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Most real world time series have transient behaviours and are non-stationary. They exhibit different type of non-stationarities, such as trends, cycles, random-walking, and generally exhibit strong intermittency. Therefore local stochastic characteristics of time series, such as the drift and diffusion coefficients, as well as the jump rate and jump amplitude, will provide very important information for understanding and quantifying “real time” variability of time series. For diffusive processes the systems have a longer memory and a higher correlation time scale and, therefore, one expects the stochastic features of dynamics to change slowly. In contrast, a rapid change of dynamics with... 

Jumps are discontinuous variations in time series and with large amplitude can be considered as an extreme event. We expect the higher the jump activity to cause higher uncertainty in the stochastic behaviour of measured time series. Therefore, building statistical evidence to detect real jump seems of primary importance. In addition jump events can participate in the observed non-Gaussian feature of the increments’ (ramp up and ramp down) statistics of many time series [1]. This is the reason that most of the jump detection techniques are based on threshold values for differential of time series. There is not, however, a robust method for detection and characterisation of such discontinuous... 

In this chapter we reconstruct stochastic dynamical equations with known drift and diffusion coefficients, as well as known properties of jumps, jump amplitude and jump rate from synthetic time series, sampled with time interval τ. The examples have Langevin (white noise- and Lévy noise-driven) and jump-diffusion dynamical equations. We also study the estimation of the Kramers–Moyal coefficients for “phase” dynamics that enable us to investigate the phenomenon of synchronisation in systems with interaction. © 2019, Springer Nature Switzerland AG  

Most real world time series have transient behaviours and are non-stationary. They exhibit different type of non-stationarities, such as trends, cycles, random-walking, and generally exhibit strong intermittency. Therefore local stochastic characteristics of time series, such as the drift and diffusion coefficients, as well as the jump rate and jump amplitude, will provide very important information for understanding and quantifying “real time” variability of time series. For diffusive processes the systems have a longer memory and a higher correlation time scale and, therefore, one expects the stochastic features of dynamics to change slowly. In contrast, a rapid change of dynamics with... 

Jumps are discontinuous variations in time series and with large amplitude can be considered as an extreme event. We expect the higher the jump activity to cause higher uncertainty in the stochastic behaviour of measured time series. Therefore, building statistical evidence to detect real jump seems of primary importance. In addition jump events can participate in the observed non-Gaussian feature of the increments’ (ramp up and ramp down) statistics of many time series [1]. This is the reason that most of the jump detection techniques are based on threshold values for differential of time series. There is not, however, a robust method for detection and characterisation of such discontinuous... 

This paper presents a new model to short-term prediction of air pollution using a new structure is based on the intelligent neural networks. A new structure known as Time Delay Cerebellar Model Arithmetic Computer (TD-CMAC), an extension to the CMAC, it requires fewer memory sizes. The new model is demonstrated and validated with three primary air pollutants known as carbon monoxide (CO), sulfur dioxide (SO2), and nitrogen dioxide (NO 2). The simulation results for the half an hour ahead-prediction of the air pollutant data set show that the suggested new model is suitable for our purpose  

Temporal synchronization of neuronal activity plays an important role in various brain functions such as binding, cognition, information processing, and computation. Patients suffering from disorders such as Alzheimer’s disease or schizophrenia show abnormality in the synchronization patterns. Electroencephalography (EEG) is a cheap, non-invasive, and easy-to-use method with fine temporal resolution. Modern multichannel EEG data are increasingly being used in brain studies. Traditional approaches for identifying synchronous activity in EEG are through univariate techniques such as power spectral density or bivariate techniques such as coherence. In this paper, we review two methods for... 

We use the detrended fluctuation analysis (DFA), the detrended cross correlation analysis (DCCA) and the magnitude and sign decomposition analysis to study the fluctuations in the turbulent time series and to probe long-term nonlinear levels of complexity in weakly and high turbulent flow. The DFA analysis indicate that there is a time scaling region in the fluctuation function, segregating regimes with different scaling exponents. We discuss that this time scaling region is related to inertial range in turbulent flows. The DCCA exponent implies the presence of power-law cross correlations. In addition, we conclude its multifractality for high Reynold's number in inertial range. Further, we... 

A model to predict air pollutants' concentrations was developed by implementing spectral decomposition of time series data, obtained by Kolmogorov-Zurbenko filter, in Artificial Neural Networks (ANN). This model was utilized to separate and individually predict three spectral components of air pollutants' time series of short, seasonal, and long-term. The best set of input variable was selected by evaluating the significance of different input variables while modeling different time series components. Moreover, different possible approaches for constructing such models were examined. Performance of the constructed model to predict air pollutants' level at a central location in Tehran, Iran,... 

The trend of gold price in the market is the most important consideration for the investors of the gold, and serves as the basis of gaining profit, so there are scholars who try to forecast the gold price. Forecasting accuracy is one of the most important factors involved in selecting a forecasting method. Besides, nowadays artificial intelligence (AI) techniques are becoming more and more widespread because of their accuracy, symbolic reasoning, flexibility and explanation capabilities. Among these techniques, particle swarm optimization (PSO) is one of the best AI techniques for optimization and parameter estimation. In this study a PSO-based time series model for the gold price... 

Intelligent solutions, based on artificial intelligence (AI) technologies, to solve complicated practical problems in various sectors are becoming more and more widespread nowadays. On the other hand, electrical load prediction is one of the important concerns of power systems so development of intelligent prediction tools for performing accurate predictions is essential. This study presents an intelligent hybrid approach called ACO-SA by hybridization of Ant Colony Optimization (ACO) and Simulated Annealing (SA). The hybrid approach consists of two general stages. At the first stage time series inputs will be fed into ACO and it performs a global search to find a globally optimum solution.... 

Understanding the behavior and estimating the magnitude of floods with specific recurrence intervals are important tasks for various applications such as flood protection strategies. Fractal analysis has proven useful in characterization of flood frequency behavior. We employ a systematic fractal approach which enables dividing streamflow data into different behavior regimes and, in particular, identifying flood regimes. Since seasonality is a key factor in flood-formation scenarios, we incorporate this concept in our analysis through generating two separate streamflow data sets for summer and winter, and next performing associated fractal analysis on each. To illustrate our approach and see... 

In this paper, a new approach to control continuous time chaotic systems with an unknown governing equation and limitation on the measurement of states, has been investigated. In many chaotic systems, disability to measure all of the states is a usual limitation, like in some economical, biological and many other engineering systems. Takens showed that a chaotic attractor has an astonishing feature in which it can embed to a mathematically similar attractor by using time series of one of the states. The new embedded attractor saves much information from the original attractor. This phenomenon has been deployed to present a new way to control continuous time chaotic systems, when only one of... 

This paper describes the application of statistical and spectral procedures that identifies trends and periodicity in streamflow time series. The results of Mann-Kendall and seasonal Kendall tests (non-parametric tests which are known as appropriate tools in detecting linear trends of hydrological time series) shows negative trends especially during low water months (August to November). This downward trend is more significant in October. But these methods can not interpret periodic behavior. Hence spectral procedures were applied on data series to investigate periodicities in streamflow data series. Fourier and Continuous Wavelet Transform (CWT) analyses produce evidence of interannual... 

Globalization is shaping a new socio-economic order with profound, and still unfolding, implications for transportation development. A prerequisite for national competitiveness in the global market place is efficacious transportation when its recent technological advances have created an unprecedented rise in mobility and accessibility. Developments of efficient and effective transportation infrastructure and services are among the principal driving forces for the globalization process. Using international databanks, this paper describes an attempt to shed some light on national trends of globalization and transportation, and their relationships. Deploying a comparative macroscopic approach... 

This paper proposes a novel 3D action recognition technique that uses time-series information extracted from depth image sequences for use in systems of human daily activity monitoring. To this end, each action is represented as a multi-dimensional time series, where each dimension represents the position variation of one skeleton joint over time. The time series is then mapped onto a vector space using Dynamic Time Warping (DTW) distance. Furthermore, to employ the correlation-distinctiveness relationship of the sequences in recognition, this vector space is remapped onto a discriminative space using the regularized Fisher method, where final decisions about the actions are made. Unlike...