Dynamic Covariance Research Articles

An Islamic Inter‐Temporal Capital Asset Pricing Model: Evidence From GCC Indexes

ABSTRACTOur study examines the multi‐period Islamic investment issue in GCC markets. We assess the validity of ICAPM by incorporating market dynamics: volatility and uncertainty. To test the predictive power of these factors over time, we employ Engle's (2002) dynamic conditional correlation framework and compute the DCC between Islamic stock index returns and three key variables: the GCC Islamic index (market index) and market state variables (volatility and uncertainty). For cross‐sectional variation, we follow Bali and Engle (2010) and estimate the seemingly unrelated regression (SUR) after measuring dynamic covariance. We report heterogeneous results revealing a complex relationship between market risk factors and expected returns. While the introduction of market volatility and uncertainty factors generally resulted in a negative risk premium, the specific impact varied across different markets. Interestingly, the Saudi index, holding significant weight within the GCC index, shows a negative risk premium and a positive uncertainty premium in the short‐term. Accordingly, investors seek a premium for uncertainty and accept a discount for volatility in the Saudi market. However, in the long term, a traditional positive risk–return relationship is observed. The cross‐sectional results reveal that both GCC index fluctuations and shifts in market volatility are associated with a negative risk premium, in the short term. Whereas, an increasing market uncertainty leads to a higher expected return in the following month. This study adds novelty to the literature related to the pricing of Shari'ah‐compliant assets by testing the inter‐temporal CAPM for these assets and showing the usefulness for investors. Indeed, the implementation of a multi‐period investment plan across Islamic GCC indexes can help investors mitigate adverse changes in market volatility and uncertainty.

State-space modelling for infectious disease surveillance data: Dynamic regression and covariance analysis

State-space modelling for infectious disease surveillance data: Dynamic regression and covariance analysis

The genetics of spatiotemporal variation in cortical thickness in youth

Prior studies have shown strong genetic effects on cortical thickness (CT), structural covariance, and neurodevelopmental trajectories in childhood and adolescence. However, the importance of genetic factors on the induction of spatiotemporal variation during neurodevelopment remains poorly understood. Here, we explore the genetics of maturational coupling by examining 308 MRI-derived regional CT measures in a longitudinal sample of 677 twins and family members. We find dynamic inter-regional genetic covariation in youth, with the emergence of regional subnetworks in late childhood and early adolescence. Three critical neurodevelopmental epochs in genetically-mediated maturational coupling were identified, with dramatic network strengthening near eleven years of age. These changes are associated with statistically-significant (empirical p-value <0.0001) increases in network strength as measured by average clustering coefficient and assortativity. We then identify genes from the Allen Human Brain Atlas with similar co-expression patterns to genetically-mediated structural covariation in children. This set was enriched for genes involved in potassium transport and dendrite formation. Genetically-mediated CT-CT covariance was also strongly correlated with expression patterns for genes located in cells of neuronal origin.

Global Probabilistic Forecasting for Multiple Tight Gas Wells Using Deep Autoregressive Networks

Summary Traditional methods for forecasting production rate, such as Arps, analytical techniques, and recurrent neural network (RNN)–based deep learning, are mainly point prediction techniques developed within the framework of single-well forecasting. These methods often face limitations stemming from single-well historical production data and model assumptions, hindering their ability to consider the influence of development patterns of other production wells within the block on the target well. In addition, they struggle to predict the multiple production rate time series simultaneously and often fail to quantify uncertainty in predictions or adequately exploit extensive relevant historical production data. To tackle these challenges, we propose a model based on the deep autoregressive recurrent neural network (DeepAR), leveraging related multiwell production rate data to enable global modeling and probabilistic forecasting. This model incorporates dynamic covariate and static categorical variable data, integrating Bayesian inference and using gradient descent algorithms and maximum likelihood estimation methods to derive a comprehensive historical-future production probability evolution pattern shared across multiple wells. Leveraging data from 943 tight gas wells, a comprehensive evaluation of the DeepAR model’s performance was undertaken, encompassing the comparison of prediction accuracy with long short-term memory (LSTM), classification prediction, cold-start prediction, and single-well multitarget prediction scenarios, summarizing the applicability conditions for each. The research findings highlight that DeepAR integrates the acquired comprehensive production probability evolution pattern with specific production historical data of the target well to formulate a “comprehensive + specific” production probability prediction approach, resulting in improved stability and accuracy. On average, DeepAR demonstrates a 58.79% reduction in normalized deviation (ND) compared to the LSTM model, showcasing enhanced stability, particularly in scenarios involving frequent well shut-ins and openings. Moreover, DeepAR can learn static categorical features, with the classification model resulting in a 27.15% reduction in the ND compared to the unclassified model. Furthermore, DeepAR adeptly addresses the challenge of limited data availability, achieving cold-start prediction and facilitating multitarget single-well training and prediction while considering the interdependency among multiple variables over time and effectively mitigating the issue of missing auxiliary variables during the prediction phase. This study contributes to a broader understanding of production forecasting and analysis of production dynamics methods from a big data perspective.

Migratory birds modulate niche tradeoffs in rhythm with seasons and life history

Movement is a key means by which animals cope with variable environments. As they move, animals construct individual niches composed of the environmental conditions they experience. Niche axes may vary over time and covary with one another as animals make tradeoffs between competing needs. Seasonal migration is expected to produce substantial niche variation as animals move to keep pace with major life history phases and fluctuations in environmental conditions. Here, we apply a time-ordered principal component analysis to examine dynamic niche variance and covariance across the annual cycle for four species of migratory crane: common crane (Grus grus, n = 20), demoiselle crane (Anthropoides virgo, n = 66), black-necked crane (Grus nigricollis, n = 9), and white-naped crane (Grus vipio, n = 9). We consider four key niche components known to be important to aspects of crane natural history: enhanced vegetation index (resources availability), temperature (thermoregulation), crop proportion (preferred foraging habitat), and proximity to water (predator avoidance). All species showed a primary seasonal niche "rhythm" that dominated variance in niche components across the annual cycle. Secondary rhythms were linked to major species-specific life history phases (migration, breeding, and nonbreeding) as well as seasonal environmental patterns. Furthermore, we found that cranes' experiences of the environment emerge from time-dynamic tradeoffs among niche components. We suggest that our approach to estimating the environmental niche as a multidimensional and time-dynamical system of tradeoffs improves mechanistic understanding of organism-environment interactions.

Generalized Propensity Score Methods to Assess CKD-Associated Physiologic Factors and Risk of Kidney Failure in the Chronic Renal Insufficiency Cohort (CRIC) Study.

Epidemiologic studies have identified many biochemical risk factors for chronic kidney disease (CKD) progression that are correlates of kidney function, termed here 'CKD-associated physiologic factors'. Uncertainty remains if these factors are risk factors or risk markers accounting for aspects of kidney function not otherwise captured. We aimed to use flexible machine learning, a dynamic covariate history including kidney function informative markers, and generalized propensity score (GPS) weighting, to better control confounding for such exposures. We studied 3,052 adults with CKD in the Chronic Renal Insufficiency Cohort Study. We established a 2-year run-in period and assembled 90 variables that characterize variability and trends of selected CKD-associated physiologic factors and confounders. Using SuperLearner, we created a GPS for each CKD-associated physiologic factor and performed GPS-weighted Cox regressions. For context, we also evaluated results from traditional multivariable Cox proportional hazards models as in prior studies. Similar to traditional approaches, bicarbonate, calcium, potassium, hemoglobin, and PTH were each associated with risk of kidney failure using GPS weighting. The GPS approach detected non-linear associations in many factors, some of which were not detected with traditional models. We conclude that many associations between CKD-associated physiologic factors and kidney outcomes remain strong after GPS weighting.

Robust Inference of Dynamic Covariance Using Wishart Processes and Sequential Monte Carlo.

Several disciplines, such as econometrics, neuroscience, and computational psychology, study the dynamic interactions between variables over time. A Bayesian nonparametric model known as the Wishart process has been shown to be effective in this situation, but its inference remains highly challenging. In this work, we introduce a Sequential Monte Carlo (SMC) sampler for the Wishart process, and show how it compares to conventional inference approaches, namely MCMC and variational inference. Using simulations, we show that SMC sampling results in the most robust estimates and out-of-sample predictions of dynamic covariance. SMC especially outperforms the alternative approaches when using composite covariance functions with correlated parameters. We further demonstrate the practical applicability of our proposed approach on a dataset of clinical depression (n=1), and show how using an accurate representation of the posterior distribution can be used to test for dynamics in covariance.

Covariance matrix filtering and portfolio optimisation: the average oracle vs non-linear shrinkage and all the variants of DCC-NLS

The Average Oracle, a simple and very fast covariance filtering method, is shown to yield superior Sharpe ratios than the current state-of-the-art (and complex) methods, Dynamic Conditional Covariance coupled to Non-Linear Shrinkage (DCC-NLS). We pit all the known variants of DCC-NLS (quadratic shrinkage, gross-leverage or turnover limitations, and factor-augmented NLS) against the Average Oracle in large-scale randomized experiments. We find generically that while some variants of DCC-NLS sometimes yield the lowest average realized volatility, albeit with a small improvement, their excessive gross leverage and investment concentration, and their 10-time larger turnover contribute to smaller average portfolio returns, which mechanically result in smaller realized Sharpe ratios than the Average Oracle. We also provide simple analytical arguments about the origin of the advantage of the Average Oracle over NLS in a changing world.

A nature‐inclusive future with healthy soils? Mapping soil organic matter in 2050 in the Netherlands

AbstractNature‐inclusive scenarios of the future can help address numerous societal challenges related to soil health. As nature‐inclusive scenarios imply sustainable management of natural systems and resources, land use and soil health are assumed to be mutually beneficial in such scenarios. However, the interplay between nature‐inclusive land use scenarios and soil health has never been modelled using digital soil mapping. We predicted soil organic matter (SOM), an important indicator of soil health, in 2050, based on a recently developed nature‐inclusive scenario and machine learning in 3D space and time in the Netherlands. By deriving dynamic covariates related to land use and the occurrence of peat for 2050, we predicted SOM and its uncertainty in 2050 and assessed SOM changes between 2022 and 2050 from 0 to 2 m depth at 25 m resolution. We found little changes in the majority of mineral soils. However, SOM decreases of up to 5% were predicted in grasslands used for animal‐based production systems in 2022, which transitioned into croplands for plant‐based production systems by 2050. Although increases up to 25% SOM were predicted between 0 and 40 cm depth in rewetted peatlands, even larger decreases, on reclaimed land even surpassing 25% SOM, were predicted on non‐rewetted land in peat layers below 40 cm depth. There were several limitations to our approach, mostly due to predicting future trends based on historic data. Furthermore, nuanced nature‐inclusive practices, such as the adoption of agroecological farming methods, were too complex to incorporate in the model and would likely affect SOM spatial variability. Nonetheless, 3D‐mapping of SOM in 2050 created new insights and raised important questions related to soil health behind nature‐inclusive scenarios. Using machine learning explicit in 3D space and time to predict the impact of future scenarios on soil health is a useful tool for facilitating societal discussion, aiding policy making and promoting transformative change.

Time-varying functional connectivity as Wishart processes

Abstract We investigate the utility of Wishart processes (WPs) for estimating time-varying functional connectivity (TVFC), which is a measure of changes in functional coupling as the correlation between brain region activity in functional magnetic resonance imaging (fMRI). The WP is a stochastic process on covariance matrices that can model dynamic covariances between time series, which makes it a natural fit to this task. Recent advances in scalable approximate inference techniques and the availability of robust open-source libraries have rendered the WP practically viable for fMRI applications. We introduce a comprehensive benchmarking framework to assess WP performance compared with a selection of established TVFC estimation methods. The framework comprises simulations with specified ground-truth covariance structures, a subject phenotype prediction task, a test-retest study, a brain state analysis, an external stimulus prediction task, and a novel data-driven imputation benchmark. The WP performed competitively across all the benchmarks. It outperformed a sliding window (SW) approach with adaptive cross-validated window lengths and a dynamic conditional correlation (DCC)-multivariate generalized autoregressive conditional heteroskedasticity (MGARCH) baseline on the external stimulus prediction task, while being less prone to false positives in the TVFC null models.

Modelling Diameter at Breast Height Distribution for Eight Commercial Species in Natural-Origin Mixed Forests of Ontario, Canada

Diameter at breast height (DBH) is a unique attribute used to characterize forest growth and development for forest management planning and to understand forest ecology. Forest managers require an array of DBHs of forest stands, which can be reconstructed using selected probability distribution functions (PDFs). However, there is a lack of practices that fit PDFs of sub-dominating species grown in natural mixed forests. This study aimed to fit PDFs and develop predictive models for PDF parameters, so that the predicted distribution would represent dynamic forest structures and compositions in mixed forest stands. We fitted three of the simplest forms of PDFs, log-normal, gamma, and Weibull, for the DBH of eight tree species, namely balsam fir (Abies balsamea [L.] Mill.), eastern white pine (Pinus strobus L.), paper birch (Betula papyrifera Marshall), red maple (Acer rubrum L.), red pine (Pinus resinosa Aiton), trembling aspen (Populus tremuloides Michx), and white spruce (Picea glauca [Moench] Voss), all grown in natural-origin mixed forests in Ontario province, Canada. We estimated the parameters of the PDFs as a function of DBH mean and standard deviation for these species. Our results showed that log-normal fit the best among the three PDFs. We demonstrated that the predictive model could estimate the recovered parameters unbiasedly for all species, which can be used to reconstruct the DBH distributions of these tree species. In addition to prediction, the cross-validated R2 for the DBH mean ranged between 0.76 for red maple and 0.92 for red pine. However, the R2 for the regression of the standard deviation ranged between 0.00 for red pine and 0.69 for sugar maple, although it produced unbiased predictions and a small mean absolute bias. As these mean and standard deviations are regressed with dynamic covariates (such as stem density and stand basal area), in addition to climate and static geographic variables, the predicted DBH distribution can reflect change over time in response to management or any type of disturbance in the regime of the given geography. The predictive model-based DBH distributions can be applied to the design of appropriate silviculture systems for forest management planning.

Space-time modeling of landslide size by combining static, dynamic, and unobserved spatiotemporal factors

Landslide spatial prediction using data-driven models has predominantly concentrated on predicting where landslides may occur. Nevertheless, few researchers have turned to jointly modeling how large and when landslides will be for a given terrain unit. This study proposes a data-driven model capable of estimating how large landslides may be, for the entire Taiwan main island in a fourteen-year time window. To address this task, we implement a space–time generalized additive model to fit the complex relationships between environmental factors and landslide size. In addition to incorporating static and dynamic covariates into the modeling process, the model takes into account spatial and temporal interactions to elucidate the spatiotemporal variations affecting landslide size. To test the effectiveness of the model, we employ a comprehensive set of cross-validation (CV) procedures, includes a randomized 10fold-CV, a spatially constrained CV, a temporal leave-one-year-out CV, and a spatio-temporal CV. The experimental results demonstrate that the space–time model delivers acceptable and interpretable prediction outcomes, demonstrating the ability to predict landslide area for a given slope unit within a specified time period. We believe that the space–time landslide modeling will lay the foundation for landslide community to analyze landslide characteristic within a dynamic context. Furthermore, given its inherent spatio-temporal nature, we anticipate that this approach may pave the way for simulation studies exploring diverse climate scenarios.

Space-time mapping of soil organic carbon stock and its local drivers: Potential for use in carbon accounting

The measurement and tracking of changes in soil organic carbon (SOC) stocks and its underpinning drivers are important in greenhouse gas accounting and carbon trading schemes. While repeated direct measurement of a location over time is the ‘gold standard’ for SOC stock change estimation, this is currently unfeasible at scale due to sample collection and analysis costs. Here, we used a data-driven, space–time digital soil mapping modelling approach (ST-DSM) coupled with an interpretive machine learning (IML) technique to both predict and quantify the relative contributions of covariates to annual SOC stocks and their uncertainty at 0–30 cm depth and at a 90 m spatial resolution for Australia between 1990 and 2018. A quantile regression forest model was calibrated using data from a datacube comprising of SOC stock values collected over the prediction years and a suite of dynamic and static environmental covariates. The evaluation of the ST-DSM model on a test set was satisfactory. Long-term annual mean (Mg C/ha), and total (Pg C) topsoil SOC stock were 37.6 (12.3 – 101.1, 90 % PI) and 28.3 (9.25 – 83.1, 90 % PI) respectively. The mean annual rate of SOC stock change over the Australian continent was 0.11 (±0.22) Mg C/ha yr−1 and the total net change was 23.5 Tg C yr−1, indicating Australia’s soils were a net sink of SOC over the 29-year period. However, SOC stocks declined in the montane ecoregion, a great concern given its fragility and high SOC stock. The long-term mean fraction of photosynthetic vegetation was the most important individual local contributor to SOC stock prediction in many parts of Australia. The aggregated effect of covariates based on the soil forming factors indicates vegetation as the principal local driver of SOC stock across most of the Australian continent, followed by climate. The evaluation of our results against independent, temporally paired field data and estimates from a nationally accepted SOC process-based model yielded promising results. Our approach demonstrates the use of readily available and inexpensive covariates to estimate SOC stock changes, as well as the underlying drivers over a larger area but at a spatial resolution suitable for decision making. This approach presents a new monitoring and verification possibility for carbon projects and national carbon accounting especially with the growing number of existing profile observations in soil databases.

Dynamic Convolution Covariance Network Using Multi-Scale Feature Fusion for Remote Sensing Scene Image Classification

Dynamic Convolution Covariance Network Using Multi-Scale Feature Fusion for Remote Sensing Scene Image Classification

Complex augmented representation network for transferable health prognosis of rolling bearing considering dynamic covariate shift

Complex augmented representation network for transferable health prognosis of rolling bearing considering dynamic covariate shift

Modelling diameter at breast height distribution of jack pine and black spruce natural stands in eastern Canada

Individual tree diameter at breast height (DBH) distribution is an important information for forest management planning. Forest managers obtain the DBH data either by field measurements or estimations using predictive models. However, probability distribution models are still lacking or need improvement. Therefore, we aimed to construct and fit diameter distribution models that reflect forest structure and composition change. We evaluated gamma, log-normal, and Weibull probability distribution functions (PDFs) for two commercially important tree species, black spruce ( Picea mariana (Mill) B.S.P.) and jack pine ( Pinus banksiana Lamb), grown in natural stands across Ontario, Canada. We modelled the parameters of the distributions as a function of stand-level variables for these species. We used DBH data from 735 permanent sample plots. Our results showed that all three evaluated PDFs reflected observed DBH distribution. We demonstrated that the moment-based recovered parameters could represent the maximum likelihood-estimated parameters precisely, and parameters of the PDFs can be modelled as a function of stand-level dynamic covariates. The models unbiasedly predicted the PDF parameters DBH means and DBH classes. The R2 of the model fit ranged between 0.35 and 0.98 for the predicted parameters and 0.90 and 0.97 for the predicted DBH.

Dynamic rainfall-induced landslide susceptibility: A step towards a unified forecasting system

The initial inception of the landslide susceptibility concept defined it as a static property of the landscape, explaining the proneness of certain locations to generate slope failures. Since the spread of data-driven probabilistic solutions though, the original susceptibility definition has been challenged to incorporate dynamic elements that would lead the occurrence probability to change both in space and in time. This is the starting point of this work, which combines the traditional strengths of the susceptibility framework together with the strengths typical of landslide early warning systems. Specifically, we model landslide occurrences in the norther sector of Vietnam, using a multi-temporal landslide inventory recently released by NASA. A set of static (terrain) and dynamic (cumulated rainfall) covariates are selected to explain the landslide presence/absence distribution via a Bayesian version of a binomial Generalized Additive Models (GAM). Thanks to the large spatiotemporal domain under consideration, we include a large suite of cross-validation routines, testing the landslide prediction through random sampling, as well as through stratified spatial and temporal sampling. We even extend the model test towards regions far away from the study site, to be used as external validation datasets. The overall performance appears to be quite high, with Area Under the Curve (AUC) values in the range of excellent model results, and very few localized exceptions.This model structure may serve as the basis for a new generation of early warning systems. However, the use of The Climate Hazards group Infrared Precipitation with Stations (CHIRPS) for the rainfall component limits the model ability in terms of future prediction. Therefore, we envision subsequent development to take this direction and move towards a unified dynamic landslide forecast. Ultimately, as a proof-of-concept, we have also implemented a potential early warning system in Google Earth Engine.

Optimizing portfolios for the BREXIT: An equity-commodity analysis of US, European and BRICS markets

The objective of this study is to create optimal two-asset portfolios consisting of stocks from Western Europe, the United States, and the BRICS (Brazil, China, India, Russia, and South Africa), as well as sixteen commodity types during the BREXIT period. We utilized dynamic variances and covariances from the GARCH model to derive weights for the two-asset portfolios, with each portfolio consisting of one equity factor and one commodity factor. Subsequently, hedge ratios were calculated for these various assets. Our findings indicate that portfolios consisting of European stocks do not require the inclusion of commodities, whereas the other equities do.

Robust Sales forecasting Using Deep Learning with Static and Dynamic Covariates

Retailers must have accurate sales forecasts to efficiently and effectively operate their businesses and remain competitive in the marketplace. Global forecasting models like RNNs can be a powerful tool for forecasting in retail settings, where multiple time series are often interrelated and influenced by a variety of external factors. By including covariates in a forecasting model, we can often better capture the various factors that can influence sales in a retail setting. This can help improve the accuracy of our forecasts and enable better decision making for inventory management, purchasing, and other operational decisions. In this study, we investigate how the accuracy of global forecasting models is affected by the inclusion of different potential demand covariates. To ensure the significance of the study’s findings, we used the M5 forecasting competition’s openly accessible and well-established dataset. The results obtained from DeepAR models trained on different combinations of features indicate that the inclusion of time-, event-, and ID-related features consistently enhances the forecast accuracy. The optimal performance is attained when all these covariates are employed together, leading to a 1.8% improvement in RMSSE and a 6.5% improvement in MASE compared to the baseline model without features. It is noteworthy that all DeepAR models, both with and without covariates, exhibit a significantly superior forecasting performance in comparison to the seasonal naïve benchmark.

Dynamical BLUP modeling of reaction norm evolution, accommodating changing environments, overlapping generations, and multivariate data

AbstractFor theoretical studies, reaction norm evolution in a changing environment can be modeled by means of the multivariate breeder's equation, with the reaction norm parameters treated as traits in their own right. This is, however, not a feasible approach for the use of field data, where the intercept and slope values are not available. An alternative approach is to use infinite‐dimensional characters and smooth covariance function estimates found by, e.g., random regression. This is difficult because of the need to find, for example, polynomial basis functions that fit the data reasonably well over time, and because reaction norms in multivariate cases are correlated, such that they cannot be modeled independently. Here, I present an alternative approach based on a multivariate linear mixed model of any order, with dynamical incidence and residual covariance matrices that reflect the changing environment. From such a mixed model follows a dynamical BLUP model for the estimation of the individual reaction norm parameter values at any given parent generation, and for updating of the mean reaction norm parameter values from generation to generation by means of Robertson's secondary theorem of natural selection. This will, for example, make it possible to disentangle the microevolutionary and plasticity components in climate change responses. The BLUP model incorporates the additive genetic relationship matrix in the usual way, and overlapping generations can easily be accommodated. Additive genetic and environmental model parameters are assumed to be known and constant, but it is discussed how they can be estimated by means of a prediction error method. The identifiability by the use of field or laboratory data containing environmental, phenotypic, fitness, and additive genetic relationship data is an important feature of the proposed model.