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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]

This year is the 50th anniversary of Besag's classic auto‐models publication, a cornerstone in the development of modern‐day spatial statistics/econometrics. Besag struggled for nearly two decades to make his conceptualization collectively successful across a wide suite of random variables. But only his auto‐normal, and to a lesser degree his auto‐logistic/binomial, were workable. Others, like his auto‐Poisson, were effectively failures, whereas still others, such as potentials like an auto‐Weibull, defied even awkward mathematical incorporations of spatial lag terms. Besag circumvented this impediment by introducing an auto‐normal random effects components (within a Bayesian estimation context), building upon his single total success. This article describes an alternative approach, partly paralleling his reformulation while avoiding inserting spatial lag terms directly into probability density/mass functions, implanting spatial autocorrelation into cumulative distributions functions (CDFs), instead, via a spatially autocorrelated uniform distribution. The already existing probability integral transform and quantile function mathematical statistics theorems enable this mechanism to spatialize any random variable, with these new ones labeled sui‐models. [ABSTRACT FROM AUTHOR]

AbstractSpatial autoregressive (SAR) models are often used to explicitly account for the spatial dependence underlying geographic phenomena. However, traditional SAR models are specified using a single SAR coefficient, assuming constant spatial dependence over space. This assumption oversimplifies the situation where the true spatial autoregressive process varies in strength; the consequences of ignoring heterogeneous autocorrelation remain to be discussed. This study proposes a heterogeneous spatial autocorrelation model by extending the spatial lag model (SLM). The new model includes change point detection for identifying patterns of spatially varying autocorrelation strengths, a SAR coefficient matrix for representing heterogeneous spatial autocorrelation, and maximum likelihood estimation for determining multiple SAR coefficients. Monte Carlo simulations demonstrate that the proposed method is effective in modeling SAR processes with heterogeneous autocorrelation patterns, while traditional SLM inflates uncertainties in the regression coefficients when a heterogeneous autocorrelation structure is not accounted for. We further applied the new method to an empirical analysis of traffic crashes in the Greater Perth Area, Australia. The heterogeneous spatial autocorrelation model reduces model RMSE by 42% (compared with traditional SLM). Results from both simulation and empirical studies indicate that spatially varying autocorrelation strengths should be considered for SAR processes and relevant applications. [ABSTRACT FROM AUTHOR]

In the United States, several land use and land cover (LULC) data sets are available based on satellite data, but these data sets often fail to accurately represent features on the ground. Alternatively, detailed mapping of heterogeneous landscapes for informed decision-making is possible using high spatial resolution orthoimagery from the National Agricultural Imagery Program (NAIP). However, large-area mapping at this resolution remains challenging due to radiometric differences among scenes, landscape heterogeneity, and computational limitations. Various machine learning (ML) techniques have shown promise in improving LULC maps. The primary purposes of this study were to evaluate bagging (Random Forest, RF), boosting (Gradient Boosting Machines [GBM] and extreme gradient boosting [XGB]), and stacking ensemble ML models. We used these techniques on a time series of Sentinel 2A data and NAIP orthoimagery to create a LULC map of a portion of Irion and Tom Green counties in Texas (USA). We created several spectral indices, structural variables, and geometry-based variables, reducing the dimensionality of features generated on Sentinel and NAIP data. We then compared accuracy based on random cross-validation without accounting for spatial autocorrelation and target-oriented cross-validation accounting for spatial structures of the training data set. Comparison of random and target-oriented cross-validation results showed that autocorrelation in the training data offered overestimation ranging from 2% to 3.5%. The XGB-boosted stacking ensemble on-base learners (RF, XGB, and GBM) improved model performance over individual base learners. We show that meta-learners are just as sensitive to overfitting as base models, as these algorithms are not designed to account for spatial information. Finally, we show that the fusion of Sentinel 2A data with NAIP data improves land use/land cover classification using geographic object-based image analysis. [ABSTRACT FROM AUTHOR]

Monopole time reversal is an advanced noise source localization technique, but its sidelobe level in localizing sound sources is greatly affected by noise, leading to a decrease in the accuracy of sound source localization under a low signal-to-noise ratio. To address this issue, this paper proposes a time-domain monopole time reversal technique that excludes autocorrelation to reduce the impact of noise on sound source localization results. Numerical simulation and experimental results show that, compared to conventional monopole time reversal techniques, the proposed method can effectively reduce the sidelobes in sound source localization results and achieve accurate sound source localization under −20 dB low signal-to-noise ratio conditions. [ABSTRACT FROM AUTHOR]

Flicker and patterns of stripes in the modern environment can evoke visual illusions, discomfort migraine, and seizures. We measured reading speed while striped and less striped texts were illuminated with LED lights. In Experiment 1, the lights flickered at 60 Hz and 120 Hz compared to 60 kHz (perceived as steady light). In Experiment 2, the lights flickered at 60 Hz or 600 Hz (at which frequency the phantom array is most visible), and were compared to continuous light. Two types of text were used: one containing words with high horizontal autocorrelation (striped) and another containing words with low autocorrelation (less striped). We measured the number of illusions participants saw in the Pattern Glare (PG) Test. Overall, reading speed was slowest during the 60 Hz and 600 Hz flicker and was slower when reading the high autocorrelation text. Interestingly, the low PG group showed greater effects of flicker on reading speed than the high PG group, which tended to be slower overall. In addition, reading speed in the high PG group was reduced when the autocorrelation of the text was high. These findings suggest that uncomfortable visual environments reduce reading efficiency, the more so in individuals who are visually sensitive. [ABSTRACT FROM AUTHOR]

Objective To analyze the incidence trend and epidemiological characteristics of dengue fever in Fujian Province from 2009 to 2023, identify the high-incidence population and hotspot areas, and a scientific basis for formulating targeted prevention and control measures. Methods The surveillance data of dengue fever during 2009-2023 in Fujian Province were obtained from the National Disease Reporting Information System and analyzed using descriptive epidemiological methods, and the spatial autocorrelation analysis of dengue fever incidence at county/district levels was performed with ArcGlS 10.8. Results A total of 3 586 cases of dengue fever were reported in Fujian Province from 2009 to 2023, with an average annual incidence rate of 0.61/100 000, showing an overall increasing trend year by year (Z=18.35, P< 0.001). Among them, there were 2 362 local cases and 1 224 imported cases, with a local/imported ratio of 1.93:1 (2 362/1 224). The local cases were mainly distributed in Fuzhou, Putian, and Nanping, accounting for 87.81% (2 074/2 362). The imported cases were mainly distributed in Quanzhou, Fuzhou, and Xiamen, accounting for 72.55% (888/1 224). The local/imported ratio in Fuzhou, Nanping, and Putian was 6.20:1 (1 557/251), 3.92:1 (145/37), and 3.32:1 (372/112), respectively, all significantly higher than the provincial average level. The spatial distribution of the local cases showed a clustered pattern, with 12 hotspots of incidence, all located in the counties and districts under the jurisdiction of Fuzhou. The onset of the disease had obvious seasonality: imported cases from other countries or regions mainly occurred from July to September (accounting for 45.73%, 519/1 135), imported cases from other provinces mainly occurred from August to November (accounting for 93.25%, 83/89), and local cases mainly occurred from August to October (accounting for 97.50%, 2 303/2 362). The gender ratio for local cases was 0.88:1, and for imported cases, it was 3.04:1. The average age of onset for local cases was 48 years old (Q1=32 years old, Q3=62 years old), while the average age for imported cases was 35 years old (Q1=28 years old, Q3=44 years old). Conclusions From 2009 to 2023, the dengue fever epidemic in Fujian Province showed a continuous upward trend, with spatiotemporal clustering of incidence. Therefore, prevention and control measures should be strengthened in key areas and populations during the high-incidence season. [ABSTRACT FROM AUTHOR]

In the convolutional retinex approach to image lightness processing, an image is filtered by a centre/surround operator that is designed to mitigate the effects of shading (illumination gradients), which in turn compresses the dynamic range. Typically, the parameters that define the shape and extent of the filter are tuned to provide visually pleasing results, and a mapping function such as a logarithm is included for further image enhancement. In contrast, a statistical approach to convolutional retinex has recently been introduced, which is based upon known or estimated autocorrelation statistics of the image albedo and shading components. By introducing models for the autocorrelation matrices and solving a linear regression, the optimal filter is obtained in closed form. Unlike existing methods, the aim is simply to objectively mitigate shading, and so image enhancement components such as a logarithmic mapping function are not included. Here, the full mathematical details of the method are provided, along with implementation details. Significantly, it is shown that the shapes of the autocorrelation matrices directly impact the shape of the optimal filter. To investigate the performance of the method, we address the problem of shading removal from text documents. Further experiments on a challenging image dataset validate the method. [ABSTRACT FROM AUTHOR]

Due to the nonlinear nature of continuous phase modulation (CPM), most existing unambiguous acquisition algorithms are ineffective in eliminating the ambiguity threat faced by semi‐integer CPM signals. To address this issue, this letter proposes an unambiguous acquisition algorithm based on sub‐correlation functions combination (SCFC). The main idea of this algorithm is to decompose the first pulse amplitude modulation waveform derived from the Laurent decomposition into sub‐signal waveforms that are appropriate for CPM signals. The final unambiguous function is obtained by combining the autocorrelation function of the received CPM signal with the sub‐correlation functions derived from the sub‐signal waveforms and the received CPM signal. Simulation results demonstrate that the SCFC algorithm can eliminate the ambiguity threat of semi‐integer CPM signals with relatively minor detection loss. Moreover, the proposed algorithm successfully retains a narrow main peak and exhibits superior multipath resistance. [ABSTRACT FROM AUTHOR]

The principle of independence is a fundamental yet often disregarded assumption in statistical inference. It is observed that the implications of correlations, if not considered, can lead to a conservative estimation of Type I error in the presence of positive linear correlations when utilizing the Kolmogorov-Smirnov (KS) test. Conversely, negative linear correlations may engender a liberal estimation of Type I error. To address the impact of spatial autocorrelation in the analysis of Positron Emission Tomography (PET) images, we have proposed an innovative methodology to reconstruct a grid map of human heart scans using spherical coordinates. We have examined the distribution of the KS test statistic under spatial autocorrelation through Monte Carlo (MC) simulation and have introduced a KS test with a spatial adjustment. The newly proposed KS test with spatial adjustment demonstrates a controlled Type I error and power that is not inferior when compared to the original KS test. This suggests its potential utility in the analysis of spatially autocorrelated data. [ABSTRACT FROM AUTHOR]

When using ground-based synthetic aperture radar (GB-SAR) for monitoring open-pit mines, dynamic atmospheric conditions can interfere with the propagation speed of electromagnetic waves, resulting in atmospheric phase errors. These errors are particularly complex in rapidly changing weather conditions or steep terrain, significantly impacting monitoring accuracy. In such scenarios, traditional regression model-based atmospheric phase correction (APC) methods often become unsuitable. To address this issue, this paper proposes a clustering method based on the spatial autocorrelation function. First, the interferogram is uniformly divided into multiple blocks, and the phase consistency of each block is evaluated using the spatial autocorrelation function. Then, a region growing algorithm is employed to classify each block according to its phase pattern, followed by merging adjacent blocks based on statistical data. To verify the feasibility of the proposed method, both the traditional regression model-based method and the proposed method were applied to deformation monitoring of an open-pit mine in Northwest China. The experimental results show that for complex atmospheric phase scenarios, the proposed method significantly outperformed traditional methods, demonstrating its superiority. [ABSTRACT FROM AUTHOR]

Frequency estimation of sinusoid is an important research topic in the field of statistical signal processing. Efficient frequency estimation is of great significance for applications with high real-time requirements. In this paper, two efficient frequency estimators of complex sinusoid by using autocorrelation and discrete time Fourier transform (DTFT) are presented in additive white noise background. Firstly, autocorrelation algorithm is adopted to obtain the coarse frequency estimate. Then, three DTFT samples with arbitrary intervals located near the coarse estimate are used to get the fine frequency estimate. In order to evaluate the calculation complexity and estimation accuracy, the proposed estimators are compared with the competing algorithms. The computational complexity of the presented estimators is much lower than that of the competitive estimators. Simulation results show that the mean square errors of the presented estimators are close to the Cramer–Rao lower bound when the signal-to-noise ratio varies in a large range. [ABSTRACT FROM AUTHOR]

Access to housing data in Ghana has been a challenge for researchers due to the lack of comprehensive data sources. However, the recent availability of big data sources has presented opportunities to bridge this data access gap. Using Greater Accra as a case, this study uses web scraping techniques to acquire publicly available housing data from two major E-commerce websites in Ghana and explores the Greater Accra Metropolitan Area's (GAMA) prevailing housing market. Spatial autocorrelation statistics show clustering of high median prices in known high-class neighborhoods. Median prices in high-class neighborhoods were three to five times higher than median prices in the entire metropolis, highlighting high housing costs in high-class neighborhoods. This research highlights the high housing cost in GAMA, making it impossible for the average resident to afford to buy a house. Hence, a more inclusive housing strategy is needed to provide affordable housing options for all. [ABSTRACT FROM AUTHOR]

Site occupancy models (SOMs) are a common tool for studying the spatial ecology of wildlife. When observational data are collected using passive monitoring field methods, including camera traps or autonomous recorders, detections of animals may be temporally autocorrelated, leading to biased estimates and incorrectly quantified uncertainty. We presently lack clear guidance for understanding and mitigating the consequences of temporal autocorrelation when estimating occupancy models with camera trap data.We use simulations to explore when and how autocorrelation gives rise to biased or overconfident estimates of occupancy. We explore the impact of sampling design and biological conditions on model performance in the presence of autocorrelation, investigate the usefulness of several techniques for identifying and mitigating bias and compare performance of the SOM to a model that explicitly estimates autocorrelation. We also conduct a case study using detections of 22 North American mammals.We show that a join count goodness‐of‐fit test previously proposed for identifying clustered detections is effective for detecting autocorrelation across a range of conditions. We find that strong bias occurs in the estimated occupancy intercept when survey durations are short and detection rates are low. We provide a reference table for assessing the degree of bias to be expected under all conditions. We further find that discretizing data with larger windows decreases the magnitude of bias introduced by autocorrelation. In our case study, we find that detections of most species are autocorrelated and demonstrate how larger detection windows might mitigate the resulting bias.Our findings suggest that autocorrelation is likely widespread in camera trap data and that many previous studies of occupancy based on camera trap data may have systematically underestimated occupancy probabilities. Moving forward, we recommend that ecologists estimating occupancy from camera trap data use the join count goodness‐of‐fit test to determine whether autocorrelation is present in their data. If it is, SOMs should use large detection windows to mitigate bias and more accurately quantify uncertainty in occupancy model parameters. Ecologists should not use gaps between detection periods, which are ineffective at mitigating temporal structure in data and discard useful data. [ABSTRACT FROM AUTHOR]

A new test to detect the change-point in the quasi-autocorrelation coefficient (QAC) structure of a simple linear model with heavy-tailed series was developed. It is more general than previous approaches to the change-point problem in that it allows for the process with innovations in the domain of the attraction of a stable law with index κ (0 < κ < 2). Since the existing methods for QAC change detection are not satisfactory, we converted QAC change to mean change through the moving window method, which greatly improved the efficiency. Thus, the aim of this paper was to construct a ratio-typed test based on M-estimation for the testing of mean change. Under regular conditions, the asymptotic distribution under the no change null hypothesis was functional of a Wiener process, not that of a Lévy stable process. The divergent rate under the alternative hypothesis was also given. The simulation results demonstrate that the performances of our proposed tests were outstanding. Finally, the theoretical results were applied to an analysis of daily USD/CNY exchange rates with respect to QAC change. [ABSTRACT FROM AUTHOR]

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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]

In this paper we introduce first-order spatial random coefficient non-negative integer-valued autoregressive (SRCINAR(1,1)) model to fit the spatial count data on a two-dimensional regular lattice. We use a thinning operator in order to define the processes. The mean, variance and autocorrelation function of the model are derived. Three methods (Yule-Walker, Conditional least squares and Conditional maximum likelihood) for the estimation of the parameters of the model are discussed and are compared with respect to the root mean squared error (RMSE), in a simulation study. Finally, SRCINAR(1,1) model is applied to a real data set of striga counts at the ICRISAT Sahelian Center near Niamey (Niger). [ABSTRACT FROM AUTHOR]

Road safety has now become a major concern in many countries. In Algeria, as elsewhere, many factors are involved in the phenomena of road accidents. In this field of research, our study aims to spatial identification along a road network the hazardous road segments which present a dangerousness index. We proceeded the use of geostatistical approach, in particular global G(d) statistic and local Gi*(d) statistic of Getis-Ord. However, in an operational framework, this approach is highly dependent on hypothesis on the process of the measurement of the spatial proximity based on the distances between the BSUs. Thus, the interpretation of empirical results based on the optimal choice of the weighting structure and the critical distance. Methodologically, this work allowed to test an approach for assess the safety levels experimented in the case of road network specifically higher accidents risk in the Wilaya of Mascara (north west of Algeria). The first results confirm the validity of the method and allow a recoverable mapping by managers in the choice of measures of preventive management. [ABSTRACT FROM AUTHOR]

The study explored the relationship between tax avoidance and the cost of capital among publicly listed firms in Nigeria from 2010 to 2022. Using a simple random sampling technique, the sample included 30 firms across five sectors. Secondary data were sourced from annual reports of the selected firms and fact books from the Nigerian Stock Exchange (NSE). The cost of capital, comprising cost of equity and cost of debt, was analyzed with tax avoidance measured by the firm's cash effective tax rate. Control variables included leverage, return on assets, return on equity, firm size, and board size. A panel fixed effects panel regression analysis, selected after a Hausman pre-test, was employed alongside "Driscoll-Kraay standard errors" to address heteroscedasticity and autocorrelation issues. Results from the panel fixed effects analysis indicated that tax avoidance significantly and positively affects both the cost of equity and the cost of debt, highlighting tax avoidance as a key factor in firms' financing decisions and investors' choices. Further analysis using system GMM two-step estimators confirmed the panel fixed effect results, underscoring their robustness and revealing a bidirectional relationship between tax avoidance and cost of debt, suggesting reverse causality. To address these implications, policymakers are urged to implement regulatory measures encouraging voluntary tax compliance and clear tax law interpretations to curb aggressive tax avoidance, thereby reducing firms' cost of capital. Additionally, firms should enhance transparency by disclosing operational details to shareholders, fostering investor confidence and influencing their perceptions of risk and the associated cost of capital. [ABSTRACT FROM AUTHOR]

This paper discusses the auto-correlation functions of chaotic binary sequences obtained by a one-dimensional chaotic map and two binary functions. The two binary functions are alternately used to obtain a binary sequence from a chaotic real-valued sequence. We consider two similar methods and give the theoretical auto-correlation functions of the new binary sequences, which are expressed by the auto-/cross-correlation functions of the two chaotic binary sequences generated by a single binary function. Furthermore, some numerical experiments are performed to confirm the validity of the theoretical auto-correlation functions. [ABSTRACT FROM AUTHOR]

The authors present an analysis of the correlation between demographic and territorial indicators and greenhouse gas (GHG) emissions, emphasizing the spatial aspect using statistical methods. Particular attention is given to the application of correlation techniques, considering the spatial correlation between the involved variables, such as demographic, territorial, and environmental indicators. The demographic data include factors such as population, demographic distribution, and population density; territorial indicators include land use, particularly settlements, and road soil occupancy. The aims of this study are as follows: (1) to identify the direct relationships between these variables and emissions; (2) to evaluate the spatial dependence between geographical entities; and (3) to contribute to generating a deeper understanding of the phenomena under examination. Using spatial autocorrelation analysis, our study aims to provide a comprehensive framework of the territorial dynamics that influence the quantity of emissions. This approach can contribute to formulating more targeted environmental policies, considering the spatial nuances that characterize the relationships between demographics, territory, and GHGs. The outcome of this research is the identification of a direct formula to obtain greenhouse gas emissions from data about land use starting from the case study of Pavia Province in Italy. In the paper, the authors highlight different methodologies to compare land use and GHG emissions to select the most feasible correlation formula. The proposed procedure has been tested and can be used to promote awareness of the spatial dimension in the analysis of complex interactions between anthropogenic factors and environmental impacts. [ABSTRACT FROM AUTHOR]

Optimizing the correlation properties of spreading codes is critical for minimizing inter-channel interference in satellite navigation systems. By improving the codes' correlation sidelobes, we can enhance navigation performance while minimizing the required spreading code lengths. In the case of low-earth orbit (LEO) satellite navigation, shorter code lengths (on the order of a hundred) are preferred due to their ability to achieve fast signal acquisition. Additionally, the relatively high signal-to-noise ratio in LEO systems reduces the need for longer spreading codes to mitigate inter-channel interference. In this work, we propose a two-stage block coordinate descent (BCD) method which optimizes the codes' correlation properties while enforcing the autocorrelation sidelobe zero property. In each iteration of the BCD method, we solve a mixed-integer convex program over a block of 25 binary variables. Our method is applicable to spreading code families of arbitrary sizes and lengths, and we demonstrate its effectiveness for a problem with 66 length-127 codes and a problem with 130 length-257 codes. [ABSTRACT FROM AUTHOR]

Doppler lidar (DL) applications with a focus on turbulence measurements sometimes require measurement settings with a relatively small number of accumulated pulses per ray in order to achieve high sampling rates. Low pulse accumulation comes at the cost of the quality of DL radial velocity estimates and increases the probability of outliers, also referred to as "bad" estimates or noise. Careful filtering is therefore the first important step in a data processing chain that begins with radial velocity measurements as DL output variables and ends with turbulence variables as the target variable after applying an appropriate retrieval method. It is shown that commonly applied filtering techniques have weaknesses in distinguishing between "good" and "bad" estimates with the sensitivity needed for a turbulence retrieval. For that reason, new ways of noise filtering have been explored, taking into account that the DL background noise can differ from generally assumed white noise. It is shown that the introduction of a new coordinate frame for a graphical representation of DL radial velocities from conical scans offers a different perspective on the data when compared to the well-known velocity–azimuth display (VAD) and thus opens up new possibilities for data analysis and filtering. This new way of displaying DL radial velocities builds on the use of a phase-space perspective. Following the mathematical formalism used to explain a harmonic oscillator, the VAD's sinusoidal representation of the DL radial velocities is transformed into a circular arrangement. Using this kind of representation of DL measurements, bad estimates can be identified in two different ways: either in a direct way by singular point detection in subsets of radial velocity data grouped in circular rings or indirectly by localizing circular rings with mostly good radial velocity estimates by means of the autocorrelation function. The improved performance of the new filter techniques compared to conventional approaches is demonstrated through both a direct comparison of unfiltered with filtered datasets and a comparison of retrieved turbulence variables with independent measurements. [ABSTRACT FROM AUTHOR]

In the global challenge of Coronavirus disease 2019 (COVID-19) pandemic, accurate prediction of daily new cases is crucial for epidemic prevention and socioeconomic planning. In contrast to traditional local, one-dimensional time-series data-based infection models, the study introduces an innovative approach by formulating the shortterm prediction problem of new cases in a region as multidimensional, gridded time series for both input and prediction targets. A spatial-temporal depth prediction model for COVID-19 (ConvLSTM) is presented, and further ConvLSTM by integrating historical meteorological factors (Meteor-ConvLSTM) is refined, considering the influence of meteorological factors on the propagation of COVID-19. The correlation between 10 meteorological factors and the dynamic progression of COVID-19 was evaluated, employing spatial analysis techniques (spatial autocorrelation analysis, trend surface analysis, etc.) to describe the spatial and temporal characteristics of the epidemic. Leveraging the original ConvLSTM, an artificial neural network layer is introduced to learn how meteorological factors impact the infection spread, providing a 5-day forecast at a 0.01° × 0.01° pixel resolution. Simulation results using real dataset from the 3.15 outbreak in Shanghai demonstrate the efficacy of Meteor-ConvLSTM, with reduced RMSE of 0.110 and increased R2 of 0.125 (original ConvLSTM: RMSE = 0.702, R2 = 0.567; Meteor-ConvLSTM: RMSE = 0.592, R2 = 0.692), showcasing its utility for investigating the epidemiological characteristics, transmission dynamics, and epidemic development. [ABSTRACT FROM AUTHOR]

Identifying precursor information to rock failure is key to rock dynamic disaster warning. To solve the problem that a single in-situ monitoring method cannot accurately identify the precursors to rock failure, this paper combined a digital image correlation method, thermal infrared radiation and acoustic emission technology to conduct a multi-physical field joint monitoring experiment of granite under three-point bending. The information about strain, thermal infrared and acoustic emission of the rock brittle failure process could be obtained, and the variations in multi-physical field indices of the rock brittle failure process were analysed. Based on the theory of critical slowing-down, the study of the multi-physical field effects of critical slowing-down characteristics in the rock failure process, and further exploration of the precursor characteristics of the brittle failure of rock were undertaken. The results indicate that the strain, infrared, and acoustic emission parameters show sudden changes during brittle failure of granite. The lag step size has little effect on the variance of changes in multi-physical field parameters and exerts a similar influence on the changes in the autocorrelation coefficient curve. The degree of influence of the window length on the variance and autocorrelation coefficient curves of multi-physical field parameters is as follows: infrared field > strain field > acoustic emission field. Compared with the autocorrelation coefficient, the variance parameter is more universal and is better when the critical slowing-down theory is used to investigate the characteristics of multi-physical fields. The four parameters of the strain field variance, infrared field variance, the variance and autocorrelation coefficient for acoustic emission field increase sharply before fracture, representing precursor information to the brittle failure of granite. The four parameters can be used as disaster warning indicators in rock. Multi-mode joint monitoring and a comprehensive analysis of multi-physical information are beneficial to accurately determine the precursor points of rock failure disaster. [ABSTRACT FROM AUTHOR]

We enhanced the performance of linear prediction (LP) for bone-conducted (BC) speech signals by deriving a regularized version of the modified covariance (MC) method. The spectral estimation accuracy is discussed for the purpose of assessing the performance of LP. Inherently, BC speech has an expanded spectral dynamic range that causes ill-condition in conventional spectral estimation methods. To overcome this problem, we focus on the covariance method and its modified version, the MC method. In the field of numerical analysis, we often face the situation where an ill-conditioned case occurs in finding the solution. To deal with this situation, the regularized least squares method is utilized. Motivated by this idea, we derive the regularized MC (RMC) method in this study for BC speech analysis. The RMC method has the effect of compressing the spectral dynamic range of the input speech signal, and this effect mitigates the ill-conditioned problem of LP. Through experiments, we show that the RMC method provides a more accurate spectral estimation than conventional spectral estimation methods for BC speech where synthetic and real BC speeches are considered. The performance of the RMC method is affected by the setting of the regularization parameter. A way to determine the regularization parameter in practice is experimentally derived. The RMC method with such a setting provides the best performance of spectral estimation for BC speech. [ABSTRACT FROM AUTHOR]

In a quantum many-body system, autocorrelation functions can determine linear responses nearby equilibrium and quantum dynamics far from equilibrium. In this letter, we bring out the connection between the operator complexity and the autocorrelation function. In particular, we focus on a particular kind of operator complexity called the Krylov complexity. We find that a set of Lanczos coefficients { b n } computed for determining the Krylov complexity can reveal the universal behaviors of autocorrelations, which are otherwise impossible. When the time axis is scaled by b 1 , different autocorrelation functions obey a universal function form at short time. We further propose a characteristic parameter deduced from { b n } that can largely determine the behavior of autocorrelations at the intermediate time. This parameter can also largely determine whether the autocorrelation function oscillates or monotonically decays in time. We present numerical evidences and physical intuitions to support these universal hypotheses of autocorrelations. We emphasize that these universal behaviors are held across different operators and different physical systems. [ABSTRACT FROM AUTHOR]

This work derives a theoretical value for the entropy of a Linear Additive Markov Process (LAMP), an expressive but simple model able to generate sequences with a given autocorrelation structure. Our research establishes that the theoretical entropy rate of a LAMP model is equivalent to the theoretical entropy rate of the underlying first-order Markov Chain. The LAMP model captures complex relationships and long-range dependencies in data with similar expressibility to a higher-order Markov process. While a higher-order Markov process has a polynomial parameter space, a LAMP model is characterised only by a probability distribution and the transition matrix of an underlying first-order Markov Chain. This surprising result can be explained by the information balance between the additional structure imposed by the next state distribution of the LAMP model, and the additional randomness of each new transition. Understanding the entropy of the LAMP model provides a tool to model complex dependencies in data while retaining useful theoretical results. To emphasise the practical applications, we use the LAMP model to estimate the entropy rate of the LastFM, BrightKite, Wikispeedia and Reuters-21578 datasets. We compare estimates calculated using frequency probability estimates, a first-order Markov model and the LAMP model, also considering two approaches to ensure the transition matrix is irreducible. In most cases the LAMP entropy rates are lower than those of the alternatives, suggesting that LAMP model is better at accommodating structural dependencies in the processes, achieving a more accurate estimate of the true entropy. [ABSTRACT FROM AUTHOR]

Wetlands provide a wide range of ecosystem services; however, little is known about their perception value or use for improving urban planning and wetland management. This study explores the perception values towards the Los Batros Wetland in Chile, by inhabitants from different neighborhood typologies. A sample of 457 responses evaluated the wetland by applying the Kellert framework of 9 biophilic values using a Public Participation Geographic Information Systems (PPGIS) approach. A spatial autocorrelation analysis with hotspot revealed that the spatial distribution of biophilic values varies by neighborhood typology. Subsequent ANOVA and T-test suggest that such distribution is affected by perceived accessibility and visitation purposes, and is influenced by socio-demographic aspects that vary among neighborhood typology. Inhabitants of the garden city typology located next to the wetland area, whose residents have higher education and income levels and who have easy and moderate access to the wetland, agreed with a diverse type of biophilic values. In the garden city, the ecologistic-scientific value has the higher spatial concentration. In the condominium typology, with similar education and income levels and accessibility, but situated far from the wetland, there was less agreement with biophilic values, and these were more dispersed, i.e. biophilic values are less representative. In this case, the aesthetic value prevails over others. At the north area of the neighborhood unit, where residents had lower education and income levels along with moderate to difficult physical access to the wetland, but they developed horticultural activities alongside the wetland, inhabitants agree with various biophilic values, highlighting its symbolic value. Conversely, biophilic values of people in the favela were not in agreement nor disagreement, regardless they have similar physical access and distance to the wetland as residents in the condominium typology, but have the lowest income and education level. Findings suggest that effective wetlands management requires appreciation of the clusters of values assigned to wetland environments, which in this case relate to neighborhood typologies. These clusters should be considered when planning to restore, protect, and improve urban wetlands. [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]

The research of Art Getis has had many positive direct effects on the fields of regional science and spatial statistics. There already have been, and will continue to be, many indirect effects as well, as the repercussions of his work ripple through the field. With his contributions to spatial statistics, Art Getis laid out a rich research agenda for future work in the field. In this presentation, I describe several research problems inspired by his work. These include (a) the multiple testing problem, (b) the effects of global spatial autocorrelation on the power and use of local statistics, (c) the effects of weight misspecification on the power of local statistics, and (d) the statistical distribution of his local spatial heterogeneity (LOSH) statistic. In addition, there are a number of connections between the local statistics he developed and other statistics. These include the relationships between (a) the Getis-Ord statistic and the two-sample t statistic, (b) the Getis-Ord statistic and the maximum of Gaussian random fields, and (c) the LOSH statistic and the well-known Geary statistic. [ABSTRACT FROM AUTHOR]

Taxi fare is related to the daily life of residents. Reasonable taxi fare not only meets the travel demand of residents but also improves the income of drivers and promotes employment. The spatial variation of taxi fares exists between different regions and cities. Previous studies on taxi fares have been conducted mostly in individual cities, and there has been no study on the spatial differentiation pattern of taxi fares on a national scale. Taking 336 cities across China as the research object, a multiple linear regression model of taxi fares was established by demonstrating the spatial variation pattern of taxi fares, the global differentiation index, spatial autocorrelation analysis, and kernel density analysis, etc. The significance of the study is to explore the law of spatial differentiation of taxi fares in China and to provide a stenographic record of taxi fare adjustment. The results show that: (1) the spatial variation of taxi fares across the country is significant, with the starting taxi fare range being between RMB 4 and RMB 14. (2) The global differentiation index of taxi fares is large, with two low-low clusters and three high-high clusters appearing spatially, and the results of the kernel density analysis surface a dispersion distribution centered on provincial capitals. (3) The divergence pattern of taxis nationwide is influenced by several factors. A multiple linear regression model is selected to establish a multiple linear regression model of urban disposable income per capita, regional GDP, urbanization rate, and urban population density, which shows that urban disposable income per capita has the greatest influence on taxi fares. The model shows that urban disposable income per capita has the greatest influence on taxi fares, and the fare of a 5 km taxi ride is 6.07. Taxi fares have a clear pattern of spatial differentiation in China and are most affected by urban disposable income per capita. Through this study, we can gain a deeper understanding of the variation in taxi fares across the country and provide data and theoretical support for the rationality of taxi fare adjustments. [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]

Objective: This research aimed to investigate the relationship between gaze behaviour dynamics and operator performance. Background: Individuals differ in their approach when learning a new task often resulting in performance disparity. During training some individuals learn the structure and dynamics of the task and develop a systematic approach, whereas others may achieve the same result albeit with increased perceived workload, or indeed some may fail to achieve superior performance levels. Previous research has shown that comparing gaze of experts with novices can provide unique insights into cognitive functioning of superior performers. Methods: Twenty-five individuals participated in a computer-based simulation task. The concept of coefficient of variation (CoV) of task scores was used to compute the participants' consistency of performance. Based on CoV, the cohort was split into two performance categories. The temporal patterns in participants gaze data were transformed using autocorrelation, and recurrence quantification analysis (RQA) was employed to analyse and quantify the patterns. Results: A Mann–Whitney U analysis demonstrated significantly (p <.01) higher determinism, entropy and laminarity in the superior group compared to the moderate group. Pearson's correlation revealed a significant (p <.01) negative correlation between the consistency of task performance (CoV) and the RQA measures. Conclusion: The results demonstrated that eye gaze dynamics can be used as an objective measure of performance. Participants classified as superior performers consistently demonstrated a systematic gaze activity which were in line with the task structure. Application: The methods presented here are applicable to observe and evaluate operators' strategic distribution of gaze. Specifically, for tactical monitoring and decision making in task environments where spatial locations of elements-of-interest vary continuously. [ABSTRACT FROM AUTHOR]

In this article, we derive the asymptotic distributions of residual and normalized residual empirical autocovariances and autocorrelations of (parsimonious) periodic autoregressive moving‐average (PARMA) models under the assumption that the errors are uncorrelated but not necessarily independent. We then deduce the modified portmanteau statistics. We establish the asymptotic behavior of the proposed statistics. It is shown that the asymptotic distribution of the modified portmanteau tests is that of a weighted sum of independent chi‐squared random variables, which can be different from the usual chi‐squared approximation used under independent and identically distributed assumption on the noise. We also propose another test based on a self‐normalization approach to check the adequacy of PARMA models. A set of Monte Carlo experiments and an application to financial data are presented. [ABSTRACT FROM AUTHOR]

For decades, conventional wisdom maintained that binary 0–1 Bernoulli random variables cannot contain extra-binomial variation. Taking an unorthodox stance, Hilbe actively disagreed, especially for correlated observation instances, arguing that the universally adopted diagnostic Pearson or deviance dispersion statistics are insensitive to a variance anomaly in a binary context, and hence simply fail to detect it. However, having the intuition and insight to sense the existence of this departure from standard mathematical statistical theory, but being unable to effectively isolate it, he classified this particular over-/under-dispersion phenomenon as implicit. This paper explicitly exposes his hidden quantity by demonstrating that the variance in/deflation it represents occurs in an underlying predicted beta random variable whose real number values are rounded to their nearest integers to convert to a Bernoulli random variable, with this discretization masking any materialized extra-Bernoulli variation. In doing so, asymptotics linking the beta-binomial and Bernoulli distributions show another conventional wisdom misconception, namely a mislabeling substitution involving the quasi-Bernoulli random variable; this undeniably is not a quasi-likelihood situation. A public bell pepper disease dataset exhibiting conspicuous spatial autocorrelation furnishes empirical examples illustrating various features of this advocated proposition. [ABSTRACT FROM AUTHOR]

This paper looks at a novel type of seasonality labeled as a seasonal Generalized auto-regressive (GAR) model. The seasonal GAR models are found to be short-memory models, and expressions for the autocorrelation function and large sample results for the parameter estimates are established. Traditional Box-Jenkins seasonality models and Gegenbauer seasonality models are compared with the seasonal GAR model. Finally, the three methods are compared in the analysis of a specific process - the Mauna Loa CO2 data - showing that in this case, the seasonal GAR model provides forecasts with a lower mean squared error. [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]

This research suggests an efficient method that is better suited for speech processing applications to retrieve the accurate fundamental frequencies from speech in noisy conditions. For this objective, a fundamental frequency extraction algorithm that is tolerant to the non-stationary changes of the amplitude and frequency of the input signal is presented. Moreover, autocorrelation function is used as a pre-processor, which uses the power spectrum of the input signal to reduce the noise characteristics of the speech signals. In order to increase the accuracy of the fundamental frequency extraction, the focus has been on maintaining the speech harmonics in their original state and suppressing the noise elements involved in the noisy speech signal. The two stages that make up the suggested fundamental frequency extraction approach are producing the autocorrelation function of the speech signal as a pre-processor and applying it with the spectral subtraction method. As per the experiment results, the proposed technique appears to be better in noisy situations than other existing state-of-the-art methods. [ABSTRACT FROM AUTHOR]

Spatial proxies such as coordinates and Euclidean distance fields are often added as predictors in random forest models; however, their suitability in different predictive conditions has not yet been thoroughly assessed. We investigated 1) the conditions under which spatial proxies are suitable, 2) the reasons for such adequacy, and 3) how proxy suitability can be assessed using cross-validation. In a simulation and two case studies, we found that adding spatial proxies improved model performance when both residual spatial autocorrelation, and regularly or randomly-distributed training samples, were present. Otherwise, inclusion of proxies was neutral or counterproductive and resulted in feature extrapolation for clustered samples. Random k-fold cross-validation systematically favoured models with spatial proxies even when not appropriate. As the benefits of spatial proxies are not universal, we recommend using spatial exploratory and validation analyses to determine their suitability, and considering alternative inherently spatial RF-GLS models. [ABSTRACT FROM AUTHOR]

This paper deals with some probabilistic and statistical properties of a periodic generalized integer-valued autoregressive PINAR (1) model. The autocovariance structure is studied while establishing the closed-form of the periodic autocorrelation function. The Conditional Least Squares CLS-estimators of the underlying parameters are obtained. In addition, the asymptotic distribution of these estimators is provided, whether the innovation process mean is considered to be known or not, also for the nearly unstable and unstable integer-valued autoregressive PINAR(1) model. The performance of these estimators and their asymptotic distribution behavior are shown via a simulation study. [ABSTRACT FROM AUTHOR]

Statistical process monitoring, maintenance policy, and production have commonly been studied separately in the literature, whereas their integration can lead to more favorable conditions for the entire production system. Among all studies on integrated models, the underlying process is assumed to generate independent data. However, there are practical examples in which this assumption is violated because of the extraction of correlation patterns. Autocorrelation causes numerous false alarms when the process is in the in-control state or makes the traditional control charts react slowly to the detection of an out-of-control state. The auto-regressive moving average (ARMA) control chart is selected as an effective tool for monitoring autocorrelated data. Therefore, an integrated model subject to some constraints is proposed to determine the optimal decision variables of the ARMA control chart, economic production quantity, and maintenance policy in the presence of autocorrelated data. Due to the complexity of the model, a particle swarm optimization (PSO) algorithm is applied to search for optimal decision variables. An industrial example and some comparisons are provided for more investigations. Moreover, sensitivity analysis is carried out to study the effects of model parameters on the solution of the economic-statistical design. [ABSTRACT FROM AUTHOR]

It is crucial for the development of carbon reduction strategies to accurately examine the spatial distribution of carbon emissions. Limited by data availability and lack of industry segmentation, previous studies attempting to model spatial carbon emissions still suffer from significant uncertainty. Taking Pudong New Area as an example, with the help of multi-source data, this paper proposed a research framework for the amount calculation and spatial distribution simulation of its CO2 emissions at the scale of urban functional zones (UFZs). The methods used in this study were based on mapping relations among the locations of geographic entities and data of multiple sources, using the coefficient method recommended by the Intergovernmental Panel on Climate Change (IPCC) to calculate emissions. The results showed that the emission intensity of industrial zones and transport zones was much higher than that of other UFZs. In addition, Moran's I test indicated that there was a positive spatial autocorrelation in high emission zones, especially located in industrial zones. The spatial analysis of CO2 emissions at the UFZ scale deepened the consideration of spatial heterogeneity, which could contribute to the management of low carbon city and the optimal implementation of energy allocation. [ABSTRACT FROM AUTHOR]

Technology-driven population expansion is closely linked to land use change. Unregulated mining, urbanization, industrialization, and forest clearing threaten land use and cover. This study used GIS and statistical methods to examine land use and cover changes in eastern India's Asansol-Durgapur Development Authority (ADDA). The Kappa coefficient was used to validate each year's LULC map accuracy. This region is changing rapidly due to industrial and urban development, which might cause environmental issues. Thus, this area is ideal for a scientific land-use change study. The central hypothesis of this study is that the LULC of an industrial area is spatially heterogeneous and that the number of hotspots is gradually increasing in response to the dynamicity of land use change over time and space. Three years (1992, 2007, and 2022) were used to determine the estimated transition rate. Hotspots of land use change were identified using autocorrelation statistics for LULC clustering using Moron's I and Gi Z statistics. The proportion of land encompassed by natural vegetation experienced a decline from 12% in 1992 to 4% in 2022. Similarly, the extent of land occupied by agricultural activities decreased from 47 to 38% during the period spanning from 1992 to 2022. The industrial and coal mining sectors experienced a modest growth rate of 1% during the period spanning from 1992 to 2022. If the current rate of land use change persists, it will gradually and consistently alter the existing landscape. This study's findings can potentially inform strategies to mitigate the adverse impacts of industrialization and urbanization on the region's natural resources. [ABSTRACT FROM AUTHOR]

Atmospheric CO2 flux inversions require as input an estimate of spatial and temporal correlations of errors in their estimate of the prior mean. Some previous studies have used the differences in CO2 daily average flux estimates produced by terrestrial carbon cycle models and eddy covariance measurements to constrain the flux error correlations. Since inversions are starting to resolve the daily cycle, we set out to examine the correlations at sub‐daily time scales, as well as the correlations across years. To this end, we examine the autocorrelations in the difference between net ecosystem‐atmosphere exchange measurements from 75 AmeriFlux towers and temporally downscaled high‐spatial‐resolution flux estimates from the Carnegie‐Ames‐Stanford Approach (CASA) terrestrial carbon cycle model. We find that the daily cycle is prominent in these hourly autocorrelations and that these autocorrelations persist across years. We propose a family of functions to model these temporal correlations in atmospheric inversions, and use cross validation to determine which of the correlation functions best fits autocorrelation data from towers not in the training set. Correlation functions with a component that attempts to model the daily cycle in the differences match correlations from other towers better than those without. Those models that reproduce the same correlation structures at 1‐year intervals while modulating the amplitudes of the correlations between those intervals improve the fit still further. Plain Language Summary: Atmospheric CO2 flux inversions rely heavily on assumptions about errors in the initial flux estimate. If these errors are related in time or in space, inversions need to represent both the shape and the size of the likely errors. Previous studies have looked at the shape of the errors in daily average fluxes, but fewer have looked at the relationship between errors in one part of a day and in another part of that day, or between 1 year and the next. The study examines relationships in differences between measured and computer‐predicted ecosystem‐atmosphere carbon dioxide fluxes. There are strong relationships between flux errors separated by multiple years. Current attempts to solve for true ecosystem‐atmosphere fluxes using atmospheric data do not take these multi‐year relationships into consideration. Accounting for the multi‐year relationships may improve our ability to determine the true ecosystem‐atmosphere CO2 fluxes. We look for descriptions of these relationships that researchers can use when using atmospheric data to improve the computer‐predicted CO2 fluxes. Key Points: CO2 flux model‐data differences have autocorrelations that recur at intervals of a year with little decay over multiple yearsThese autocorrelations are largely caused by errors in the representation of the daily cycleWe can treat these persistent errors in the daily cycle either as prior flux error correlations or by corrections to the prior flux model [ABSTRACT FROM AUTHOR]

Aims: Calls to prescribe safer supply hydromorphone (SSHM) as an alternative to the toxic drug supply increased during the COVID-19 pandemic but it is unknown whether prescribing behaviour was altered. We aimed to evaluate how the number of new SSHM dispensations changed during the pandemic in Ontario. Methods: We conducted a retrospective interrupted time-series analysis using provincial administrative databases. We counted new SSHM dispensations in successive 28-day periods from March 22, 2016 to August 30, 2021. We used segmented Poisson regression methods to test for both a change in level and trend of new dispensations before and after March 17, 2020, the date Ontario's pandemic-related emergency was declared. We adjusted the models to account for seasonality and assessed for over-dispersion and residual autocorrelation. We used counterfactual analysis methods to estimate the number of new dispensations attributable to the pandemic. Results: We identified 1489 new SSHM dispensations during the study period (434 [mean of 8 per 28-day period] before and 1055 [mean of 56 per 28-day period] during the pandemic). Median age of individuals initiating SSHM was 40 (interquartile interval 33–48) with 61.7% (N = 919) male sex. Before the pandemic, there was a small trend of increased prescribing (incidence rate ratio [IRR] per period 1.002; 95% confidence interval [95CI] 1.001–1.002; p<0.001), with a change in level (immediate increase) at the pandemic date (relative increase in IRR 1.674; 95CI 1.206–2.322; p = 0.002). The trend during the pandemic was not statistically significant (relative increase in IRR 1.000; 95CI 1.000–1.001; p = 0.251). We estimated 511 (95CI 327–695) new dispensations would not have occurred without the pandemic. Conclusion: The pandemic led to an abrupt increase in SSHM prescribing in Ontario, although the rate of increase was similar before and during the pandemic. The absolute number of individuals who accessed SSHM remained low throughout the pandemic. [ABSTRACT FROM AUTHOR]