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For checking time series models, the Ljung–Box, Li–Mak and Zhu–Wang statistics play an important role, which use the Pearson's correlation coefficient to implement (squared) residual (partial) autocorrelation tests. In this paper, we replace the Pearson's correlation coefficient with a new rank correlation coefficient and propose a new test statistic to conduct diagnostic checks for residuals in autoregressive moving average models, autoregressive conditional heteroscedasticity models and integer-valued time series models, respectively. We conduct simulations to assess the performance of the new test statistic, and compare it with existing ones, and the results show the superiority of the proposed one. We use three real examples to exhibit its usefulness. [ABSTRACT FROM AUTHOR]

Linear ARMA model fitting requires to select the order of the model as accurately as possible. Many past studies are based on portmanteau tests, originally derived for the white noise hypothesis, but applied to the autocorrelations of the estimated residuals, and employ sums of the scaled squares of the first d residual autocorrelations. An automatic choice of d was proposed by Escanciano and Lobato (J Econom 151:140–149, 2009) based on the largest (in absolute value) residual autocorrelation. Such maximal autocorrelation may be itself employed as a test statistic, and Baragona et al. (Test 31:675–698, 2022) proposed white noise tests based on a bivariate statistic consisting of both the portmanteau and the largest autocorrelation. However, the derivation of the asymptotic null distribution requires asymptotic independence of the autocorrelation estimates and this is not true when they are computed on the residuals of a fitted ARMA model. Therefore, we propose to use a linear transformation of the estimated residual autocorrelation in order to achieve independence, in the same spirit as recursive residuals in regression. Monte Carlo experiments are performed for comparing the effectiveness of our new method to the Escanciano Lobato and a more classical portmanteau test. We find that the two data-driven tests are approximately equivalent if non negligible residual autocorrelation is found only at the first lags, while our test is more powerful if autocorrelations at larger lags arises. [ABSTRACT FROM AUTHOR]

It is around a century that sample autocorrelation function has been introduced and used as a standard tool in time series analysis. A vast literature can be found on the statistical properties of the sample autocorrelation function. However, it has been highlighted recently that the sum of the sample autocorrelation function over the lags 1 to T − 1 is −0.5 for all time series of length T. This property produces a big concern for the cases in which all available sample autocorrelations are used in the inference. This paper provides two new alternative for estimating the autocorrelation function. These estimators come from the idea of singular spectrum analysis which is a non-parametric technique for time series analysis. The paper utilizes a simulation study to illustrate the performance of the new approach. The results suggest that further improvement to the sample autocorrelation is possible and the new methods provide an attractive alternative to the classical approach. [ABSTRACT FROM AUTHOR]

We propose a new time series model called Rational Gaussian Noise (rGn) to describe a pattern of long-range dependence. The rGn model is shown to be an extension of the traditional fractional Gaussian noise (fGn). Theoretical formulas such as autocorrelation function, and some properties of rGn are derived and compared to that of fGn. Transformed S&P500 daily excessive return data is used as a case study where parameters for both the rGn and fGn models are estimated. [ABSTRACT FROM AUTHOR]

Time series forecasting is an important application of many statistical methods. When it is appropriate to assume that the data may be projected towards the future based on the past history of the dataset, a preliminary examination is usually required to ensure that the data sequence is autocorrelated. This is a quite obvious assumption that has to be made and can be the object of a formal test of hypotheses. The most widely used test is the portmanteau test, i.e., a sum of the squared standardized autocorrelations up to an appropriate maximum lag (the truncation point). The choice of the truncation point is not obvious and may be data-driven exploiting supplementary information, e.g. the largest autocorrelation and the lag where such maximum is found. In this paper, we propose a portmanteau test with a truncation point equal to the lag of the largest (absolute value) estimated autocorrelation. Theoretical and simulation-based comparisons based on size and power are performed with competing portmanteau tests, and encouraging results are obtained. [ABSTRACT FROM AUTHOR]

Recently, there has been an emerging trend to analyse time series data and utilise sophisticated tools for optimally fitting time series models. To date, Malaysian industrial accident data is underutilised and lacks informative records. Thus, this paper aims to investigate the Malaysian accident database and further evaluate the optimal forecasting models in accident prediction. The model's input was based on available data from the Department of Occupational Safety and Health, Malaysia (DOSH), from 2018 until 2021, with 80% of the dataset to train the models and the remaining 20% for validation. The negative binomial and Poisson distribution prediction showed a mean absolute percentage error (MAPE) of 33% and 51%, respectively. It indicated that the negative binomial performed better than the Poisson distribution in accident frequency prediction. The available time series accident data were gathered for four years, and stationarity was checked in R Studio software for the Augmented Dickey-Fuller test. The lowest Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC) and other error values were used to justify the best model, which was the ARIMA(2,0,2)(2,0,0)(12) model. The ARIMA models were considered after the data showed autocorrelation. The MAPE for both ARIMA in R and manual time series were 40% and 49%, respectively. Therefore, the accident prediction by using R Studio would outperform the manually negative binomial and Poisson distribution. Based on the findings, industrial safety practitioners should report accidents to DOSH truthfully in the era of digitalisation. It could enable future data-driven accident predictions to be carried out. [ABSTRACT FROM AUTHOR]

Smoothed returns that can occur as a result of an appraisal-based valuation process distort asset characteristics and, in particular, volatility and correlations. Using a simple but often-used model for smoothed return series, this article analyzes what unsmoothing techniques can achieve with respect to uncovering the true time-series properties. The properties of interest are volatility, autocorrelation, self-correlation, and cross-asset correlation. It is shown that, specifically for heavily smoothed return series, volatility estimates might overstate the true volatility, and cross-asset correlations cannot fully be recovered. [ABSTRACT FROM AUTHOR]

A new portmanteau test statistic is proposed for detecting nonlinearity in time series data. The new portmanteau statistic is calculated from the log of the determinant of a matrix comprised of the autocorrelations and cross-correlations of the residuals and squared residuals of a fitted time series. The asymptotic distribution of the proposed test statistic is derived as a linear combination of chi-square distributed random variables and can be approximated by a gamma distribution. A bootstrapping approach is shown to be robust when distributional assumptions are relaxed. The efficacy of the statistic is studied against linear and nonlinear dependency structures of some stationary time series models. It is shown that the new test can provide higher power than other tests in many situations. We demonstrate the advantages of the proposed test by investigating linear and nonlinear effects in an economic series and two environmental time series. [ABSTRACT FROM AUTHOR]

The determination of errors in the runoff probability distribution parameters when estimating them on a heterogeneous sample is considered. For the case that allows using composite curves (or a mixture of distributions), some expressions for errors of the estimates of the mean and the variation coefficient are proposed. It has been found that accounting of the sample heterogeneity based on a probabilistic model of the time series, which allows its examination in the form of two stationary sections without accounting the averaged autocorrelation, magnifies the error of the mean value estimate. It is shown that the overestimation of the first autocorrelation coefficient assessed on the entire series without taking into account inhomogeneity should be considered. [ABSTRACT FROM AUTHOR]

In different scientific fields, some parts of the collected dataset may include incomplete data with at least one missing value. To tackle this issue, statisticians and machine learning experts have introduced different missing value imputation (MVI) approaches. Hydrological data are mostly time series with stationary (or cyclic) trends that its observations have high autocorrelation (or cyclic auto-correlation). In addition, these time series frequently exhibit random and non-constant oscillations from their trends. Therefore, the selected MVI approach for hydrological time series should consider these serious aspects. One aspect of hydrological time series data that has not been closely examined in the MVI studies up to now is the existence of cyclic trend, named cyclostationarity. In this paper, a novel MVI approach for cyclostationary hydrological time series, called cyclic clustering, will be discussed. The performance of the proposed method is studied by employing numerous simulated datasets. The results indicate that the cyclic clustering approach is robust to impute missing values for both stationary and cyclostationary hydrological time series. The applicability of the introduced approach is also investigated in a real-world problem. [ABSTRACT FROM AUTHOR]

The current study investigates the effect of within‐profile and between‐profile autocorrelations on the performance of four monitoring methods of simple linear profiles in Phase II. To this end, a general correlation model between error terms is considered such that the correlation structure of within‐profiles errors and the error terms between consecutive profiles follow an autoregressive (AR) times series model of order one. Extensive simulations have been done to assess the effect of both autocorrelation types and the profile size on the estimations of the model parameters as well as the performance of control charts. The performance of the monitoring schemes is investigated and compared with respect to the average run length (ARL) metric. The simulation study results show that the autocorrelation within and between profiles has a negative impact on the monitoring technique's performance. It reduces the control chart's ability to detect process shifts compared to no or weak autocorrelation cases. Moreover, the performance of all the methods is improved by increasing the profile size. An illustrative example is also provided to demonstrate the use of the proposed methods for monitoring the stability of profiles in the chemical industry. [ABSTRACT FROM AUTHOR]

A piecewise function can sometimes provide the best fit to a time series. The breaks in this function are called change points, which represent the point at which the statistical properties of the model change. Often, the exact placement of the change points is unknown, so an efficient algorithm is required to combat the combinatorial explosion in the number of potential solutions to the multiple change point problem. Bayesian solutions to the multiple change point problem can provide uncertainty estimates on both the number and location of change points in a dataset, but there has not yet been a systematic study to determine how the choice of hyperparameters or the presence of autocorrelation affects the inference made by the model. Here, we propose Bayesian model averaging as a way to address the uncertainty in the choice of hyperparameters and show how this approach highlights the most probable solution to the problem. Autocorrelation is addressed through a pre-whitening technique, which is shown to eliminate spurious change points that emerge due to a red noise process. However, pre-whitening a dataset tends to make true change points harder to detect. After an extensive simulation study, the model is applied to two climate applications: the Pacific Decadal Oscillation and a global surface temperature anomalies dataset. [ABSTRACT FROM AUTHOR]

In this article we first revisit some earlier work on fractionally differenced white noise and correct some issues with previously published formulae. We then look at vector processes and derive formula for the Autocorrelation function, which is extended in this work to a larger range of parameter values than considered elsewhere, and compare this with previously published work. [ABSTRACT FROM AUTHOR]

Many widely used observational data sets are comprised of several overlapping instrument records. While data inter-calibration techniques often yield continuous and reliable data for trend analysis, less attention is generally paid to maintaining higher-order statistics such as variance and autocorrelation. A growing body of work uses these metrics to quantify the stability or resilience of a system under study and potentially to anticipate an approaching critical transition in the system. Exploring the degree to which changes in resilience indicators such as the variance or autocorrelation can be attributed to non-stationary characteristics of the measurement process – rather than actual changes in the dynamical properties of the system – is important in this context. In this work we use both synthetic and empirical data to explore how changes in the noise structure of a data set are propagated into the commonly used resilience metrics lag-one autocorrelation and variance. We focus on examples from remotely sensed vegetation indicators such as vegetation optical depth and the normalized difference vegetation index from different satellite sources. We find that time series resulting from mixing signals from sensors with varied uncertainties and covering overlapping time spans can lead to biases in inferred resilience changes. These biases are typically more pronounced when resilience metrics are aggregated (for example, by land-cover type or region), whereas estimates for individual time series remain reliable at reasonable sensor signal-to-noise ratios. Our work provides guidelines for the treatment and aggregation of multi-instrument data in studies of critical transitions and resilience. [ABSTRACT FROM AUTHOR]

Time series statistical analyses (TSSA) have been employed to evaluate the variability of resistive switching memories and to model the set and reset voltages for modeling purposes. The conventional procedures behind time series theory have been used to obtain autocorrelation and partial autocorrelation functions and determine the simplest analytical models to forecast the set and reset voltages in a long series of resistive switching processes. To do so, and for the sake of generality in our study, a wide range of devices have been fabricated and measured. Different oxides and electrodes have been employed, including bilayer dielectrics in devices such as Ni/HfO2/Si-n+, Cu/HfO2/Si-n+, and Au/Ti/TiO2/SiOx/Si-n+. The TSSA models obtained allowed one to forecast the reset and set voltages in a series if previous values were known. The study of autocorrelation data between different cycles in the series allows estimating the inertia between cycles in long resistive switching series. Overall, TSSA seems to be a very promising method to evaluate the intrinsic variability of resistive switching memories. [ABSTRACT FROM AUTHOR]

This study investigates the time-series properties of accounting earnings and their components. We propose a new measure of earnings persistency in accordance with the vector autoregressive (VAR) model–linked earnings and stock returns. As a preliminary analysis, we estimate the first-order autocorrelations and test the stationarity of five variables: earnings, cash flows from operations, total accruals, current accruals, and noncurrent accruals. We then confirm that earnings and noncurrent accruals have a more persistent time-series than cash flows and current accruals. Next, we formulate and estimate the first-order autoregressive model composed of the three variables of utmost interest to accounting researchers, namely, cash flows, current accruals, and noncurrent accruals, and explore how future predictions of these three earnings components are affected by unit impulse shocks. Given the results of the impulse response function analysis, we forecast changes in stock prices based on future innovations of these components, finding that a 1% unit shock in the earnings components affects stock prices by 2% to 2.5%. Finally, we are able to demonstrate excess returns by using the portfolio formation method based on our measure of persistence. [ABSTRACT FROM AUTHOR]

The study of water sources such as rivers and lakes is increasingly important in the modern world, mainly due to their scarcity and the large number of cities flooded by heavy rains. In this paper, we aim to analyze the dynamics of the daily flow of water in the Torata, Tumilaca, and Huaracane rivers, which form the Moquegua watershed (Peru). To study these fluctuations, we apply the DFA method (estimate long-range autocorrelation in non-stationary time series) and the DCCA cross correlation coefficient (which strongly dominates the standard Pearson coefficient in time series analysis) to analyze the flow in the basin of Moquegua. Among the rivers that we analyzed descriptively, we identified greater variability in flows in the Huaracane River and less in the Torata, and in general a seasonal component of approximately one year. With the modeling via DFA, it was possible to identify persistent behavior and also annual seasonality. With the DCCA coefficient (cross correlation), as a function of the time scale, positive values of cross correlation are found between river flows at different levels (weak, medium, strong). With this study, considering the properties of the applied methods, it is possible to predict the oscillations of one river in relation to another, which can help the authorities in the management of freshwater over time. [ABSTRACT FROM AUTHOR]

The celebrated Ljung-Box residual analysis is a widely used method in time series for the parameter estimation and the goodness of fit test for theARMAtime series models. The question is whether the autocorrelation function of the fitted ARMA(p, q) model for an observed time series, at different lags, in the Ljung-Box estimation method, is close to the correlogram of observed series. The answer indeed is not affirmative. In this article, firstly, we present a new procedure in solving the Yule-Walker equations for the exact computation of the autocorrelation functions of ARMA(p, q) models. Secondly, we provided a goodness of fit procedure using the limiting distribution of the the sample correlation function. Thirdly, we establish a new parameters estimation method based on examining the model autocorrelation function against the series autocorrelation coefficients. The effectiveness of the procedure is brought into sight using simulated data. [ABSTRACT FROM AUTHOR]

In this paper, we propose a portmanteau test for whether a graph-structured network dataset without replicates exhibits autocorrelation across units connected by edges. Specifically, the well known Ljung-Box test for serial autocorrelation of time series data is generalized to the network setting using a specially derived central limit theorem for a weakly stationary random field. The asymptotic distribution of the test statistic under the null hypothesis of no autocorrelation is shown to be chi-squared, yielding a simple and easy-to-implement procedure for testing graph-structured autocorrelation, including spatial and spatial-temporal autocorrelation as special cases. Numerical simulations are carried out to demonstrate and confirm the derived asymptotic results. Convergence is found to occur quickly depending on the number of lags included in the test statistic, and a significant increase in statistical power is also observed relative to some recently proposed permutation tests. An example application is presented by fitting spatial autoregressive models to the distribution of COVID-19 cases across counties in New York state. [ABSTRACT FROM AUTHOR]

Detecting critical transitions before they occur is challenging, especially for complex dynamical systems. While some early-warning indicators have been suggested to capture the phenomenon of slowing down in the system's response near critical transitions, their applicability to real systems is yet limited. In this paper, we propose the concept of predictability based on machine learning methods, which leads to an alternative early-warning indicator. The predictability metric takes a black-box approach and assesses the impact of uncertainties itself in identifying abrupt transitions in time series. We have applied the proposed metric to the time series generated from different systems, including an ecological model and an electric power system. We show that the predictability changes noticeably before critical transitions occur, while other general indicators such as variance and autocorrelation fail to make any notable signals. [ABSTRACT FROM AUTHOR]

This article considers changepoint detection in serially correlated categorical time series. While changepoint aspects in correlated sequences of continuous random variables have been extensively explored in the literature, changepoint methods for independent categorical time series are only now coming into vogue. This study extends changepoint methods by developing techniques for correlated categorical time series. Here, a cumulative sum type test is devised to test for a single changepoint in a correlated categorical data sequence. Our categorical series is constructed from a latent Gaussian process through clipping techniques. A sequential parameter estimation method is proposed to estimate the parameters in this model. The methods are illustrated via simulations and applied to a real categorized rainfall time series from Albuquerque, New Mexico. [ABSTRACT FROM AUTHOR]

This study aimed to determine the spatiotemporal distribution and epidemiological characteristics of hospital admissions for carbon monoxide poisoning (COP) in Guangdong, China, from 2013 to 2020. Data on age- and sex- specific numbers of hospital admissions due to COP in Guangdong (2013–2020) were collected. Daily temperatures were downloaded through the China Meteorological Data Sharing Service System. We analyzed temporal trends through time series decomposition and used spatial autocorrelation analysis to detect spatial clustering. The distributed lag nonlinear model was used to quantify the effects of temperature. There were 48,854 COP admissions over the study period. The sex ratio (male to female) was 1:1.74. The concentration ratios (M) ranged from 0.73–0.82. The highest risk occurred in January (season index = 3.59). Most cases were concentrated in the northern mountainous areas of Guangdong with high-high clustering. COP in the study region showed significant spatial autocorrelation, and the global Moran's I value of average annual hospital admission rates for COP was 0.447 (P < 0.05). Low temperatures were associated with high hospital admission rates for COP, with a lag lasting 7 days. With a lag of 0 days, the effects of low temperatures [5th (12 °C)] on COP were 2.24–3.81, as compared with the reference temperature [median (24 °C)]. COP in Guangdong province showed significant temporal and spatial heterogeneity. Low temperature was associated with a high risk of COP, and the influence had a lag lasting 7 days. [ABSTRACT FROM AUTHOR]

The Mann–Kendall (MK) test was widely used to detect significant trends in hydrologic and climate time series (HCTS), but it cannot deal with significant autocorrelations in HCTS. To solve this problem, the modified MK (MMK) test and the over-whitening (OW) operation were successively proposed. However, there are still limitations for these two methods, especially for the OW operation. When an HCTS has unknown interaction scenarios of trends and autocorrelations, it is obviously unclear which of these two methods will perform better in the trend test. Additionally, the trend test is always accompanied by an autocorrelations test. In the dual test, it is also unknown how the significance level affects the accuracy of the trend test. To address these issues, this study first proposes a strategy of adding an outer loop to modify the OW-operation-based trend test. Then, two simulation experiments are designed to evaluate the performances of MMK-test-based and OW-operation-based methods, and the influence of the significance level on the trend test is analyzed. Moreover, six HCTSs in the Huaihe River basin are taken as examples to examine the consistence and difference of trend test results of these two methods. Results show that: (1) previous OW operations still have the risk of misjudging trends in the presence of significant autocorrelations, and the proposed strategy is necessary and effective to modify the OW operation; (2) these two methods are similar in the accuracy of the trend test results, but they may also produce opposite results when determining whether a significant trend is a pseudo trend or not; and (3) at a given significance level α, the accuracy rates of two methods are always less than 1-α, and the accuracy rate of the trend test tends to decrease for short HCTSs and increase for long HCTSs as the significance level decreases. This study would provide a new perspective for the trend test of HCTS based on the MK test. [ABSTRACT FROM AUTHOR]

Given observations from a stationary time series, permutation tests allow one to construct exactly level α tests under the null hypothesis of an i.i.d. (or, more generally, exchangeable) distribution. On the other hand, when the null hypothesis of interest is that the underlying process is an uncorrelated sequence, permutation tests are not necessarily level α, nor are they approximately level α in large samples. In addition, permutation tests may have large Type 3, or directional, errors, in which a two‐sided test rejects the null hypothesis and concludes that the first‐order autocorrelation is larger than 0, when in fact it is less than 0. In this article, under weak assumptions on the mixing coefficients and moments of the sequence, we provide a test procedure for which the asymptotic validity of the permutation test holds, while retaining the exact rejection probability α in finite samples when the observations are independent and identically distributed. A Monte Carlo simulation study, comparing the permutation test to other tests of autocorrelation, is also performed, along with an empirical example of application to financial data. [ABSTRACT FROM AUTHOR]

The variety of communication services and the growing number of different sensors with the appearance of IoT (Internet of Things) technology generate significantly different types of network traffic. This implies that the structure of network traffic will be heterogeneous, which requires deep analysis to find the internal features underlying the data. A common model for analyzing the processes of a multiservice network is a model based on time series. Numerous empirical data studies indicate that the packet intensity time series do not belong to the general aggregates of a normal distribution. The problem of predicting network traffic is still relevant due to managing information that flows into a heterogeneous network. In this work, the authors studied the time series for stationarity in order to select an appropriate forecasting model. A visual assessment of the series assumed non-stationarity. The Augmented Dickey-Fuller Test is applied, and the measured network traffic is predicted using the ARIMA (Auto-Regressive Integrated Moving Average) statistical method. Results were obtained using the Econometric Modeler Matlab (R2021b) application. The results of the autocorrelation function (ACF) and partial ACF are analyzed, with the help of which the ARIMA model is optimized. As a result of the study, a software algorithm for the ARIMA (0,2,1) model was developed. [ABSTRACT FROM AUTHOR]

Ideally, a patient's response to medication can be monitored by measuring changes in performance of some activity. In observational studies, however, any detected association between treatment ("on-medication" vs "off-medication") and the outcome (performance in the activity) might be due to confounders. In particular, causal inferences at the personalized level are especially vulnerable to confounding effects that arise in a cyclic fashion. For quick acting medications, effects can be confounded by circadian rhythms and daily routines. Using the time-of-the-day as a surrogate for these confounders and the performance measurements as captured on a smartphone, we propose a personalized statistical approach to disentangle putative treatment and "time-of-the-day" effects, that leverages conditional independence relations spanned by causal graphical models involving the treatment, time-of-the-day, and outcome variables. Our approach is based on conditional independence tests implemented via standard and temporal linear regression models. Using synthetic data, we investigate when and how residual autocorrelation can affect the standard tests, and how time series modeling (namely, ARIMA and robust regression via HAC covariance matrix estimators) can remedy these issues. In particular, our simulations illustrate that when patients perform their activities in a paired fashion, positive autocorrelation can lead to conservative results for the standard regression approach (i.e., lead to deflated true positive detection), whereas negative autocorrelation can lead to anticonservative behavior (i.e., lead to inflated false positive detection). The adoption of time series methods, on the other hand, leads to well controlled type I error rates. We illustrate the application of our methodology with data from a Parkinson's disease mobile health study. [ABSTRACT FROM AUTHOR]

Network latency is a crucial factor affecting the quality of communications networks due to the irregularity of vehicular traffic. To address the problem of performance degradation or instability caused by latency in vehicular networks, this paper proposes a time delay prediction algorithm, in which digital twin technology is employed to obtain a large quantity of actual time delay data for vehicular networks and to verify autocorrelation. Subsequently, to meet the prediction conditions of the ARMA time series model, two neural networks, i.e., Radial basis function (RBF) and Elman networks, were employed to construct a time delay prediction model. The experimental results show that the average relative error of the RBF is 7.6%, whereas that of the Elman-NN is 14.2%. This indicates that the RBF has a better prediction performance, and a better real-time performance than the Elman-NN. [ABSTRACT FROM AUTHOR]

Fractional Gaussian noise models the time series with long-range dependence; when the Hurst index H(1/2, 1), it has positive correlation reflecting a persistent autocorrelation structure. This paper studies the numerical method for solving the stochastic fractional diffusion equation driven by fractional Gaussian noise. Using the operator theoretical approach, we present the regularity estimate of the mild solution and the fully discrete scheme with finite element approximation in space and backward Euler convolution quadrature in time. The O(H-pα) convergence rate in time in space are obtained, showing the relationship between the regularity of noise and convergence rates, where p is a parameter to measure the regularity of noise and α (0, 1). Finally, numerical experiments are performed to support the theoretical results. [ABSTRACT FROM AUTHOR]

In this article we develop an asymptotic theory for sample tail autocorrelations of time series data that can exhibit serial dependence in both tail and non-tail regions. Unlike with the traditional autocorrelation function, the study of tail autocorrelations requires a double asymptotic scheme to capture the tail phenomena, and our results do not impose any restrictions on the dependence structure in non-tail regions and allow processes that are not necessarily strongly mixing. The newly developed asymptotic theory reveals a previously undiscovered phase transition phenomenon, where the asymptotic behaviour of sample tail autocorrelations, including their convergence rate, can transition from one phase to another as the lag index moves past the point beyond which serial tail dependence vanishes. The phase transition discovery fills a gap in existing research on tail autocorrelations and can be used to construct the lines of significance, in analogy to the traditional autocorrelation plot, when visualizing sample tail autocorrelations to assess the existence of serial tail dependence or to identify the maximal lag of tail dependence. [ABSTRACT FROM AUTHOR]

BACKGROUND: Developing a model that adequately explains pest population dynamics based on weather‐related parameters is fundamentally important for proper pest management. Autocorrelation with past occurrences should be considered when modeling the relationship between the time series of pest occurrence data and meteorological factors; however, few attempts have been made to model these factors simultaneously. In this study, we constructed an autoregressive integrated moving average with exogenous variables (ARIMAX) model to represent the occurrence of the common cutworm, Spodoptera litura (F.) (Lepidoptera: Noctuidae), a major moth pest species in Asia, using the trap catch data of S. litura recorded approximately every 5 days. The multiple meteorological measurements taken over several past periods before S. litura occurrence were included as explanatory variables to evaluate their lag effects on future occurrences. RESULTS: It was suggested that temperature had the most important effect on S. litura occurrences among other meteorological factors (i.e., humidity, wind speed, and precipitation). Especially, higher temperatures during the larval/egg stage seemed to presage a higher moth abundance. When the model was fitted using independent data that were not used for calibrating the model, the model was able to capture trends in increases in the scale of occurrence, particularly after July, when the occurrence rapidly increased. CONCLUSION: Past temperature condition, particularly during the larval and egg states, is suggested to be highly important for predicting future S. litura occurrences. The ARIMAX model proposed here will allow preventive measures to be taken, effectively safeguarding food resources against pest outbreaks. © 2022 Society of Chemical Industry. [ABSTRACT FROM AUTHOR]

This article defines the Autoregressive Fractional Unit Root Integrated Moving Average (ARFURIMA) model for modelling ILM time series with fractional difference value in the interval of 1 < d < 2. The performance of the ARFURIMA model is examined through a Monte Carlo simulation. Also, some applications were presented using the energy series, bitcoin exchange rates and some financial data to compare the performance of the ARFURIMA and the Semiparametric Fractional Autoregressive Moving Average (SEMIFARMA) models. Findings showed that the ARFURIMA outperformed the SEMIFARMA model. The study's conclusion provides another perspective in analysing large time series data for modelling and forecasting, and the findings suggest that the ARFURIMA model should be applied if the studied data show a type of ILM process with a degree of fractional difference in the interval of 1 < d < 2. [ABSTRACT FROM AUTHOR]

The outputs of many real-world complex dynamical systems are time series characterized by power-law correlations and fractal properties. The first proposed model for such time series comprised fractional Gaussian noise (fGn), defined by an autocorrelation function C (k) with asymptotic power-law behavior, and a complicated power spectrum S (f) with power-law behavior in the small frequency region linked to the power-law behavior of C (k) . This connection suggested the use of simpler models for power-law correlated time series: time series with power spectra of the form S (f) ∼ 1 / f β , i.e., with power-law behavior in the entire frequency range and not only near f = 0 as fGn. This type of time series, known as 1 / f β noises or simply 1 / f noises, can be simulated using the Fourier filtering method and has become a standard model for power-law correlated time series with a wide range of applications. However, despite the simplicity of the power spectrum of 1 / f β noises and of the known relationship between the power-law exponents of S (f) and C (k) , to our knowledge, an explicit expression of C (k) for 1 / f β noises has not been previously published. In this work, we provide an analytical derivation of C (k) for 1 / f β noises, and we show the validity of our results by comparing them with the numerical results obtained from synthetically generated 1 / f β time series. We also present two applications of our results: First, we compare the autocorrelation functions of fGn and 1 / f β noises that, despite exhibiting similar power-law behavior, present some clear differences for anticorrelated cases. Secondly, we obtain the exact analytical expression of the Fluctuation Analysis algorithm when applied to 1 / f β noises. [ABSTRACT FROM AUTHOR]

The brain must extract behaviorally relevant latent variables from the signals streamed by the sensory organs. Such latent variables are often encoded in the dynamics that generated the signal rather than in the specific realization of the waveform. Therefore, one problem faced by the brain is to segment time series based on underlying dynamics. We present two algorithms for performing this segmentation task that are biologically plausible, which we define as acting in a streaming setting and all learning rules being local. One algorithm is model based and can be derived from an optimization problem involving a mixture of autoregressive processes. This algorithm relies on feedback in the form of a prediction error and can also be used for forecasting future samples. In some brain regions, such as the retina, the feedback connections necessary to use the prediction error for learning are absent. For this case, we propose a second, model-free algorithm that uses a running estimate of the autocorrelation structure of the signal to perform the segmentation. We show that both algorithms do well when tasked with segmenting signals drawn from autoregressive models with piecewise-constant parameters. In particular, the segmentation accuracy is similar to that obtained from oracle-like methods in which the ground-truth parameters of the autoregressive models are known. We also test our methods on data sets generated by alternating snippets of voice recordings. We provide implementations of our algorithms at https://github.com/ttesileanu/bio-time-series. [ABSTRACT FROM AUTHOR]

Many studies have identified the influences of PM2.5. However, very little research has addressed the spatiotemporal dependence and heterogeneity in the relationships between impact factors and PM2.5. This study firstly utilizes spatial statistics and time series analysis to investigate the spatial and temporal dependence of PM2.5 at the city level in China using a three-year (2015–2017) dataset. Then, a new local regression model, multiscale geographically weighted regression (MGWR), is introduced, based on which we measure the influence of PM2.5. A spatiotemporal lag is constructed and included in MGWR to account for spatiotemporal dependence and spatial heterogeneity simultaneously. Results of MGWR are comprehensively compared with those of ordinary least square (OLS) and geographically weighted regression (GWR). Experimental results show that PM2.5 is autocorrelated in both space and time. Compared with existing approaches, MGWR with a spatiotemporal lag (MGWRL) achieves a higher goodness-of-fit and a more significant effect on eliminating residual spatial autocorrelation. Parameter estimates from MGWR demonstrate significant spatial heterogeneity, which traditional global models fail to detect. Results also indicate the use of MGWR for generating local spatiotemporal dependence evaluations which are conditioned on various covariates rather than being simple descriptions of a pattern. This study offers a more accurate method to model geographic events. [ABSTRACT FROM AUTHOR]

The time series analysis was performed with Seasonal Autoregressive Integrated Moving Average (SARIMA) and Sama circular model (SCM) for the rainfall of Ampan, Karaveddi, and Puloly regions of Jaffna to understand the behaviour of rainfall and forecast it with a suitable model. Minitab 17 software was used to run the model with the available monthly data from 2013 to 2019. Time series plots were used for pattern recognition, the independence of the residuals was checked using autocorrelation function (ACF), and Lijung-Box Q statistics (LBQ). The normality of residuals was checked using probability plot. The model with the lowest predicting errors was selected to forecast the future values. The monthly rainfall fluctuates around the mean of 41.6, 71.9, and 35.3 mm for Ampan, Karaveddi, and Puloly respectively. The models SARIMA (0,0,0) (0,1,1)6, SARIMA (1,2,1) (0,1,1)6, and SARIMA (1,1,0) (0,1,1)6 were found as most appropriate for Ampan, Karaveddi, and Puloly respectively and Yt = Yt-1 -- 0.18 + 23.5 sin 2ωt + 28.5 cos 1.5ωt + 20.10 cos 2ωt -- 26.47 cos 5.5ωt, Yt = Yt-1 -- 2Yt-2 -- 5.9 + 73.5 sin 4.5ωt and Yt = Yt-1 -- 2Yt-2 + 0.69 + 23.17 cos 5.5ωt were found as most appropriate SCM for Ampan, Karaveddi, and Puloly respectively. Among these models, SCM predicts reliable data with minimum error and it finds the seasonal and cyclic pattern of the rainfall. A five-month seasonal pattern and cyclic behaviour at 13 - months interval was noted in Ampan. Similarly, 10 - months seasonal pattern was observed in Karaveddi. The Puloly region expressed the cyclic pattern of rainfall only at 13-month interval. AD value is 0.40, 0.63 and 0.68 for Ampan, Karaveddi and Puloly respectively. The decreasing trend of estimated rainfall in Ampan (0.21 mm/year) and increasing trend in Puloly (1.15 mm/year) and Karaveddi (0.61 mm/year) is an alarming sign to the agriculture sector. [ABSTRACT FROM AUTHOR]

Accurate knowledge of individual tree ages is critical for forestry and ecological research. However, previous methods suffer from flaws such as tree damage, low efficiency, or ignoring autocorrelation among residuals. In this paper, an approach for estimating the ages of individual trees is proposed based on the diameter series of Cinnamomum camphora (Cinnamomum camphora (L.) Presl), Schima superba (Schima superba Gardn. et Champ.), and Liquidambar formosana (Liquidambar formosana Hance). Diameter series were obtained by stem analysis. Panel data contains more information, more variability, and more efficiency than pure time series data or cross-sectional data, which is why diameter series at stump and breast heights were chosen to form the panel data. After choosing a base growth equation, a constraint was added to the equation to improve stability. The difference method was used to reduce autocorrelation and the parameter classification method was used to improve model suitability. Finally, the diameter increment equation of parameter a-classification was developed. The mean errors of estimated ages based on the panel data at breast height for C. camphora, S. superba, and L. formosana were 0.47, 2.46, and −0.56 years and the root mean square errors were 2.04, 3.15 and 2.47 years, respectively. For C. camphora and L. formosana, the estimated accuracy based on the panel data was higher at breast height than at stump height. This approach to estimating individual tree ages is highly accurate and reliable, and provides a feasible way to obtain tree ages by field measurement. [ABSTRACT FROM AUTHOR]

We study the distributed (Δ + 1)-vertex-coloring and (2Δ - 1)-edge-coloring problems. These problems are among the most important and intensively studied problems in distributed computing. Despite very intensive research in the last 30 years, no deterministic algorithms for these problems with sublinear (in Δ) time have been known so far. Moreover, for more restricted scenarios and some related problems there are lower bounds of Ω(Δ) [GÖÖs et al. 2014; Hirvonen and Suomela 2012; Kuhn and Wattenhofer 2006; Szegedy and Vishwanathan 1993]. The question of the possibility to devise algorithms that overcome this challenging barrier is one of the most fundamental questions in distributed symmetry breaking [Barenboim and Elkin 2009, 2011; GÖÖs et al. 2014; Hirvonen and Suomela 2012; Kuhn 2009; Panconesi and Rizzi 2001]. In this article, we settle this question for (Δ+1)-vertex-coloring and (2Δ-1)-edge-coloring by devising deterministic algorithms that require Õ(Δ3/4 logΔ + log* n) time in the static, dynamic, and faulty settings. (The term log* n is unavoidable in view of the lower bound of Linial [1987].) Moreover, for (1 + o(1))Δ-vertex-coloring and (2 + o(1))Δ-edge-coloring we devise algorithms with Õ(Δ + log* n) deterministic time. This is roughly a quadratic improvement comparing to the state-of-the-art that requires Õ(Δ+log* n) time [Barenboim and Elkin 2009; Kuhn 2009; Panconesi and Rizzi 2001]. Õur results are actually more general than that since they apply also to a variant of the list-coloring problem that generalizes ordinary coloring. Õur results are obtained using a novel technique for coloring partially colored graphs (also known as fixing). We partition the uncolored parts into a small number of subgraphs with certain helpful properties. Then we color these subgraphs gradually using a technique that employs constructions of polynomials in a novel way. Õur construction is inspired by the algorithm of Linial [1987] for ordinary Õ(Δ2)-coloring. However, it is a more sophisticated construction that differs from that of Linial [1987] in several important respects. These new insights in using systems of polynomials allow us to significantly speed up the Õ(Δ)- coloring algorithms. Moreover, they allow us to devise algorithms with the same running time also in the more complicated settings of dynamic and faulty networks. [ABSTRACT FROM AUTHOR]

This paper devotes to give a comprehensive review of Z -valued time series models, which allow negative autocorrelations besides positive autocorrelations. Z -valued versions of integer-valued autoregressive (INAR) models are mainly based on three different operators: signed thinning operators, difference operators and rounding operators, while Z -valued versions of integer-valued generalized autoregressive conditional heteroscedastic (INGARCH) models can be classified into four categories: some Z -valued discrete distributions, difference of two independent nonnegative INGARCH models, nonnegative INGARCH models multiplying by some special Z -valued discrete random variables, and random rounding operators. We review stochastic properties, briefly discuss the estimation methods of the Z -valued INAR-type and INGARCH-type models and use two real examples to show their applications. In addition, we also consider some other Z -valued models, including the Bernoulli difference model with taking values − 1 , 0 , 1 , and the discrete ARMA model. Finally, some possible extensions are discussed. [ABSTRACT FROM AUTHOR]

The traffic data of the intelligent network with the Space-Integrated Ground Information Network have the characteristics of robust traffic burst, large traffic data, and high volatility compared with the ground traffic. We propose a Gated Temporal Convolution Network (GTCN) algorithm to solve the above problems, the algorithm segments the traffic time series into equal length according to the autocorrelation of the network traffic, and creates the feature sequence by extracting the segmented features using Temporal Convolution Network (TCN), to learn the burst and fluctuation of the intelligent network traffic of the Space-Integrated Ground Information Intelligent Network and to improve the processing efficiency of the traffic time series. Then, the feature sequences of each subsection data are stored, screened, and retained through the gated unit. Finally, the network traffic data are accurately predicted using the characteristics of the sequences stored by the TCN and the gating unit. The simulation experiments showed that, compared with the comparison algorithms, the accuracy of the proposed algorithm is improved by at least 58.72%, the training speed of the algorithm is improved by 84.05%, and the algorithm execution speed is improved by 71.92%, which meet the requirements of the accuracy and timeliness of the traffic prediction model of the Space-Integrated Ground Information Intelligent Network. [ABSTRACT FROM AUTHOR]

We study change-points tests based on U-statistics for absolutely regular observations. Our method avoids some technical assumptions on the data and the kernel. The asymptotic properties of the U-statistics are studied under the null hypothesis, under fixed alternatives and under a sequence of local alternatives. The asymptotic distributions of the test statistics under the null hypothesis and under the local alternatives are given explicitly and the tests are shown to be consistent. A small set of simulations is done for evaluating the performance of the tests in detecting changes in the mean, variance and autocorrelation of some simple time series. [ABSTRACT FROM AUTHOR]

In this paper additive models with p-order autoregressive conditional symmetric errors based on penalized regression splines are proposed for modeling trend and seasonality in time series. The aim with this kind of approach is try to model the autocorrelation and seasonality properly to assess the existence of a significant trend. A backfitting iterative process jointly with a quasi-Newton algorithm are developed for estimating the additive components, the dispersion parameter and the autocorrelation coefficients. The effective degrees of freedom concerning the fitting are derived from an appropriate smoother. Inferential results and selection model procedures are proposed as well as some diagnostic methods, such as residual analysis based on the conditional quantile residual and sensitivity studies based on the local influence approach. Simulations studies are performed to assess the large sample behavior of the maximum penalized likelihood estimators. Finally, the methodology is applied for modeling the daily average temperature of San Francisco city from January 1995 to April 2020. [ABSTRACT FROM AUTHOR]

This paper focuses on using time series and spatial analysis methods to detect climate change indicators in Malaybalay, Bukidnon. We look at 56 years of historical rainfall data between the years 1961 to 2017 and perform a computational method for data processing to arrive at spatial statistics and provide data visualization. We demonstrate the use of the Augmented Dickey-Fuller test (ADF), where a p-value is tested versus a threshold to reject or accept the null hypothesis for a stationarity test. For the seasonality test, we perform a time-domain signal processing by an autocorrelation function. The time-series analysis shows that for Malaybalay, Bukidnon rainfall data shows ADF statistic of −16.348964, a p-value  = 0.000000 with critical values 1%:−3.431, 5%:−2.862, 10%:−2.567. Hence, the significant negative values indicate more likely to reject the null hypothesis. We showed that rainfall does not demonstrate periodicity, is not seasonal, and is non-stationary. This work does not cover those that can be detected and attributed to anthropogenic causes. [ABSTRACT FROM AUTHOR]

Statistical trend analyses of observed precipitation (P) time series are key to validate theoretical arguments and climate projections suggesting that extreme P will increase in a warmer climate. Recent work warned about possible misinterpretation of trend tests if the presence of serial correlation and field significance are not considered. Here, we investigate these two aspects focusing on extreme P frequencies derived from 100‐year daily records of 1,087 worldwide gauges of the Global Historical Climatology Network. For this aim, we perform Monte Carlo experiments based on count time series generated with the Poisson integer autoregressive model and characterized by different sample size, level of autocorrelation, and trend magnitude. The main results are as follows. (a) Empirical autocorrelations are consistent with those of uncorrelated and stationary or nonstationary count time series, while empirical trends cannot be explained as the exclusive effect of autocorrelation; incorporating the impact of serial correlation in trend tests on extreme P frequency has then limited impacts on tests' performance. (b) Accounting for field significance improves interpretation of test results by limiting type‐I errors, but it also decreases test power; results of local tests could complement field significance outcomes and help identify weak trend signals where several trends of coherent sign are detected. (c) Based on these findings, evident patterns of statistically significant increasing (decreasing) trends emerge in central and eastern North America, northern Eurasia, and central Australia (southwestern America, southern Europe, and southern Australia). The methodological insights of this work support trend analyses of any hydroclimatic variable. Key Points: Monte Carlo simulations based on the integer autoregressive model allow assessing trends on observed extreme precipitation frequencyAccounting for serial correlation in observed extreme precipitation frequency has limited impact on statistical trend analysesAccounting for field significance limits type‐I error of statistical trend tests, but reduces power when the trend signal is low [ABSTRACT FROM AUTHOR]

The self-affine mode of ice softening during friction is investigated within the rheological model for viscoelastic medium approximation. The different modes of ice rubbing, determined by formation of surface liquid-like layer, are studied. The analysis of time series of friction force is carried out, namely Fourier analysis, construction of autocorrelation and difference autocorrelation functions. The spectral power law is detected for modes of crystalline ice as well as of a mixture of stable ice and metastable softening. The self-similarity and a periodic character of corresponding time series of friction force are proved. [ABSTRACT FROM AUTHOR]

Traditional Parametric spectral estimation methods have been widely used to obtain spectral estimate, resolution and variance distribution in signals or time series data across several fields. But the challenges of how to select an optimal and efficient model order were often encountered. In this research work, modified forms of Final Prediction Error, Akaike Information Criteria, Bayesian Information Criteria and Minimum Description Length which involved the replacement of variance error with sample autocorrelation function that has capabilities of detecting non-randomness in time series data were used to select the optimal model order. In order to determine the efficiency of the modified criteria, Autoregressive model, AR(11) was selected based on all the modified information criteria while AR(7) was selected based on all the traditional information criteria as the optimal model orders. Using the AR spectral estimation method, AR(11) and AR(7) models were used to analyse 1000 points Heartbeat readings. The results indicated that the spectral estimate and resolution of AR(11) were better than that of AR(7). Conclusively, the optimal model order selected using the modified information criteria gives a better result when compared to the traditional information criteria based on the spectral estimate and resolution of the Autoregressive spectral estimation method. [ABSTRACT FROM AUTHOR]

Close encounters or resonances overlaps can create chaotic motion in small bodies in the Solar System. Approaches that measure the separation rate of trajectories that start infinitesimally near, or changes in the frequency power spectrum of time series, among others, can discover chaotic motion. In this paper, we introduce the ACF index (ACFI), which is based on the auto-correlation function of time series. Auto-correlation coefficients measure the correlation of a time-series with a lagged duplicate of itself. By counting the number of auto-correlation coefficients that are larger than 5% after a certain amount of time has passed, we can assess how the time series auto-correlates with each other. This allows for the detection of chaotic time-series characterized by low ACFI values. [ABSTRACT FROM AUTHOR]

We investigated the finite properties as well as the goodness of fit test for the cubic smoothing spline selection methods like the Generalized Maximum Likelihood (GML), Generalized Cross-Validation (GCV) and Mallow CP criterion (MCP) estimators for time-series observation when there is the presence of Autocorrelation in the error term of the model. The Monte-Carlo study considered 1,000 replication with six sample sizes: 30; 60; 120; 240; 480 and 960, four degree of autocorrelations; 0.1; 0.3; 0.5; and 0.9 and three smoothing parameters; λGML= 0.07271685, λGCV= 0.005146929, λMCP= 0.7095105. The cubic smoothing spline selection methods were also applied to a real-life dataset. The Predictive mean square error, R-square, and adjusted R-square criteria for assessing finite properties and goodness of fit among competing models discovered that the performance of the estimators is affected by changes in the sample sizes and autocorrelation levels of the simulated and real-life data set. The study concluded that the Generalized Cross-Validation estimator provides a better fit for Autocorrelated time series observation. It is recommended that the GCV works well at the four autocorrelation levels and provides the best fit for time-series observations at all sample sizes considered. This study can be applied to; non -parametric regression, non -parametric forecasting, spatial, survival and econometric observations. [ABSTRACT FROM AUTHOR]

Studies detecting trends in climate elements typically concentrate on their local significance, ignoring the question of whether the significant local trends may or may not have occurred as a result of chance. This paper fills this gap by examining several approaches to detecting statistical significance of trends defined on a grid (i.e., on a regional scale). To this end, we introduce a novel simple procedure of significance testing that is based on counting signs of local trends (sign test), and we compare it with five other approaches to testing collective significance of trends: counting, extended Mann–Kendall, Walker, false detection rate (FDR), and regression tests. Synthetic data are used to construct null distributions of trend statistics, to determine critical values of the tests, and to assess the performance of tests in terms of type-II error. For lower values of spatial and temporal autocorrelations, the sign test and extended Mann–Kendall test perform slightly better than the counting test; these three tests outperform the Walker, FDR, and regression tests by a wide margin. For high autocorrelations, which is a more realistic case, all tests become similar in their performance, with the exception of the regression test, which performs somewhat worse. Some tests cannot be used under specific conditions because of their construction: the Walker and FDR tests for high temporal autocorrelations, and the sign test under high spatial autocorrelations. [ABSTRACT FROM AUTHOR]

Monitoring of winding faults is of great significance for the assessment of the transformer maintenance status. In this study, the time series analysis is combined with frequency response analysis (FRA) for better interpretation and analysis of FRA results. Here, healthy baseline residual data are modeled using the time series analysis for faults detection of the transformer winding. Different statistical software, such as R 4.0.2 and ITSM2000, are used to analyze measured data. To detect the transformer’s winding faults, various analyses, such as the autocorrelation and partial autocorrelation functions plot, the Box–Pierce test, the Ljung–Box test, the McLeod–Li test, the turning points test, the Wallis and Moore phase–frequency test, and the Jarque–Bera test, and the order of minimum corrected Akaike’s information criteria are used. The simulation results show that the suggested method is able to classify and discriminate mechanical and electrical faults of the transformer’s winding with good accuracy. [ABSTRACT FROM AUTHOR]