Autocorrelation In Time Series Research Articles

Analysis on Effectiveness of Surrogate Data-Based Laser Chaos Decision Maker

The laser chaos decision maker has been demonstrated to enable ultra-high-speed solutions of multiarmed bandit problems or decision-making in the GHz order. However, the underlying mechanisms are not well understood. In this paper, we analyze the chaotic dynamics inherent in experimentally observed laser chaos time series via surrogate data and further accelerate the decision-making performance via parameter optimization. We first evaluate the negative autocorrelation in a chaotic time series and its impact on decision-making detail. Then, we analyze the decision-making ability using three different surrogate chaos time series to examine the underlying mechanism. We clarify that the negative autocorrelation of laser chaos improves decision-making and that the amplitude distribution of the original laser chaos time series is not optimal. Hence, we introduce a new parameter for adjusting the amplitude distribution of the laser chaos to enhance the decision-making performance. This study provides a new insight into exploiting the supremacy of chaotic dynamics in artificially constructed intelligent systems.

A Markov chain approach to the predictability of surface temperature over the northeastern part of India

The present study reports a two-state Markov chain approach as well as an autoregressive approach to study the behavior of the surface temperature time series over northeast India. Considering the minimum requirement of the chi-square test, 1998–2007 (> 100 months) have been considered for testing the Markovian and autoregressive behavior. The monthly surface temperature time series involves monthly data that corresponds to a continuous random variable. This random variable has been discretized to binary data, and the transition probabilities have been computed up to the fourth-order Markov chain model. The best order of Markov chain has been derived through the minimization of the Bayesian information criterion (BIC). By analyzing the time series autocorrelation function and the Akaike information criteria (AIC), the autoregressive model of order two has been found to be a representative and the best autoregressive method for the average monthly time series of surface temperatures over northeast India.

ROBUST TESTS FOR WHITE NOISE AND CROSS-CORRELATION

Commonly used tests to assess evidence for the absence of autocorrelation in a univariate time series or serial cross-correlation between time series rely on procedures whose validity holds for i.i.d. data. When the series are not i.i.d., the size of correlogram and cumulative Ljung–Box tests can be significantly distorted. This paper adapts standard correlogram and portmanteau tests to accommodate hidden dependence and nonstationarities involving heteroskedasticity, thereby uncoupling these tests from limiting assumptions that reduce their applicability in empirical work. To enhance the Ljung–Box test for non-i.i.d. data, a new cumulative test is introduced. Asymptotic size of these tests is unaffected by hidden dependence and heteroskedasticity in the series. Related extensions are provided for testing cross-correlation at various lags in bivariate time series. Tests for the i.i.d. property of a time series are also developed. An extensive Monte Carlo study confirms good performance in both size and power for the new tests. Applications to real data reveal that standard tests frequently produce spurious evidence of serial correlation.

Thick cloud removal in Landsat images based on autoregression of Landsat time-series data

Thick-cloud contamination causes serious missing data in Landsat images, which substantially limits applications of these images. To remove thick clouds from Landsat data, the most popular methods employ auxiliary data such as a cloud-free image of the same area acquired on another date (referred to as the “reference image”). However, the performance of most previous methods strongly depends on the usefulness of the specific reference image, but in some cases high-quality cloud-free reference images are rarely available. In addition, some of these methods ignore the use of partially cloud-contaminated reference images, but clear pixels in these images can be very useful. To address these issues, a new cloud-removal method (AutoRegression to Remove Clouds (ARRC)) has been developed in this study. The most important improvement of ARRC is that it considers autocorrelation of Landsat time-series data and employs multi-year Landsat images including partially cloud-contaminated images in the cloud-removing process. ARRC also addresses the cases in which autocorrelation of Landsat time series might be adversely affected by abrupt land cover changes over multiple years. We compared ARRC with the widely-used MNSPI (modified neighborhood similar pixel interpolator) method at four challenging sites, including an urban area in Beijing and three croplands, in the North China Plain, northeastern Vietnam, and Iowa, USA. Results from the cloud-simulated images showed that ARRC performed better than MNSPI and achieved lower RMSE values (e.g., 0.02129 vs. 0.03005, 0.03293 vs. 0.04725, 0.02740 vs. 0.03556, and 0.03303 vs. 0.03973 in the near-infrared band at the four testing sites, respectively). Moreover, the experiments demonstrated improved performance when clear pixels in partially cloud-contaminated images were used by ARRC. Furthermore, cloud-free images reconstructed by ARRC were visually better than those reconstructed by MNSPI when both approaches were applied to actual cloud-contaminated Landsat images.

EXTREME EVENTS ANALYSIS OF NON-STATIONARY TIME SERIES BY USING HORIZONTAL VISIBILITY GRAPH

In this paper, we analyze the extreme events of non-stationary time series in the framework of horizontal visibility graph (HVG). We give a new definition of extreme events, which incorporates the temporal structure of the series and the degree of the nodes in the HVG. An advantage of the new concept is that it does not require ad hoc treatment even when the non-stationarity arises in time series. We also use the information-theoretic methods to analyze the degree of nodes in the HVG. In the numerical analysis, we study the statistical characterizations of the extreme events of synthetic time series, including the random noises, periodic time series, random walk processes, and the long-range auto-correlated time series. Then, we study 9 time series in stock markets to identify the extreme events evolving in these non-stationary systems. Interestingly, we find that the daily closing price series perform rather close to the random walk processes, while the daily trading volume series behave quite similar to the random noises.

Comparison of tobacco import and tobacco control in five countries: lessons learned for Indonesia

BackgroundWith a 264 million population and the second highest male smoking prevalence in the world, Indonesia hosted over 60 million smokers in 2018. However, the government still has not ratified the Framework Convention on Tobacco Control. In the meantime, tobacco import increases rapidly in Indonesia. These create a double, public health and economic burden for Indonesia’s welfare.ObjectiveOur study analyzed the trend of tobacco import in five countries: Indonesia, Pakistan, Bangladesh, Zimbabwe, and Mozambique. Also, we analyze the tobacco control policies implemented in these countries and determine some lessons learn for Indonesia.MethodsWe conducted quantitative analyses on tobacco production, consumption, export, and import during 1990–2016 in the five countries. Data were analyzed using simple ordinary least square regressions, correcting for time series autocorrelation. We also conducted a desk review on the tobacco control policies implemented in the five countries.ResultsWhile local production decreased by almost 20% during 1990–2016, the proportion of tobacco imports out of domestic production quadrupled from 17 to 65%. Similarly, the ratio of tobacco imports to exports reversed from 0.7 (i.e., exports were higher) to 2.9 (i.e., import were 2.9 times higher than export) in 1990 and 2016, respectively. This condition is quite different from the other four respective countries in the observation where their tobacco export is higher than the import. From the tobacco control point of view, the four other countries have ratified the Framework Convention on Tobacco Control (FCTC).ConclusionThe situation is unlikely for Indonesia to either reduce tobacco consumption or improve the local tobacco farmer’s welfare, considering that the number of imports continued to increase. Emulating from the four countries, Indonesia must ratify the FCTC and implement stricter tobacco control policies to decrease tobacco consumption and import.

Using autoregressive-dynamic conditional correlation model with residual analysis to extract dynamic functional connectivity

Objective. Statistical methods that simultaneously model temporal and spatial variations of fMRI data are promising tools for dynamic functional connectivity (FC) estimation. Although different approaches are available, they need to manually set the parameters, or may disregard some important fMRI features such as the autocorrelation. In addition, no reliable method exists for the validation of dynamic FC analysis models. Approach. In the present study, we have proposed an autoregressive dynamic conditional correlation model to deal with the temporal autocorrelation and non-stationarity in fMRI time-series. This model assumes that the brain time courses follow a multivariate Gaussian distribution, and that the conditional mean, variance and covariances change in an autoregressive form. Also, we proposed a new measurement index for the evaluation of the statistical consistency between the inferred dynamic functional connectivity and the real fMRI data. The performance of our model was tested in both simulated and real fMRI data. Main results. The model was associated with independent Gaussian residuals, and identified the dynamic connectivity patterns with high precision. Applying the model to the fMRI data from typically developing and attention deficit hyperactivity disorder subjects, brain connectivities were significantly different between the two groups. Significance. Prominent features of our model were the consideration of the fMRI autocorrelation, no need to adjust the window length, and also elimination of the variance changes in each brain time-course from its connectivity changes.

Modeling Daily and Monthly Water Quality Indicators in a Canal Using a Hybrid Wavelet-Based Support Vector Regression Structure

Accurate prediction of water quality indicators plays an important role in the effective management of water resources. The models which studied limited water quality indicators in natural rivers may give inadequate guidance for managing a canal being used for water diversion. In this study, a hybrid structure (WA-PSO-SVR) based on wavelet analysis (WA) coupled with support vector regression (SVR) and particle swarm optimization (PSO) algorithms was developed to model three water quality indicators, chemical oxygen demand determined by KMnO4 (CODMn), ammonia nitrogen (NH3-N), and dissolved oxygen (DO), in water from the Grand Canal from Beijing to Hangzhou. Modeling was independently conducted over daily and monthly time scales. The results demonstrated that the hybrid WA-PSO-SVR model was able to effectively predict non-linear stationary and non-stationary time series and outperformed two other models (PSO-SVR and a standalone SVR), especially for extreme values prediction. Daily predictions were more accurate than monthly predictions, indicating that the hybrid model was more suitable for short-term predictions in this case. It also demonstrated that using the autocorrelation and partial autocorrelation of time series enabled the construction of appropriate models for water quality prediction. The results contribute to water quality monitoring and better management for water diversion.

Evaluation and validation of a high spatial resolution satellite soil moisture product over the Continental United States

The soil moisture (SM) data retrieved from the Soil Moisture Active and Passive (SMAP) satellite are available at a 9 km grid spacing since April 2015. This product can provide valuable information for research and applications in hydrology and other related fields. However, the resolution may be too coarse for applications at catchment or field scale. In this study, an established downscaling methodology, which had a major modification regarding its application on the SMAP 33 km domain, was implemented to develop a 1 km soil moisture product based on the SMAP 9 km data. The algorithm proposed here is based on the thermal inertia principle and developed by modeling the relationship between surface temperature difference and SM for different Normalized Difference Vegetation Index (NDVI) classes. The model functions were established and tuned using data from the NASA’s Land Information System (LIS) North America Land Data Assimilation System (NLDAS) and remotely sensed VISible/InfRared (VIS/IR) reflectance data from Long Term Data Record (LTDR) AVHRR (Advanced Very High Resolution Radiometer) for the growing season months of April-September 1981–2018. These were then implemented using the MODIS (Moderate Resolution Imaging Spectroradiometer) data over the Continental United States (CONUS) domain. Validation activities were carried out using in situ measurements distributed through the International Soil Moisture Network (ISMN). The validation results computed using the 1 km SM data showed that the R2, unbiased RMSE (root mean square error) and bias were improved relative to the 9 km SMAP product by 0.045, 0.018 m3/m3 and 0.001 m3/m3, respectively. The 1 km SM also exhibited a strong time-series autocorrelation. Further accuracy assessment analyses indicated that precipitation might contribute to the uncertainties in both the 9 km SMAP and 1 km downscaled SMAP SM products.

Multiway dynamic nonlinear global neighborhood preserving embedding method for monitoring batch process

Aiming at the dynamic and nonlinear characteristics of batch process, a multiway dynamic nonlinear global neighborhood preserving embedding algorithm is proposed. For the nonlinear batch process monitoring, kernel mapping is widely used to eliminate nonlinearity by projecting the data into high-dimensional space, but the nonlinear relationships between batch process variables are limited by many physical constraints, and the infinite-order mapping is inefficient and redundant. Compared with the basic kernel mapping method which provides an infinite-order nonlinear mapping, the proposed method considers the dynamic and nonlinear characteristics with many physical constraints and preserves the global and local structures concurrently. First, the time-lagged window is used to remove the auto-correlation in time series of process variables. Second, a nonlinear method named constructive polynomial mapping is used to avoid unnecessary redundancy and reduce computational complexity. Third, the global neighborhood preserving embedding method is used to extract structures fully after the dynamic and nonlinear characteristics are processed. Finally, the effects of the proposed algorithm are demonstrated by a mathematical model and the penicillin fermentation process.

Correlated power time series of individual wind turbines: A data driven model approach

Wind farms can be regarded as complex systems that are, on the one hand, coupled to the nonlinear, stochastic characteristics of weather and, on the other hand, strongly influenced by supervisory control mechanisms. One crucial problem in this context today is the predictability of wind energy as an intermittent renewable resource with additional non-stationary nature. In this context, we analyze the power time series measured in an offshore wind farm for a total period of one year with a time resolution of 10 min. Applying detrended fluctuation analysis, we characterize the autocorrelation of power time series and find a Hurst exponent in the persistent regime with crossover behavior. To enrich the modeling perspective of complex large wind energy systems, we develop a stochastic reduced-form model of power time series. The observed transitions between two dominating power generation phases are reflected by a bistable deterministic component, while correlated stochastic fluctuations account for the identified persistence. The model succeeds to qualitatively reproduce several empirical characteristics such as the autocorrelation function and the bimodal probability density function.

Estimating Long Memory in Panel Random‐Coefficient AR(1) Data

We construct an asymptotically normal estimator for the tail index β of a distribution on (0,1) regularly varying at x=1, when its N independent realizations are not directly observable. The estimator is a version of the tail index estimator of Goldie and Smith (1987) [Goldie CM, Smith RL. 1987. The Quarterly Journal of Mathematics 38: 45–71] based on suitably truncated observations contaminated with arbitrarily dependent ‘noise’ which vanishes as N increases. We apply to panel data comprising N random‐coefficient AR(1) series, each of length T, for estimation of the tail index of the random coefficient at the unit root, in which case the unobservable random coefficients are replaced by sample lag 1 autocorrelations of individual time series. Using asymptotic normality of , we construct a statistical procedure to test if the panel random‐coefficient AR(1) data exhibit long memory. A simulation study illustrates finite‐sample performance of the introduced inference procedures.

Analyses on Volatility Clustering in Financial Time-Series Using Clustering Indices, Asymmetry, and Visibility Graph

The volatility clustering has critical implications in financial risk management. This paper aims to analyze the existence and cause of volatility clustering in financial time-series using different measures simultaneously. Specifically, we utilize the clustering indices, asymmetry measures, and the power of the scale freeness in the visibility graph. For the experiment, we utilize four representing financial time-series, including the S&P500, one-year US Treasury Constant Maturity rate, Euro-Dollar exchange rate, and Crude oil for the stock, bond, exchange, and commodity markets, respectively. The duration of the experiment is from 2009 to 2018, which is divided into two sub-periods: crisis and post-crisis periods. At first, we identify the positive and slowly decaying non-linear autocorrelation in all markets, which indicates the power-law decay. Also, the autocorrelation of the simulated time-series suggests that the order of return-series with respect to its magnitude contributes more to the volatility clustering than the heavy-tailed distributions. Secondly, we detect that the scale of the return contributes more to volatility clustering than the sign of the return. Lastly, we observe that the clustering and asymmetry measures are more robust measures to the return distribution changes than the PSVG to analyze the volatility clustering.

Autocorrelate Your Assets or, It's Not All White Noise: A Practical Means for Generating Autocorrelated Time Series Data in Monte Carlo Simulations

The inherent assumption with most Monte Carlo techniques is that one may ignore autocorrelations, but doing so compromises the quality of the prediction from the data. Simulations that do not take account of autocorrelation will not properly model reality, as there is significant autocorrelation in many asset returns, for example in T-Bills and hedge fund strategies that involve illiquid, long-term holdings, which do not satisfy the “random walk” assumption with a “white noise” spectrum. A detailed mathematical method is proposed for simulating market returns by generating random time series that satisfy the statistics of any serial autocorrelation, as well as the actual (possibly non-Gaussian) joint probability distributions.

Maize yield in Mexico under climate change

Understanding the effects of climate change on maize yield in Mexico is important from both a national and international perspective. Maize is Mexico's staple food crop, thus, decrements in national production would strongly compromise food security in the country.Internationally, maize is the most important grain crop in terms of human consumption and the conservation in situ of its germplasm should be a global priority. Mexico harbors half of the known genetic diversity for this crop in the American continent, which is instrumental for future genetic improvement efforts that could generate new, environmentally resilient varieties. In this study, we analyze the link between maize yield and several climate variables in rainfed and irrigated crop areas in Mexico to project yield variations under future climate change scenarios. We used municipality-level data for seven states that account for ∼65% of the annual maize production in Mexico and cover an important amount of national climatic variability. We used public data published by the Mexican government on yield and climate from 2003 to 2015 and built linear models to assess the impact of climate on maize yield. We considered the municipality to be a random effect and accounted for potential autocorrelation in the 13-year time series. We also evaluated how many municipalities reached their states' breakeven point in order to project the geographic areas that will earn higher profits due to increased yields. Our results showed that the municipality had a significant effect on yield, and consequently, our results could not be extrapolated to other geographic areas in the country. We found temperature to be the most influential factor on yield under rainfed conditions, while precipitation was the most influential factor for irrigated crops. Like earlier studies at a global scale, we found higher yield stability for irrigated fields than for rainfed fields when considering different climate change scenarios. Our projections indicate that yields from rainfed fields will be reduced significantly under future scenarios. We argue that average yield data in rainfed fields does not include data on the diversity of native maize varieties or their potentially different responses to changes in the environment. Finally, under current conditions, there are by far more municipalities reaching their breakeven point in rainfed fields than in irrigated fields, suggesting that higher yields do not necessarily translate into greater profits for farmers because costs can also increase depending on the type of agriculture practiced.

Robust Tests for White Noise and Cross-Correlation

Commonly used tests to assess evidence for the absence of autocorrelation in a univariate time series or serial cross-correlation between time series rely on procedures whose validity holds for i.i.d. data. When the series are not i.i.d., the size of correlogram and cumulative Ljung-Box tests can be significantly distorted. This paper adapts standard correlogram and portmanteau tests to accommodate hidden dependence and non-stationarities involving heteroskedasticity, thereby uncoupling these tests from limiting assumptions that reduce their applicability in empirical work. To enhance the Ljung-Box test for non-i.i.d. data a new cumulative test is introduced. Asymptotic size of these tests is unaffected by hidden dependence and heteroskedasticity in the series. Related extensions are provided for testing cross-correlation at various lags in bivariate time series. Tests for the i.i.d. property of a time series are also developed. An extensive Monte Carlo study confirms good performance in both size and power for the new tests. Applications to real data reveal that standard tests frequently produce spurious evidence of serial correlation.

Control charts based on fuzzy costs for monitoring short autocorrelated time series

Monitoring the stability of processes described by autocorrelated time series requires dedicated tools such as the Shewhart control chart for residuals. This paper discusses and extends a recently introduced ensemble prediction framework for time series called weighted averaged models (WAM). Central to the WAM approach are the weights of the base and alternative predictive models. We propose eliciting these in a novel way from domain experts using imprecise (fuzzy) costs. We use them to define an X control chart for autocorrelated time series called XWAM. Its application is illustrated by a real-world psychiatric problem, in which the self-assessment data on bipolar disorder patients' moods is used to detect the changes of their mental states.

An experimental study on the precursory characteristics of EP before sandstone failure based on critical slowing down

The electric potential (EP) generated during coal rock deformation and fracture reflects coal rock mass stress and damage states. However, identifying the EP signal precursory signs that characterize a coal rock mass tending toward instability and failure is difficult. In this paper, we established an acoustic-electric multiparameter test experimental system, synchronously tested and collected acoustic emission (AE), surface potential (SP), and axial strain (AS) and observed surface crack propagation during the sandstone sample failure process. Meanwhile, by introducing the critical slowing down theory, the EP signal precursory characteristics before the sandstone sample unstable failure were explored. The results showed that EP signal time series autocorrelation coefficients and variances increased abruptly and continuously before the main fracture of the sandstone samples, which could be used as sandstone failure precursory information. Compared with the autocorrelation coefficient, the variance mutation point was easy to identify and was not affected by lag length selection, which was an effective precursory point to predict sandstone sample failure. From the precursory point to the main fracture of the sandstone samples, the AE events gradually gathered at the fracture damage location, high-energy AE events gradually increased, and the crack propagation rate gradually accelerated. Compared with the AE count time series, the variance mutation point (precursory point) of the EP signal time series appeared earlier. The research results were of theoretical significance for the monitoring and early warning of coal rock mass instability and failure and for identifying precursory characteristics using the EP response.

Generalized early warning signals in multivariate and gridded data with an application to tropical cyclones.

Tipping events in dynamical systems have been studied across many applications, often by measuring changes in variance or autocorrelation in a one-dimensional time series. In this paper, methods for detecting early warning signals of tipping events in multidimensional systems are reviewed and expanded. An analytical justification of the use of dimension-reduction by empirical orthogonal functions, in the context of early warning signals, is provided and the one-dimensional techniques are also extended to spatially separated time series over a 2D field. The challenge of predicting an approaching tropical cyclone by a tipping-point analysis of the sea-level pressure series is used as the primary example, and an analytical model of a moving cyclone is also developed in order to test predictions. We show that the one-dimensional power spectrum indicator may be used following dimension-reduction or over a 2D field. We also show the validity of our moving cyclone model with respect to tipping-point indicators.

Fallowing temporal patterns assessment in rainfed agricultural areas based on NDVI time series autocorrelation values

Fallowing is a common practice in Mediterranean areas where water scarcity becomes a limiting factor, affecting soil productivity, crop yield and biodiversity. In mainland Spain, fallow lands expand across three million hectares every year, constituting around 30% of rainfed arable lands and 6% of the national surface. There is a need of monitoring fallow lands to better map land use intensity and therefore achieve a sustainable expansion and intensification of agriculture. However, most of current land use classification systems do not include lands under fallowing practices as a specific class. In this research, a new and highly operative methodology based on NDVI time series autocorrelation values to assess fallowing temporal patterns across rainfed agricultural areas is proposed. This approach was tested in mainland Spain, using the autocorrelation function of MODIS NDVI time series from 2001 to 2012 at 250 m spatial resolution. The field observational database from the Spanish Ministry of Agriculture, Fisheries and Food was used for validation purposes. The dataset used includes 338 pixels with annual information about the cultivated and fallowed surface within the entire study period. It was demonstrated that specific autocorrelation values at lags corresponding to one, two, and three years contained relevant information to identify lands under fallowing practices and assess their temporal pattern. Integrating autocorrelation variables in a random forest model made it possible to improve the assessment. The classification results were in agreement with the field dataset with an overall accuracy higher than 80%. Results revealed that approximately half of rainfed agricultural areas were regularly cultivated and distributed mainly in the northwestern Spain. The other half mainly located across northeast, center and south of Spain, showed crop-fallow rotation patterns. This methodology is a promising technique to map land management intensity using the entire time series in a highly operative manner. It is expected that in the near future the availability of remote sensing time series with better spatial resolution will make it possible to improve the assessment of agricultural intensification.