Autocorrelation Structure Research Articles

Urban Geography Compression Patterns: Non-Euclidean and Fractal Viewpoints

The intersection of fractals, non-Euclidean geometry, spatial autocorrelation, and urban structure offers valuable theoretical and practical application insights, which echoes the overarching goal of this paper. Its research question asks about connections between graph theory adjacency matrix eigenfunctions and certain non-Euclidean grid systems; its explorations reflect accompanying synergistic influences on modern urban design. A Minkowski metric with an exponent between one and two bridges Manhattan and Euclidean spaces, supplying an effective tool in these pursuits. This model coalesces with urban fractal dimensions, shedding light on network density and human activity compression. Unlike Euclidean geometry, which assumes unique shortest paths, Manhattan geometry better represents human movements that typically follow multiple equal-length network routes instead of unfettered straight-line paths. Applying these concepts to urban spatial models, like the Burgess concentric ring conceptualization, reinforces the need for fractal analyses in urban studies. Incorporating a fractal perspective into eigenvector methods, particularly those affiliated with spatial autocorrelation, provides a deeper understanding of urban structure and dynamics, enlightening scholars about city evolution and functions. This approach enhances geometric understanding of city layouts and human behavior, offering insights into urban planning, network density, and human activity flows. Blending theoretical and applied concepts renders a clearer picture of the complex patterns shaping urban spaces.

Deep Learning Unravels Differences Between Kinematic and Kinetic Gait Cycle Time Series from Two Control Samples of Healthy Children Assessed in Two Different Gait Laboratories.

We investigate the application of deep learning in comparing gait cycle time series from two groups of healthy children, each assessed in different gait laboratories. Both laboratories used similar gait analysis protocols with minimal differences in data collection. Utilizing a ResNet-based deep learning model, we successfully identified the source laboratory of each dataset, achieving a high classification accuracy across multiple gait parameters. To address the inter-laboratory differences, we explored various pre-processing methods and time series properties that may have been detected by the algorithm. We found that the standardization of the time series values was a successful approach to decrease the ability of the model to distinguish between the two centers. Our findings also reveal that differences in the power spectra and autocorrelation structures of the datasets play a significant role in the model performance. Our study emphasizes the importance of standardized protocols and robust data pre-processing to enhance the transferability of machine learning models across clinical settings, particularly for deep learning approaches.

Groundwater Responses to Deluge and Drought in the Fraser Valley, Pacific Northwest

AbstractGroundwater level variations represent signals of superimposed physical processes, with memory. Groundwater level records are used to understand how aquifer systems respond to natural and anthropogenic perturbations. Here we analyze groundwater levels across the South Coast of British Columbia (BC) in the Pacific Northwest with the objective of determining groundwater responses to atmospheric rivers (ARs) and drought. An AR catalog was derived and used to associate precipitation amounts to AR occurrence. Droughts were quantified using dry day metrics, in conjunction with the standardized precipitation index. Historically (1980–2023), from September to January, approximately 40% of total precipitation was contributed by ARs. From April to September, more than 50% of days received no precipitation, with typically 26 consecutive dry days. We used the autocorrelation structure of groundwater levels, commonly used to characterize aquifer memory, to identify two distinct clusters of observation well responses. Cluster 1 wells respond to recharge from local precipitation, primarily rainfall, and respond rapidly to both ARs during winter recharge and significant rainfall deficits during summer. Cluster 2 wells are driven by local precipitation but are influenced by the Fraser River's large summer freshet which briefly recharges the aquifers, thereby delaying drought propagation. The results suggest that groundwater memory encapsulates multiple hydrogeological factors, including boundary conditions, influencing the response outcome to extreme events.

A Bayesian Model for 20th Century Antarctic Sea Ice Extent Reconstruction

AbstractAntarctic sea ice, a key component in the complex Antarctic climate system, is an important driver and indicator of the global climate. In the relatively short satellite‐observed period from 1979 to 2022 the sea ice extent has continuously increased (contrasting a major decrease in Arctic sea ice) up to a dramatic decrease between 2014 and 2017. Recent years have seen record sea ice lows in February 2022–February 2023. We use a statistical ensemble reconstruction of Antarctic sea ice to put the observed changes into the historical context of the entire 20th century. We propose a seasonal Vector Auto‐Regressive Moving Average (VARMA) model fit in a Bayesian framework using regularized horseshoe priors on the regression coefficients to create a stochastic ensemble reconstruction of monthly Antarctic Sea ice extent from 1900 to 1979. This novel model produces a set of 2,500 plausible sea ice extent reconstructions for the sea ice by sector that incorporate the autocorrelation structure of sea ice over time as well as the dependence of sea ice between the sectors. These fully observed reconstructions exhibit plausible month‐to‐month changes in reconstructed sea ice as well as plausible interactions between the sectors and the total. We reconstruct an overall higher sea ice extent earlier in the 20th century with a relatively sharp decline in the 1970s. These trends agree well with previous reconstructions of Antarctic sea ice based on ice core data, whaling locations, and climatological data, as well as early satellite observations in the reconstruction period.

Random forest regression kriging modeling for soil organic carbon density estimation using multi-source environmental data in central Vietnamese forests

Forest soil organic carbon plays a vital role in the terrestrial carbon cycle. Accurately analyzing the spatial distribution of soil organic carbon density (SOCD) is therefore necessary for sustainable forest management and climate change mitigation. Previous studies explored the potential of random forest (RF) in modeling forest SOCD using various environmental data sources. However, how forest SOCD prediction would be affected by using random forest regression kriging (RFRK), which integrates the predictive power of RF in generating deterministic trends and the capability of the ordinary kriging (OK) in handling spatial autocorrelation structure of residuals, based on the environmental data sources and their combinations remains elusive and deserves further exploration. For this purpose, 104 soil samples were collected at a depth of 30 cm in forest ecosystems of Central Vietnam, and 33 environmental covariates were derived from Sentinel-2 (S2) imagery, Advanced Land Observing Satellite-2 Phased Array L-band Synthetic Aperture Radar-2 (AL2) imagery, digital elevation model (DEM), and climatic data. Using a leave-one-out cross-validation procedure to evaluate and compare the model performances, four metrics, including coefficient of determination (R2), mean absolute error (MAE), root mean square error (RMSE), and relative improvement (RI), were calculated. The results showed that enhanced RFRK performance for forest SOCD estimation was found with the inclusion of additional environmental data sources, with RFRK based on all data sources achieving a high accuracy (R2 = 0.78, MAE = 8.28 t·ha−1, and RMSE = 10.54 t·ha−1). The comparison of the RF and RFRK models exhibited that additionally interpolated residuals by OK were more accurate than only considering the influences of predictor covariates. The relative improvement of the RFRK models over the RF models in forest SOCD estimation was notable, with RIR2 ranging from 8.20 to 65.00%, RIMAE ranging from 8.18 to 21.07%, and RIRMSE ranging from 6.76 to 18.18%. The result from our case study emphasizes the robustness of RFRK using S2, AL2, DEM, and climatic data in accurately predicting forest SOCD.

Wavelet-based generation of fully non-stationary random processes with application to seismic ground motions

Assessing the performance of earthquake-resistant structural and geotechnical systems is crucial for achieving a desired reliability level and enhancing the resilience of the built environment in seismic-prone regions. Nonlinear dynamic analyses are widely used to quantify structural and geotechnical performance. Still, they require an accurate representation of nonlinear behaviours and proper modelling of the expected seismic events. Stochastic approaches are popular strategies for modelling dynamic actions to account for the uncertain nature of ground shaking. In this framework, joint time–frequency signal representations of seismic records are powerful tools to analyze signals’ time-varying amplitude and frequency content. This paper presents a new method for the stochastic generation of artificial accelerograms using the circular harmonic wavelet transform, which possesses joint time–frequency localization capabilities and offers the engineers a clear and transparent interpretation of the results. The proposed approach adopts a new exponential auto-correlation structure for generating the random phases in the “child (generated) signals” starting from the deterministic ones in the “parent record”. The effects of the correlation structure and different subdivisions of earthquake records in frequency bands are investigated and discussed, leading to practical considerations for identifying an effective trade-off between localization in time and frequency domains. The method can be used for seismic assessment and design purposes, and numerical applications illustrate its potency.

A Copula Discretization of Time Series-Type Model for Examining Climate Data

The study presents a comparative analysis of climate data under two scenarios: a Gaussian copula marginal regression model for count time series data and a copula-based bivariate count time series model. These models, built after comprehensive simulations, offer adaptable autocorrelation structures considering the daily average temperature and humidity data observed at a regional airport in Mobile, AL.

State space reconstruction of Markov chains via autocorrelation structure

Understanding the state space of observed Markov processes is essential for advancing causal inference in a wide range of scientific fields. This paper demonstrates how the previously unknown state space can be reconstructed by exploring the spectrum of the time-delay embedding matrix derived from the autocorrelation sequence of the observed series. It also highlights that the eigenvector associated with the smallest eigenvalue can provide valuable insights into the hidden data generation process itself. The presented results provide a deeper understanding of the complex dynamics of Markov chains and hold promise for enhancing various scientific applications.

Spatiotemporal smoothing of water quality in a complex riverine system with physical barriers

Freshwater ecosystems offer a variety of ecosystem services, and water quality is essential information for understanding their environment, biodiversity, and functioning. Interpolation by smoothing methods is a widely used approach to obtain temporal and/or spatial patterns of water quality from sampled data. However, when these methods are applied to freshwater systems, ignoring terrestrial areas that act as physical barriers may affect the structure of spatial autocorrelation and introduce bias into the estimates. In this study, we applied stochastic partial differential equation (SPDE) smoothing methods with barriers to spatial interpolation and spatiotemporal interpolation on water quality indices (chemical oxygen demand, phosphate phosphorus, and nitrite nitrogen) in a freshwater system in Japan. Then, we compared the estimation bias and accuracy with those of conventional non-barrier models. The results showed that the estimation bias of spatial interpolations of snapshot data was improved by considering physical barriers (5.8 % for (chemical oxygen demand, 22.5 % for phosphate phosphorus, and 21.6 % for nitrite nitrogen). The prediction accuracy was comparable to that of the non-barrier model. These were consistent with the expectation that accounting for physical barriers would capture realistic spatial correlations and reduce estimation bias, but would increase the variance of the estimates due to the limited information that can be gained from the neighbourhood. On the other hand, for spatiotemporal smoothing, the barrier model was comparable to the non-barrier model in terms of both estimation bias and prediction accuracy. This may be due to the availability of information in the time direction for interpolation. These results demonstrate the advantage of considering barriers when the available data are limited, such as snapshot data. SPDE smoothing methods can be widely applied to interpolation of various environmental and biological indices in river systems and are expected to be powerful tools for studying freshwater systems spatially and temporally.

A trinomial difference autoregressive process for the bounded ℤ‐valued time series

This article tackles the modeling challenge of bounded ‐valued time series by proposing a novel trinomial difference autoregressive process. This process not only maintains the autocorrelation structure presenting in the classical binomial GARCH model, but also facilitates the analysis of bounded ‐valued time series with negative or positive correlation. We verify the stationarity and ergodicity of the couple process (comprising both the observed process and its conditional mean process) while also presenting several stochastic properties. We further discuss the conditional maximum likelihood estimation and establish their asymptotic properties. The effectiveness of these estimators is assessed through simulation studies, followed by the application of the proposed models to two real datasets.

Recalibration of missing low-frequency variability and trends in the North Atlantic Oscillation

Multi-decadal trends in the wintertime North Atlantic Oscillation (NAO) are under-represented by coupled general circulation models (CGCMs), consistent with a lack of autocorrelation in their NAO index series. This study proposes and tests two simple “reddening” approaches for correcting this problem in simulated indices based on simple one parameter short-term (AR; Auto-Regressive order 1) and long-term (FD; Fractional-Difference) time series filters. Using CGCMs from the Coupled Model Intercomparison Project Phase 6 (CMIP6), the FD filter successfully improves the autocorrelation structure of the NAO, and in turn the simulation of extreme trends, while the AR filter is less successful. The 1963–1993 NAO trend is the maximum 31-year trend in the historical period. Raw CGCMs underestimate the likelihood of this trend by a factor of ten but this discrepancy is corrected after reddening. CMIP6 future projections show that long-term (2024–2094) NAO ensemble mean trends systematically increase with the magnitude of radiative forcing: -2.4 to 3.5 hPa/century for low-to-high forcing after reddening (more than double the range using raw output). The related likelihood of future maximum 31year trends comparable to 1963–1993 ranges from 3 to 7% whereas none of these CMIP6 projections simulate this without reddening. Near-term projections of the next 31 years (2024–2054) are less sensitive than long term trends to the future scenario, showing weak-to-no forced trend. However, reddening increases the ensemble range by 74% (to +/-1 standard deviation/decade), which could increase/decrease regional climate change signals in the Northern Hemisphere by magnitudes that are underestimated when using raw CGCM output.

An Efficient Way to Find Optimal Crossover Designs Using CVX for Precision Medicine

Crossover designs play an increasingly important role in precision medicine. We show the search of an optimal crossover design can be formulated as a convex optimization problem and convex optimization tools, such as CVX, can be directly used to search for an optimal crossover design. We first demonstrate how to transform crossover design problems into convex optimization problems and show CVX can effortlessly find optimal crossover designs that coincide with a few theoretical crossover optimal designs in the literature. The proposed approach is especially useful when it becomes problematic to construct optimal designs analytically for complicated models. We then apply CVX to find crossover designs for models with auto-correlated error structures or when the information matrices may be singular and analytical answers are unavailable. We also construct N-of-1 trials frequently used in precision medicine to estimate treatment effects on the individuals or to estimate average treatment effects, including finding dual-objective optimal crossover designs.

Temporal changes in spatial scale and autocorrelation structure of forest openings based on taxonomic, phylogenetic, and functional turnover

ContextDuring European settlement, Illinois grasslands were converted for agricultural purposes. Remaining natural areas in southern Illinois include natural xeric forest openings, with communities representative of remnant grasslands and adjacent hardwood forests. Previous research in these openings shows plant communities are driven by edaphic conditions. ObjectivesThe first objective aimed to characterize spatial scale and autocorrelation structure of these openings based on climatic, environmental, and diversity variables. The second objective was to predict taxonomic, phylogenetic, and functional turnover between 1988 and 2019, using climatic and environmental variables. MethodsSurveys were conducted to calculate taxonomic, phylogenetics and functional trait metrics and analyses of these dimensions of diversity. Randomization tests were used to assess phylogenetic and functional clustering and over-dispersion at each site. Spatially-explicit climatic and environmental variables were included from earlier surveys and data repositories. Global Moran's I and spatial autocorrelograms were used to assess spatial structure of climatic, environmental, and diversity variables and generalized dissimilarity modeling was used to characterize taxonomic, phylogenetic, and functional turnover based on environmental variables. ResultsSoil depth was the only environmental variable which exhibited significant global spatial autocorrelation. Overall, sandstone sites were phylogenetically over-dispersed while loess sites were phylogenetically clustered. Climate variables and diversity metrics exhibited significant spatial structure during surveys. Generalized dissimilarity models showed that geographic distance between openings was the most influential driver of turnover across surveys. ConclusionsPrevious glacial events explained the spatial structure of soil depth across sites, due to Quaternary loess deposition in loess sites. High diversity values were clustered in the southeastern portions of the study area. Functional generalized dissimilarity models best predicted turnover in these openings compared to taxonomic and phylogenetic models.

The entropy rate of Linear Additive Markov Processes.

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.

Statistical downscaling of GCMs wind speed data for trend analysis of future scenarios: a case study in the Lombardy region

Near-surface wind speed is a key climatic variable, affecting many sectors, such as energy production, air pollution, and natural hazard. Lombardy region of Italy is among the European areas with lowest average wind speed, leading generally to low air quality and wind energy potential. However, it is also one of the most affected area by tornadoes in Italy. Here we investigate possible changes in wind circulation as due to prospective global warming. We analysed wind speed WS under future scenarios (SSP1-2.6 and SSP5-8.5) from six Global Climate Models (GCMs) until 2100, tuned against observed WS data. We employed a statistical downscaling method, namely Stochastic Time Random Cascade (STRC) to correct locally GCMs outputs. Three statistical tests, i.e. Linear Regression, Mann Kendall, Moving Window Average, were carried out to analyse future trends of: annual WS averages, 95th quantile (as an indicator of large WS), and the number of days of calm wind per year (NWC). The proposed STRC algorithm can successfully adjust the mean, standard deviation, and autocorrelation structure of the GCM outputs. No strong trends are found for the future. The chosen variables would all display non-stationarity, and the 95th percentile display a positive trend for most of the stations. Concerning NWC, notable discrepancies among GCMs are seen. The STRC algorithm can be used to successfully adjust GCMs outputs to reflect locally observed data and to then generate credible long-term scenarios for WSs as a tool for decision-making.

Marshall-Olkin Bilal distribution with associated minification process and acceptance sampling plans

In this paper, a new two parameters lifetime distribution, called Marshall-Olkin Bilal distribution is introduced and the structural properties are discussed. The proposed model results from the Marshall and Olkin class of distributions with the baseline model as Bilal distribution. We examined the statistical aspects like moments, quantile function, order statistics and entropy. The hazard function can model increasing and upside-down bathtub shaped data sets. The model parameter estimation is carried out by maximum likelihood estimation and a simulation study is performed. The flexibility of the proposed model is evaluated by two real data sets, compared with the competing models. Its application in time series is studied by the associated autoregressive minification process and the auto-correlation structure is derived. The acceptance sampling plans formulated for the proposed model and the characteristic results are illustrated.

Testing unit root non-stationarity in the presence of missing data in univariate time series of mobile health studies.

The use of digital devices to collect data in mobile health studies introduces a novel application of time series methods, with the constraint of potential data missing at random or missing not at random (MNAR). In time-series analysis, testing for stationarity is an important preliminary step to inform appropriate subsequent analyses. The Dickey-Fuller test evaluates the null hypothesis of unit root non-stationarity, under no missing data. Beyond recommendations under data missing completely at random for complete case analysis or last observation carry forward imputation, researchers have not extended unit root non-stationarity testing to more complex missing data mechanisms. Multiple imputation with chained equations, Kalman smoothing imputation, and linear interpolation have also been used for time-series data, however such methods impose constraints on the autocorrelation structure and impact unit root testing. We propose maximum likelihood estimation and multiple imputation using state space model approaches to adapt the augmented Dickey-Fuller test to a context with missing data. We further develop sensitivity analyses to examine the impact of MNAR data. We evaluate the performance of existing and proposed methods across missing mechanisms in extensive simulations and in their application to a multi-year smartphone study of bipolar patients.

Simple Moving Average Applied to "ISO Method" CPAM Concentration Estimates: An Unexpected Result.

A surprisingly large amount of variance reduction has been observed when filtering International Organization for Standardization (ISO) "ISO Method" continuous particulate air monitor (CPAM) airborne radioactivity concentration estimates with a simple three-point moving average. This processing has relatively little lag relative to the amount of variance reduction obtained. The key factor producing this effect is the specific autocorrelation structure of the estimated concentrations, which are based on taking first differences of integrated-count data; this scheme results in successive count differences that contain a common count value between them. The observed variance reduction factor has also been derived analytically.

Operator dynamics in Lindbladian SYK: a Krylov complexity perspective

We use Krylov complexity to study operator growth in the q-body dissipative Sachdev-Ye-Kitaev (SYK) model, where the dissipation is modeled by linear and random p-body Lindblad operators. In the large q limit, we analytically establish the linear growth of two sets of coefficients for any generic jump operators. We numerically verify this by implementing the bi-Lanczos algorithm, which transforms the Lindbladian into a pure tridiagonal form. We find that the Krylov complexity saturates inversely with the dissipation strength, while the dissipative timescale grows logarithmically. This is akin to the behavior of other \U0001d52e-complexity measures, namely out-of-time-order correlator (OTOC) and operator size, which we also demonstrate. We connect these observations to continuous quantum measurement processes. We further investigate the pole structure of a generic auto-correlation and the high-frequency behavior of the spectral function in the presence of dissipation, thereby revealing a general principle for operator growth in dissipative quantum chaotic systems.

Persistence of return distribution sequence in financial markets

The analysis of return distribution is an important topic in risk management and investment practice. This study analyzes time-varying distribution sequences and characterizes persistence with topological correlation coefficients (TCC), where the distribution consists of cross-sectional returns. We used some models to show that TCC can effectively analyze persistence, and found that both the autocorrelation structure and volatility clustering of time series can lead to the persistence of the distribution sequence. We analyzed the persistence of the return distribution sequences in the Chinese market and the US market. The calculation shows that some sequences have significant persistence. In addition, we analyzed factors that affect the persistence, where model-based analysis provides a baseline for comparison. The analysis shows that neither autocorrelation structure nor volatility clustering can fully explain persistence, so the generation mechanism of persistence is complex. In particular, dynamic analysis shows that persistence is time-varying and that there are significant differences between the two markets. This study provides a way to study distribution sequences, which can help analyze the predictability of distributions.