Artificial Time Series Research Articles

Comparison of Different Techniques to Calculate Properties of Atmospheric Turbulence from Low-Resolution Data

In this work we study different techniques to estimate basic properties of turbulence, that is its characteristic velocity and length scale from low-resolution data. The methods are based on statistics of the signals like the velocity spectra, second-order structure function, number of signal’s zero-crossings and the variance of velocity derivative. First, in depth analysis of estimates from artificial velocity time series is performed. Errors due to finite averaging window, finite cut-off frequencies and different fitting ranges are discussed. Next, real atmospheric measurement data are studied. It is demonstrated that differences between results of the methods can indicate deviations from the Kolmogorov’s theory or the presence of external intermittency, that is the existence of alternating laminar/turbulent flow patches.

Two-dimensional correlation analysis of periodicity in active galactic nuclei time series

Abstract The active galactic nuclei (AGN) are among the most powerful sources with an inherent, pronounced and random variation of brightness. The randomness of their time series is so subtle as to blur the border between aperiodic fluctuations and noisy oscillations. This poses challenges to analysing of such time series because neither visual inspection nor pre-exisitng methods can identify well oscillatory signals in them. Thus, there is a need for an objective method for periodicity detection. Here we review our a new data analysis method that combines a two-dimensional correlation (2D) of time series with the powerful methods of Gaussian processes. To demonstrate the utility of this technique, we apply it to two example problems which were not exploited enough: damped rednoised artificial time series mimicking AGN time series and newly published observed time series of changing look AGN (CL AGN) NGC 3516. The method successfully detected periodicities in both types of time series. Identified periodicity of ~4 yr in NGC 3516 allows us to speculate that if the thermal instability formed in its accretion disc (AD) on a time scale resembling detected periodicity then AD radius could be ~0.0024 pc.

Forecasting MSW generation using artificial neural network time series model: a study from metropolitan city

Forecasting the quantity of municipal solid waste generation is an essential task for sustainable solid waste management and strategy implementation. The estimation of future waste generation rates can help to motivate for analyzing gaps in existing waste management and better planning strategies. Improper management and unsafe disposal of solid waste create a threat to the environment and human health. Hence, a sound forecasting of solid waste generation is very crucial for planning and management accordingly. Artificial intelligence is an excellent and new application of soft computing which is used as a forecasting tool. The main objective of this study is to apply ANN time series model along with autoregressive technique to forecast the monthly solid waste generation in Kolkata. For the same, data related to the monthly solid waste generation was gathered from 2010 to 2017. Total data of 96 months were divided into three categories, i.e., 70%, 15%, and 15% for training, validation, and testing, respectively. The model was evaluated based on performance value of mean square error, root mean square error, and regression coefficient. The ANN structure of 1-19-1 was considered as optimized model for solid waste forecasting because it has the lowest mean square error and the highest regression coefficient. The applied time series model forecasts that Kolkata will generate about 5205 MT/day municipal solid waste in 2030 which will add more than 1000 MT/day waste with the existing rate of generation. The present study helps in estimating and allocating essential resources that need in future for sound solid waste management and preparing alternative strategies to reach the sustainable goals.

Forecasting Automobile Sales in Turkey with Artificial Neural Networks

This study aims to reveal significant factors which affect automobile sales and estimate the automobile sales in Turkey by using Artificial Neural Network (ANN), ARIMA, and time series decomposition techniques. The forecasting model includes automobile sales, automobile price, Euro and Dollar exchange rate, employment rate, consumer confidence index, oil prices and industrial production confidence index, the probability of buying an automobile, female employment rate, general economic situation, the expectation of general economic situation, financial status of households, expectation of financial status of households. According to the regression results, changes in Dollar exchange rate, the expectation of financial status of households, seasonally adjusted industrial production index, logarithmic form of automobile sales before-one-month which have a significant effect on automobile sales, are found to be the significant variables. The results show that ANN has a better estimation performance with MAPE=1.18% and RMSE=782 values than ARIMA and time series decomposition techniques.

DeePr-ESN: A deep projection-encoding echo-state network

As a recurrent neural network that requires no training, the reservoir computing (RC) model has attracted widespread attention in the last decade, especially in the context of time series prediction. However, most time series have a multiscale structure, which a single-hidden-layer RC model may have difficulty capturing. In this paper, we propose a novel multiple projection-encoding hierarchical reservoir computing framework called Deep Projection-encoding Echo State Network (DeePr-ESN). The most distinctive feature of our model is its ability to learn multiscale dynamics through stacked ESNs, connected via subspace projections. Specifically, when an input time series is projected into the high-dimensional echo-state space of a reservoir, a subsequent encoding layer (e.g., an autoencoder or PCA) projects the echo-state representations into a lower-dimensional feature space. These representations are the principal components of the echo-state representations, which removes the high frequency components of the representations. These can then be processed by another ESN through random connections. By using projection layers and encoding layers alternately, our DeePr-ESN can provide much more robust generalization performance than previous methods, and also fully takes advantage of the temporal kernel property of ESNs to encode the multiscale dynamics of time series. In our experiments, the DeePr-ESNs outperform both standard ESNs and existing hierarchical reservoir computing models on some artificial and real-world time series prediction tasks.

Chaotic Time Series Prediction Using a Novel Echo State Network Model with Input Reconstruction, Bayesian Ridge Regression and Independent Component Analysis

This paper presents a novel Echo State Network (ESN) model for chaotic time series prediction, which consists of three steps including input reconstruction, dimensionality reduction and regression. First, phase-space reconstruction is used to reconstruct the original ‘attractor’ of the input time series. Then, Independent Component Analysis (ICA) is used to identify independent components, reduce dimensionality and overcome multicollinearity problem of the reconstructed input matrix. Finally, Bayesian Ridge Regression provides accurate predictions thanks to its regularization effect to avoid over-fitting and its robustness to noise owing to its probabilistic strategy. Our experimental results show that our model significantly outperforms other ESN models in predicting both artificial and real-world chaotic time series.

Deviations from normal distributions in artificial and real time series: a false positive prescription

ABSTRACT Time-series analysis allows for the determination of the Power Spectral Density (PSD) and Probability Density Function (PDF) for astrophysical sources. The former of these illustrates the distribution of power at various time-scales, typically taking a power-law form, while the latter characterizes the distribution of the underlying stochastic physical processes, with Gaussian and lognormal functional forms both physically motivated. In this paper, we use artificial time series generated using the prescription of Timmer & Koenig to investigate connections between the PDF and PSD. PDFs calculated for these artificial light curves are less likely to be well described by a Gaussian functional form for steep (Γ⪆1) PSD indices due to weak non-stationarity. Using the Fermi LAT monthly light curve of the blazar PKS2155-304 as an example, we prescribe and calculate a false positive rate that indicates how likely the PDF is to be attributed an incorrect functional form. Here, we generate large numbers of artificial light curves with intrinsically normally distributed PDFs and with statistical properties consistent with observations. These are used to evaluate the probabilities that either Gaussian or lognormal functional forms better describe the PDF. We use this prescription to show that PKS2155-304 requires a high prior probability of having a normally distributed PDF, $P(\rm {G})~$ ≥ 0.82, for the calculated PDF to prefer a Gaussian functional form over a lognormal. We present possible choices of prior and evaluate the probability that PKS2155-304 has a lognormally distributed PDF for each.

A Simple Similarity Index for the Comparison of Remotely Sensed Time Series with Scarce Simultaneous Acquisitions

Emergence of new state-of-the-art technologies has enabled an unprecedented amount of high spatial resolution satellite data having great potential for exploitation of extracted time series for a vast range of applications. Despite the high temporal resolution of time series, the number of real observations of optical data that can be utilized is reduced due to meteorological conditions (such as cloud or haze) prevailing at the time of acquisition. This fact has an effect on the density of the retrieved time series and subsequently on a number of coincidental observations when comparing the similarity of time series from two different data sources for which the simultaneous acquisition date is already scarce. Classical tools for assessing the similarity of such time series can prove to be difficult or even impossible because of a lack of simultaneous observations. In this paper, we propose a simple method in order to circumvent this scarcity issue. In the first step, we rely on an interpolation in order to produce artificial time series on the union of the original acquisition dates. Then, we extend the theory of the correlation coefficient (CC) estimator to these interpolated time series. After validation on synthetic data, this simple approach proved to be extremely efficient on a real case study where Sentinel-2 and PlanetScope NDVI time series on parcels in The Netherlands are compared. Indeed, compared to other methods, it reduced the number of undecided cases while also improving the power of the statistical test on the similarity between both types of time series and the precision of the estimated CC.

Hybrid models to improve the monthly river flow prediction: Integrating artificial intelligence and non-linear time series models

Prediction of river flow as a fundamental source of hydrological information plays a crucial role in various fields of water projects. In this study, at first, the capabilities of two time series analysis approaches, namely self-exciting threshold autoregressive (SETAR) and generalized autoregressive conditional heteroscedasticity (GARCH) models, then three artificial intelligence approaches including artificial neural networks (ANN), multivariate adaptive regression splines (MARS), and random forests (RF) models were investigated to predict monthly river flow. For this purpose, monthly river flow data of Brantford and Galt stations on Grand River, Canada, for the period from October 1948 to September 2017 were used and their performances were evaluated based on various evaluation criteria. The SETAR model showed better performance than the GARCH one in prediction of river flows at the stations of study. Additionally, the stand-alone MARS and RF models performed slightly better than the ANN. Next, hybrid models were developed by coupling the used ANN, MARS, and RF models with SETAR and GARCH models as the non-linear time series models. The performance of various models presented in this study indicated that the new hybrid models demonstrated a much better performance compared with the stand-alone ones at both stations. Among the developed hybrid models, the RF-SETAR models generally had the best accuracy to improve the river flows modeling. As a result, it can be concluded that the presented methodology can be used to predict hydrological time series such as river flow with a high level of accuracy.

An improved Elman neural network with piecewise weighted gradient for time series prediction

Time series prediction is an important tool for system analysis. Traditional forecasting methods usually achieve prediction by establishing static model or only mining the information from the sequence itself, but without considering the dynamics of the system or its triggering factors. Elman neural network (ENN) is a dynamical model that can remember historical states. In order to better establish the real multivariate time series model and improve the single-step prediction accuracy, this study proposes an improved regularized ENN method based on piecewise time weighted gradient (PWRENN). Each time the parameters of PWRENN model are updated, the weighted gradient is calculated by weighing the current gradient and the previous gradients according to a monotonically increasing temporal function. By considering both the current gradient and previous gradients, PWRENN is able to simulate the time-lag effect in the time series prediction problem. Moreover, the system environment may change with time, and the historical data of the same slot at a different time should have different effects on the predicted data. This work uses a piecewise time function with different parameters at different time periods to more accurately model the real system. In PWRENN, L2 regularization is adopted to solve the overfitting problem and enhance the generalization performance. Furthermore, the effectiveness of the proposed method is verified in an artificial Mackey-Glass time series prediction and three landslide displacement predictions.

Long-range correlation properties of stationary linear models with mixed periodicities.

We consider the problem of (stationary and linear) source systems which generate time series data with long-range correlations. We use the discrete Fourier transform (DFT) and build stationary linear models using artificial time series data exhibiting a 1/f spectrum, where the models can include only terms that contribute significantly to the model as assessed by information criteria. The result is that the optimal (best) model is only composed of mixed periodicities [that is, the model does not include all (continuous) periodicities] and the time series data generated by the model exhibit a clear 1/f spectrum in a wide frequency range. It is considered that as the 1/f spectrum is a consequence of the contributions of all periods, consecutive periods are indispensable to generate such data by stationary linear models. However, the results indicate that there are cases where this expectation is not always met. These results also imply that although we can know linear features of time series data using the DFT, we always cannot substantially infer the type of the source system, even if the system is stationary linear.

Analysis of time series through complexity–entropy curves based on generalized fractional entropy

In this paper, we propose the complexity–entropy causality plane based on the generalized fractional entropy. When applying the proposed method into artificial time series and empirical time series, we find that both results show that the stochastic and chaotic time series are clearly distinguished. On the one hand, we could distinguish them according to the trend of the normalized generalized fractional entropy H as the parameter $$\alpha $$ increases. On the other hand, the stochastic and chaotic time series can be distinguished by the trend of their corresponding extreme values $$\alpha _C$$ with the increase in embedding dimension m. However, compared with the q-complexity–entropy plane, the trend of their extreme value $$\alpha _C$$ is irregular. Moreover, when applying the complexity–entropy causality plane into financial time series, we could obtain more accurate and clearer information on the classification of different regional financial markets.

Tracking Poisson Parameter for Non-Stationary Discontinuous Time Series with Taylor’s Abnormal Fluctuation Scaling

We propose a parameter estimation method for non-stationary Poisson time series with the abnormal fluctuation scaling, known as Taylor’s law. By introducing the effect of Taylor’s fluctuation scaling into the State Space Model with the Particle Filter, the underlying Poisson parameter’s time evolution is estimated correctly from given non-stationary time series data with abnormally large fluctuations. We also developed a discontinuity detection method which enables tracking the Poisson parameter even for time series including sudden discontinuous jumps. As an example of application of this new general method, we analyzed Point-of-Sales data in convenience stores to estimate change of probability of purchase of commodities under fluctuating number of potential customers. The effectiveness of our method for Poisson time series with non-stationarity, large discontinuities and Taylor’s fluctuation scaling is verified by artificial and actual time series.

Is observation uncertainty masking the signal of land use change impacts on hydrology?

Analysis of hydrological impacts of land use change raises questions about whether, and how much, such impacts are misrepresented because of errors in river flow observations. In this paper, land use change impacts (represented by changes in watershed storage) and different ranges of discharge measurement error are compared to assess how errors in discharge measurement can potentially mask a land use change impact. Using a watershed from the Ethiopian highlands to exemplify this, we simulated five different levels of land use change impacts with five levels of watershed storage reductions (from 10% to 50% change) and the associated time series of runoff. Different levels of observation error were then introduced into these artificial time series. Comparison was made between every pair, i.e. a time series derived from a certain level of land use change (storage reduction) versus a time series corresponding to a given level of observation error, using a step-change t-test. Significant step-changes between pairs define the detectability of land use change impact. The analysis was made for the entire 30-year time series as well as for the most extreme annual weather conditions. The results showed that for the average year and wettest year, 75% or more error in observed discharge masks the maximum simulated land use change impact on hydrology. In dry years, a 50% error in discharge is enough to mask the same impact. Knowing (and improving) the level of data quality contributes to a better understanding of hydrological uncertainties and improves the precision in assessing land use change impacts. Both of these are essential elements in water resources development planning.

The influence of a scaling exponent on [formula omitted]: A spatial cross-correlation pattern of precipitation records over eastern China

To understand how factors influence ρDCCA, we analyzed cross-correlation between time series, including artificial time series generated by the autoregressive fractionally integrated moving average method and monthly precipitation record series in nature, with various scaling exponents. The results show that the contribution of ρDCCA primarily comes from scaling exponents and input excitation sources. Precipitation behavior is complicated in the real world, and the scaling exponent of precipitation series, estimated by using the detrended fluctuation analysis method, is closely relevant to the length and the starting time of the precipitation record series as well as the scaling range. ρDCCA between weather stations is related to the chosen precipitation series which possibly contain dynamic processes. In comparing ρDCCA between original monthly precipitation record series to ρDCCA between input excitation sources, the cross-correlation between input excitation sources can reflect intrinsic characteristic. There are more spatial cross-correlation patterns over eastern China on various time scales.

Digital generation of non‐Gaussian random vibration signals in railway transportation and package response analysis

SummaryThis paper presents two methods for generation artificial acceleration time series focused on the simulation of non‐Gaussian spiky fluctuation features. The random acceleration time series were recorded in railway boxcar; the simulations were performed under the PSD and higher statistical moments (skewness and kurtosis) restrictions. The first method is based on discrete Fourier transform method with EARPG(1) model, which, in nature, is a Fourier representation of time series with special selection of random Fourier phases. The synthetic time series generation are presented for a given target PSD property, skewness, and kurtosis. In the second method, we characterized the stationary and non‐Gaussian process using polynomial chaos expansion and Karhunen‐Loeve expansion approach based on the target PSD, skewness, and kurtosis. The accuracy of the methods are verified by moments and PSD comparison. The package is simplified to be a SDOF system; the acceleration response characteristics of the system are analyzed; the results can be applied in packaging system behaviors evaluation and packaging design optimization.

Using a Langevin model for the simulation of environmental conditions in an offshore wind farm

For the planning of operations and maintenance in offshore wind farms, many simulation models exist. Many rely on artificially generated weather time series to test different strategies. In this paper, we present a novel approach to modeling both the significant wave height and wind speed based on measurements from the site. We use a stochastic process called the Langevin process. First, equations are fitted to the available data, which are then used to generate the artificial weather data. The properties of these artificial weather time series are very close to the properties of the actual weather. Mean and standard deviation as well as the overall distribution and seasonality can be captured by the new model. Additionally, the persistence of waves and winds is replicated. This is especially important, as the length of weather windows is an important factor in operation and maintenance planning.

Analysis of Shannon-Fisher information plane in time series based on information entropy.

In this paper, we propose a Shannon-Fisher information plane based on the information entropy to analyze financial stock markets. In order to evaluate the effectiveness of this method, we apply this method to two types of artificial time series: Autoregressive Fractionally Integrated Moving Average models and Chebyshev map model. The results show that with the embedding dimension and the number of possible states of the system increasing, the normalized Shannon entropy increases, and the Fisher information measure (FIM) decreases. When the parameter is not so big, the embedding dimension plays a leading role in determining the FIM. In addition, compared with the classical Shannon-Fisher information through permutation entropy, we conclude that the proposed approach can give us more accurate information on the classification of financial stock markets.

Diffuse fraction estimation using the BRL model and relationship of predictors under Chilean, Costa Rican and Australian climatic conditions

In this paper a model is used to estimate the diffuse radiation using the Boland-Ridley-Lauret (BRL) model, which is developed for Chile, Costa Rica, and Australia. Additionally, artificial Direct Normal Irradiance time series are determined from the diffuse fraction results estimated by the model. Both estimates achieve excellent agreement based on the bias and normalized scatter. The relationship between the predictors of the model and the climatic conditions of each case of study, according to the Köppen-Geiger climatic classification was analyzed, which to the best of the authors' knowledge, it's the first study of this kind. An analysis on correlation and statistical significance was carried out between the model predictors and four determining geographic and climatic variables: altitude, latitude, precipitation and temperature. The statistical analysis shows that two of the six predictors correlate with temperature and precipitation and one predictor is correlated with latitude. Therefore, it can be suggested that the BRL model seems largely insensitive to the different regional climatic conditions, nevertheless, evaluation of the effect of the apparent correlation of the respective predictors and microclimatic and geographical variables points to further research in this area considering a wider selection of locations.

A method for decomposing multivariate time series into a causal hierarchy within specific frequency bands

We propose a method - Frequency extracted hierarchical decomposition (FEHD) - for studying multivariate time series that identifies linear combinations of its components that possess a causally hierarchical structure - the method orders the components so that those at the "top" of the hierarchy drive those below. The method shares many of the features of the "hierarchical decomposition" method of Repucci et al. (Annals of Biomedical Engineering, 29, 1135-1149, 2001) but makes a crucial advance - the proposed method is capable of determining this causal hierarchy over arbitrarily specified frequency bands. Additionally, a novel minimization strategy is used to generate the decomposition resulting in an increase in stability, reliability, and an improvement in the sensitivity to model parameters. We demonstrate the utility of the method by applying it to both artificial time series constructed to have specific causal graphs, and to the EEG of healthy volunteers and patient subjects who are recovering from a severe brain injury.