denoise signals, to capture trends, to identify components corresponding to the physical processes involved in the evolution of the observed system and deduce the dimensionality of the underlying dynamics. Results obtained with all of these methods on experimental total ozone columns and rainfall time series will be discussed and compared

Keywords: denoising, empirical mode decomposition, singular spectrum analysis, time series, underlying dynamics, wavelet analysis

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Authors: Nabilah Filzah Mohd Radzuan, Zalinda Othman, Azuraliza Abu Bakar, Abdul Razak Hamdan

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Uncertain data is believed to be an important issue in building up a prediction model. The main objective in the time series uncertainty analysis is to formulate uncertain data in order to gain knowledge and fit low dimensional model prior to a prediction task. This paper discusses the performance of a number of techniques in dealing with uncertain data specifically those which solve uncertain data condition by minimizing the loss of compression properties.

Keywords: compression properties, uncertainty, uncertain time series, mining technique, weather prediction

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Authors: A. K. M. Kamrul Islam, Abdelhamid Bouchachia, Suang Cang, Hongnian Yu

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Forecasting model has a great impact in terms of prediction and continues to do so into the future. Although many forecasting models have been studied in recent years, most researchers focus on different forecasting methods based on fuzzy time series to solve forecasting problems. The forecasted models accuracy fully depends on the two terms that are the length of the interval in the universe of discourse and the content of the forecast rules. Moreover, a hybrid forecasting method can be an effective and efficient way to improve forecasts rather than an individual forecasting model. There are different hybrids forecasting models which combined fuzzy time series with evolutionary algorithms, but the performances are not quite satisfactory. In this paper, we proposed a hybrid forecasting model which deals with the first order as well as high order fuzzy time series and particle swarm optimization to improve the forecasted accuracy. The proposed method used the historical enrollments of the University of Alabama as dataset in the forecasting process. Firstly, we considered an automatic clustering algorithm to calculate the appropriate interval for the historical enrollments. Then particle swarm optimization and fuzzy time series are combined that shows better forecasting accuracy than other existing forecasting models.

Keywords: fuzzy time series (fts), particle swarm optimization, clustering algorithm, hybrid forecasting model

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Authors: Amartya Hatua, Trung Nguyen, Andrew Sung

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In this paper, we study the information diffusion process on Twitter as a multivariate time series problem. Our model concerns three measures (volume, network influence, and sentiment of tweets) based on 10 features, and we collected 27 million tweets to build our information diffusion time series dataset for analysis. Then, different time series clustering techniques with Dynamic Time Warping (DTW) distance were used to identify different patterns of information diffusion. Finally, we built the information diffusion prediction models for new hashtags which comprise two phrases: The first phrase is recognizing the pattern using k-NN with DTW distance; the second phrase is building the forecasting model using the traditional Autoregressive Integrated Moving Average (ARIMA) model and the non-linear recurrent neural network of Long Short-Term Memory (LSTM). Preliminary results of performance evaluation between different forecasting models show that LSTM with clustering information notably outperforms other models. Therefore, our approach can be applied in real-world applications to analyze and predict the information diffusion characteristics of selected topics or memes (hashtags) in Twitter.

Keywords: ARIMA, DTW, information diffusion, LSTM, RNN, time series clustering, time series forecasting, Twitter

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Authors: Md Al Masum Bhuiyan, Maria C. Mariani, Osei K. Tweneboah

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In the present work, we develop a technique for estimating the volatility of financial time series by using stochastic differential equation. Taking the daily closing prices from developed and emergent stock markets as the basis, we argue that the incorporation of stochastic volatility into the time-varying parameter estimation significantly improves the forecasting performance via Maximum Likelihood Estimation. While using the technique, we see the long-memory behavior of data sets and one-step-ahead-predicted log-volatility with ±2 standard errors despite the variation of the observed noise from a Normal mixture distribution, because the financial data studied is not fully Gaussian. Also, the Ornstein-Uhlenbeck process followed in this work simulates well the financial time series, which aligns our estimation algorithm with large data sets due to the fact that this algorithm has good convergence properties.

Keywords: financial time series, maximum likelihood estimation, Ornstein-Uhlenbeck type models, stochastic volatility model

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Authors: Marina Benito-Parejo, Raul Perez-Lopez, Miguel Herraiz, Carolina Guardiola-Albert, Cesar Martinez

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Persistency, long-term memory and randomness are intrinsic properties of time-series of earthquakes. The Rescaled Range Analysis (RS-Analysis) was introduced by Hurst in 1956 and modified by Mandelbrot and Wallis in 1964. This method represents a simple and elegant analysis which determines the range of variation of one natural property (the seismic energy released in this case) in a time interval. Despite the simplicity, there is complexity inherent in the property measured. The cumulative curve of the energy released in time is the well-known fractal geometry of a devil’s staircase. This geometry is used for determining the maximum and minimum value of the range, which is normalized by the standard deviation. The rescaled range obtained obeys a power-law with the time, and the exponent is the Hurst value. Depending on this value, time-series can be classified in long-term or short-term memory. Hence, an algorithm has been developed for compiling the RS-Analysis for time series of earthquakes by days. Completeness time distribution and locally stationarity of the time series are required. The interest of this analysis is their application for a complex seismic crisis where different earthquakes take place in clusters in a short period. Therefore, the Hurst exponent has been obtained for the seismic crisis of Alhoceima (Mediterranean Sea) of January-March, 2016, where at least five medium-sized earthquakes were triggered. According to the values obtained from the Hurst exponent for each cluster, a different mechanical origin can be detected, corroborated by the focal mechanisms calculated by the official institutions. Therefore, this type of analysis not only allows an approach to a greater understanding of a seismic series but also makes possible to discern different types of seismic origins.

Keywords: Alhoceima crisis, earthquake time series, Hurst exponent, rescaled range analysis

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Authors: Hesham A. Elkaranshawy, Amr M. Abdelrazek, Hosam M. Ezzat

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The system of ordinary nonlinear differential equations describing sliding velocity during impact with friction for a three-dimensional rigid-multibody system is developed. No analytical solutions have been obtained before for this highly nonlinear system. Hence, a power series solution is proposed. Since the validity of this solution is limited to its convergence zone, a suitable time step is chosen and at the end of it a new series solution is constructed. For a case study, the trajectory of the sliding velocity using the proposed method is built using 6 time steps, which coincides with a Runge-Kutta solution using 38 time steps.

Keywords: impact with friction, nonlinear ordinary differential equations, power series solutions, rough collision

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Authors: Shreemoyee Sarkar, Vikhyat Chadha

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In this paper, the local fractal properties and chaotic properties of financial time series are investigated by calculating two exponents, the Local Hurst Exponent: LHE and Lyapunov Exponent in a moving time window of a financial series.y. For the purpose of this paper, the Dow Jones Industrial Average (DIJA) and S&P 500, two of the major indices of United States have been considered. The behaviour of the above-mentioned exponents prior to some major crashes (1998 and 2008 crashes in S&P 500 and 2002 and 2008 crashes in DIJA) is discussed. Also, the optimal length of the window for obtaining the best possible results is decided. Based on the outcomes of the above, an attempt is made to predict the crashes and accuracy of such an algorithm is decided.

Keywords: local hurst exponent, lyapunov exponent, market crash prediction, time series chaos, time series local fractal properties

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Authors: Tianhao Zhang, Cen Chen, Dawei Cheng, Yuqi Liang, Yuanyuan Liang

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Dealing with anomalies is a crucial preprocessing step for multivariate time series prediction. However, existing methods that separate anomaly preprocessing and model training into two stages have certain limitations. Specifically, these methods fail to leverage auxiliary information necessary to distinguish latent anomalies related to spatiotemporal factors during the preprocessing stage. Instead, they solely rely on data distribution for detection which may lead to incorrect processing of many samples that are beneficial for training. To address this, we propose STTS-EAD, an end-to-end method that seamlessly integrates anomaly detection into the training process of multivariate time series forecasting and aims to improve Spatio-Temporal learning based Time Series prediction via Embedded Anomaly Detection. Our proposed STTS-EAD leverages spatio-temporal information for forecasting and anomaly detection, with the two parts alternately executed and optimized for each other. To the best of our knowledge, STTS-EAD is the first to integrate anomaly detection and forecasting tasks in the training phase for improving the accuracy of multivariate time series forecasting. Extensive experiments on a public stock dataset and two real-world sales datasets from a renowned coffee chain enterprise show that our proposed method can effectively process detected anomalies in the training stage to improve forecasting performance in the inference stage and significantly outperform baselines.

Keywords: multivariate time series, anomaly detection, time series forecasting, spatiotemporal feature learning

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Authors: Abiodun Ayodele Sanyaolu

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The research was carried out to investigate the time series analysis on quarterly production of fruit juice at the National Horticultural Research Institute Ibadan from 2010 to 2018. Documentary method of data collection was used, and the method of least square and moving average were used in the analysis. From the calculation and the graph, it was glaring that there was increase, decrease, and uniform movements in both the graph of the original data and the tabulated quarter values of the original data. Time series analysis was used to detect the trend in the highest number of fruit juice and it appears to be good over a period of time and the methods used to forecast are additive and multiplicative models. Since it was observed that the production of fruit juice is usually high in January of every year, it is strongly advised that National Horticultural Research Institute should make more provision for fruit juice storage outside this period of the year.

Keywords: fruit juice, least square, multiplicative models, time series

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