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We consider local polynomial estimation for varying coefficient models and derive corresponding equivalent kernels that provide insights into the role of smoothing on the data and fill a gap in the literature. We show that the asymptotic equivalent kernels have an explicit decomposition with three parts: the inverse of the conditional moment matrix of covariates given the smoothing variable, the covariate vector, and the equivalent kernels of univariable local polynomials. We discuss finite-sample reproducing property which leads to zero bias in linear models with interactions between covariates and polynomials of the smoothing variable. By expressing the model in a centered form, equivalent kernels of estimating the intercept function are asymptotically identical to those of univariable local polynomials and estimators of slope functions are local analogues of slope estimators in linear models with weights assigned by equivalent kernels. Two examples are given to illustrate the weighting schemes and reproducing property. [ABSTRACT FROM AUTHOR]

In this study, we propose a cointegration test in which structural changes are modeled gradually through the Fourier approach and the nonlinear structure is modeled with an exponential smooth transition autoregressive (ESTAR) model. In the traditional tests, structural changes are mostly modeled by dummy variables. However, the extended literature supposes that the flexible Fourier approach is an alternative approach to dummy variables since there is no need to know the form, date, and number of breaks with the Fourier approach. The lack of a cointegration test to combine the ESTAR model and Fourier approach in the literature constitutes the motivation of this study. Monte Carlo simulation results demonstrate that the size properties are close to the nominal size and the power of the test shows good performance even in the small sample simulation experiment. Results also indicate that the proposed test shows better power performance compared to the ESTAR cointegration test ignoring breaks. [ABSTRACT FROM AUTHOR]

In areas ranging from neuroimaging to climate science, advances in data storage and sensor technology have led to a proliferation in multidimensional functional datasets. A common approach to analyzing functional data is to first map the discretely observed functional samples into continuous representations, and then perform downstream statistical analysis on these smooth representations. It is well known that many of the traditional approaches used for 1D functional data representation are plagued by the curse of dimensionality and quickly become intractable as the dimension of the domain increases. In this article, we propose a computational framework for learning continuous representations from a sample of multidimensional functional data that is immune to several manifestations of the curse. The representations are constructed using a set of separable basis functions that are defined to be optimally adapted to the data. We show that the resulting estimation problem can be solved efficiently by the tensor decomposition of a carefully defined reduction transformation of the observed data. Roughness-based regularization is incorporated using a class of differential operator-based penalties. Relevant theoretical properties are also discussed. The advantages of our method over competing methods are thoroughly demonstrated in simulations. We conclude with a real data application of our method to a clinical diffusion MRI dataset. for this article are available online. [ABSTRACT FROM AUTHOR]

A prior distribution for the underlying graph is introduced in the framework of Gaussian graphical models. Such a prior distribution induces a block structure in the graph's adjacency matrix, allowing learning relationships between fixed groups of variables. A novel sampling strategy named Double Reversible Jumps Markov chain Monte Carlo is developed for learning block structured graphs under the conjugate G-Wishart prior. The algorithm proposes moves that add or remove not just a single edge of the graph but an entire group of edges. The method is then applied to smooth functional data. The classical smoothing procedure is improved by placing a graphical model on the basis expansion coefficients, providing an estimate of their conditional dependence structure. Since the elements of a B-Spline basis have compact support, the conditional dependence structure is reflected on well-defined portions of the domain. A known partition of the functional domain is exploited to investigate relationships among portions of the domain and improve the interpretability of the results. for this article are available online. [ABSTRACT FROM AUTHOR]

This paper deals with the coupled chemotaxis-haptotaxis model with gradient-dependent flux-limitation ... where Ω ⊂ ℝn(n ≥ 1) is a bounded domain with smooth boundary, χ, ξ and μ are positive parameters. * Under the condition that 1 < p < n/ n - 1, then for any χ, ξ,μ > 0 and all reasonably smooth initial data (u0,w0), the above system possesses a globally classical solution, which is uniformly bounded in time. * Under the conditions that 1 < p < n/n - 1 and μ > χ²/8, it asserts exponential decay of w in the large time limit, whereas both u and v persist in some certain sense. [ABSTRACT FROM AUTHOR]

The number of deaths due to road accident is increasing day by day and has become an alarming global problem over the decades. India, with her rising motorization is no stranger to this global catastrophe. In this paper two relatively simple yet powerful and versatile techniques for forecasting time series data, autoregressive integrated moving average method (ARIMA) and exponential smoothing method are used to forecast the number of deaths due to road accidents in India from the year 2022-- 2031. The results based on the two methods are compared and it is found that they are in sync with each other and pre-existing literature. Furthermore, this is a unique attempt to use two time series analysis techniques on the same data and carry out a comparative analysis. The data was collected from the annual report of Ministry of Road Transport and Highways, India (2020) and Accidental Deaths & Suicides in India (ADSI) Report of National Crime Record Bureau (2021). After examining all the probable models, it is observed that ARIMA (2, 2, 2) model and exponential smoothing (M, A, N) model are suitable for the given data. Amongst the two, ARIMA (2, 2, 2) model has a lower AIC and BIC value. Thus, this comes out to be the best model as per our model selection criterion. Further, the study also reveals an upward trend of number of road accidental deaths for the upcoming 10 years in India. [ABSTRACT FROM AUTHOR]

Particle Filtering (PF) has been widely used for predicting Remaining Useful Life (RUL) of industrial products, especially for those with nonlinear degradation behavior and non-Gaussian noise. Traditional PF is a recursive Bayesian filtering framework that updates the posterior probability density function of RULs when new observation data become available. In engineering practice, due to the limited accuracy of monitoring/inspection techniques, the observation data available for PF are inevitably imprecise and often need to be treated as interval data. In this article, a novel Interval Particle Filtering (IPF) approach is proposed to effectively leverage such interval-valued observations for RUL prediction. The IPF is built on three pillars: (i) an interval contractor that mitigates the error explosion problem when the epistemic uncertainty in the interval-valued observation data is propagated; (ii) an interval intersection method for constructing the likelihood function based on the interval observation data; and (iii) an interval kernel smoothing algorithm for estimating the unknown parameters in the IPF. The developed methods are applied on the interval-valued capacity data of batteries and fatigue crack growth data of railroad tracks. The results demonstrate that the developed methods could improve the performance of RUL predictions based on interval observation data. [ABSTRACT FROM AUTHOR]

Car-following models are the cornerstones of microscopic traffic simulation tools and intelligent transportation systems, but the applicability of car-following models to disordered traffic have not been investigated in detail with longer trajectory dataset. To address this gap, two car-following models namely, Intelligent Driver Model (IDM) and Full Velocity Difference Model (FVDM) are calibrated using trajectory data collected on an urban arterial road in Chennai, India using Unmanned Aerial Vehicles. The raw data are smoothed for noise removal and the car-following pairs are identified based on the lateral overlap and following duration. The models are calibrated by minimizing the deviations between the observed and simulated longitudinal gaps between leader and follower using genetic algorithm. The obtained errors are between 2.5% and 19.5%, which are comparable with standard ranges of error reported in literature. The optimal parameter values represent the distinct characteristics of disordered traffic in comparison with the homogeneous traffic. [ABSTRACT FROM AUTHOR]

Under the long-term implementation of the low fare policy for public transport in China, the phenomenon of unsustainable subsidies is increasingly obvious. We take into account three related stakeholders including the public, operators and government, and comprehensively consider various factors affecting public transport subsidies, and establish a linkage mechanism of the subsidy based on passenger ridership, cost, fare and service quality. We propose a combination forecasting model (CFM) composed of quadratic exponential smoothing model (QESM) and Grey theory model (GM) to forecast passenger ridership. The results show that the CFM improves the forecast accuracy of passenger ridership, the factors considered in the linkage mechanism are more comprehensive, and the results are reasonable. By using this linkage mechanism, the government or operators can establish long-term or mid-term development plans to provide a systematic and theoretical reference, which is conducive to the healthy and stable development of public transport. [ABSTRACT FROM AUTHOR]

In this paper, we propose and present a nonparametric data smoothing method via the kernel smoothing functions to make structural equation modeling (SEM) robust to a specific type of model misspecification, that is an incorrect distributional assumption. Although most statistical techniques are based on an implicit assumption of normality, real data often exhibits nonnormal kurtosis (heavily peaked), skewness, or both. These characteristics, if ignored, can make model identification difficult and inference not reliable. It is important to note that these are characteristics present in most real multivariate high-dimensional datasets. There is much recent study devoted to this type of misspecification. Using a large scale Monte Carlo simulation study, we evaluate the efficacy of our proposed approach in improving the frequency with which a correctly specified model is selected by information complexity criteria when the normality is misspecified. We also show our results on a benchmark reference real dataset to study the quality of life. Our results indicate that the data smoothing kernel transformation (KDS-SEM) leads to a better fitting structural equation model (SEM) and model selection. [ABSTRACT FROM AUTHOR]

An artificial example of a coupled system of three nonlinear partial differential equations generalizing 2D thermoelastic vibrations, is used to demonstrate the effectiveness, as well as the limitations, of a non iterative direct procedure in data assimilation. A stabilized explicit finite difference scheme, run backward in time, is used to find initial values, [u(.,0),v(.,0),w(.,0)], that can evolve into a useful approximation to a hypothetical target result [u∗(.,Tmax),v∗(.,Tmax),w∗(Tmax)], at some realistic Tmax>0. Highly non smooth target data are considered, that may not correspond to actual solutions at time Tmax. Stabilization is achieved by applying a compensating smoothing operator at each time step. Such smoothing leads to a distortion away from the true solution, but that distortion is small enough to allow for useful results. Data assimilation is illustrated using 512×512 pixel images. Such images are associated with highly irregular non smooth intensity data that severely challenge ill-posed reconstruction procedures. Computational experiments show that efficient FFT-synthesized smoothing operators, based on (−Δ)q with real q>3, can be successfully applied, even in nonlinear problems in non-rectangular domains. However, an example of failure illustrates the limitations of the method in problems where Tmax, and/or the nonlinearity, are not sufficiently small. [ABSTRACT FROM AUTHOR]

A catastrophic epidemic of Severe Acute Respiratory Syndrome-Coronavirus, commonly recognised as COVID-19, introduced a worldwide vulnerability to human community. All nations around the world are making enormous effort to tackle the outbreak towards this deadly virus through various aspects such as technology, economy, relevant data, protective gear, lives-risk medications and all other instruments. The artificial intelligence-based researchers apply knowledge, experience and skill set on national level data to create computational and statistical models for investigating such a pandemic condition. In order to make a contribution to this worldwide human community, this paper recommends using machine-learning and deep-learning models to understand its daily accelerating actions together with predicting the future reachability of COVID-19 across nations by using the real-time information from the Johns Hopkins dashboard. In this work, a novel Exponential Smoothing Long-Short-Term Memory Networks Model (ESLSTM) learning model is proposed to predict the virus spread in the near future. The results are evaluated using RMSE and R-Squared values. [ABSTRACT FROM AUTHOR]

We generalize the double smoothing local linear regression method to nonparametric regression of time series. Under a strong mixing condition for the dependence of the time series, we show that after another round of smoothing based on the local linear regression estimates, the double smoothing local linear estimate will have reduced asymptotic bias, while keeping the variance at the same asymptotic order. The asymptotic bias reduces from the order of h2 for the local linear estimates to h4 for the double smoothing local linear estimates, where h is the bandwidth. Hence the double smoothing local linear method produces more optimal estimates in terms of mean squared error. Simulation studies and real time series data analysis confirm the advantages of the double smoothing method compared to the local linear method. [ABSTRACT FROM AUTHOR]

Despite strong limitations, discrete random multiplicative cascades are often used to address scale issues that are ubiquitous in geosciences. A blunt extension based on the parsimonious framework of universal multifractals has recently been suggested. It preserves its simplicity and intuitiveness while overcoming its non-stationarity features. It relies on smoothing through a geometrical moving average the increments at each cascade step. Here, a space-time extension is suggested. Theoretically expected multifractal behaviour is retrieved on numerical simulations for typical rainfall parameters. A new algorithm to generate the missing half of multifractal fields in one, two or three dimensions is developed and tested on rainfall fields and numerical simulations. It consists in stochastically generating half of the increments and deterministically iteratively reconstructing the others to retrieve the available data and ensure a smooth transition with the unknown portion while preserving the multifractal behaviour. Potential applications to nowcasting of hydro-meteorological extremes are discussed. [ABSTRACT FROM AUTHOR]

To reasonably ensure good groundwater quality for the safety of users, it is necessary to monitor the evolution of physicochemical parameters of water. This study assessed the evolution of groundwater quality in Xianyang City (Central China) for 6 years and forecasted the water quality index (WQI) using the automatic exponential smoothing model (AESM). The results revealed that pH, Mn, NH4+, HCO3− and Ca2+ increased significantly within 6 years. However, there was a slight decrease in K+, NO3−, SiO2, and Mg2+. Over the course of 6 years, seven out of fourteen wells maintained excellent or good water quality, whereas groundwater quality in the remaining wells fluctuated from excellent to good or from good to poor. The WQI index increased for nine wells, and five of them including well 173, well 457, well 46, well 26, and well C4 manifested an exponential increase of WQI, which was mainly caused by high concentrations of Mn, NH4+, and NO3−. The forecast accuracy verified by MASE and sMAPE, which ranged from 0.35 to 1.06 and from 0.04 to 0.69, respectively, demonstrated that the predictions were reliable. The AESM was tested in groundwater quality prediction, indicating that it might be used for actual scientific studies. [ABSTRACT FROM AUTHOR]

The COVID19 pandemic has significantly affected the performance of the transport sector and its overall intensity. Reduced mobility has a large impact on the number of road accidents. The aim of this study is to forecast the number of road accidents in Poland and to assess the impact of the COVID19 pandemic on the variation in road crashes. For this purpose, day-wise historical crash data from 2011 onwards have been collected and analysed. Based on real historical field data, the future has been forecasted for both pandemic and nonpandemic variants. Forecasting of the number of accidents has been carried out using selected time series models and exponential models. Based on obtained data, it can be stated that pandemic resulted in a decrease in number of road accidents in Poland with ranges of reduction varying from 11% to 30% based on different days of week. Most visible decrease is observed on 3 days viz. Monday, Wednesday, and Saturday. Further, the projections show that in view of the current situation one may expect further decrease in the number of road accidents in Poland. [ABSTRACT FROM AUTHOR]

Media regarding COVID-19 fatality counts is crucial, affecting policy and health measures nationwide. However, misinformation regarding other causes of death has led to dubious claims about the seriousness of the coronavirus. This research aims to identify the changes in a dozen causes of death during the pandemic using CDC data from 1999 to 2020. Using the Exponential Triple Smoothing (ETS) algorithm, this project estimated the mortality of eleven causes of death for 2020 under the assumption of no COVID-19 pandemic. Using Power BI and Tableau, this data was visualized together with 2020 actual death counts to determine which causes of death were significantly impacted by the coronavirus. The dashboard revealed an increase in several causes of death including Alzheimer's Disease and Diabetes, a decrease in Chronic Lower Respiratory Disease deaths, and a slight increase in Influenza deaths. These findings, while at odds with much of the media surrounding COVID-19 mortality, are corroborated by adjacent scientific research. [ABSTRACT FROM AUTHOR]

This paper gives new guidance for selection of univariate non-parametric derivative estimators with non-iid errors in finite samples. It is shown via an extensive set of Monte Carlo simulations that the generalized C P criterion of Charnigo et al. (A generalized C P criterion for derivative estimation. Technometrics. 2011;53:238–253.) with spline smoothing performs the best in situations with minimal noise. For increased noise, generalized cross-validation of Craven and Wahba (Smoothing noisy data with spline functions. Numer Math. 1978;31:377–403) with P spline smoothing and the improved Akaike Information Criterion of Hurvich et al. (Smoothing parameter selection in nonparametric regression using an improved Akaike information criterion. J R Stat Soc Ser B. 1998;60:271–293.) with P spline smoothing are preferred. In the class of kernel smoothing and local regression methods, the local-cubic estimator of Henderson et al. (Gradient-based smoothing parameter selection for nonparametric regression estimation. J Econom. 2015;184:233–241.) generally outperforms its competitors. An internal meta-analysis separately favours the generalized C P method and P spline smoothing. The empirical example given provides support for use of the local-cubic estimator. [ABSTRACT FROM AUTHOR]

The purpose of this article is the statistical surveillance of spatial autoregressive models, where the observed process is monitored over both space and time. The considered spatial model contains disturbances with heavy tails. The control procedures based on exponential smoothing or cumulative sums are constructed using characteristic quantities including the first and the second moments to monitor both means and covariances. Via Monte Carlo simulation, the in-control upper control limits of the control schemes are derived. In a further simulation study, we compare the detection speed of these procedures in the out-of-control situation. [ABSTRACT FROM AUTHOR]

This study investigates how an abrupt reduction in policing impacts upon the occurrence of homicides in a violent context in the Global South. The study utilizes a police strike in the Brazilian state of Ceará in summer 2020 as a quasi-natural experiment. Separate SARIMA and Exponential Smoothing models fitted on data on weekly homicide counts from January 2015 to the beginning of the strike are used to generate forecasts of homicides in a virtual counterfactual scenario with no police strikes. Actual homicide counts and forecasts are subsequently compared. The strike led to a statistically significant increase in homicides ranging between 110% and 250%. A difference-in-differences analysis confirms this result. The elasticity of homicides with respect to police presence is tentatively estimated at between -1.5 and -5.0. Even in a violent context, the perception of a higher risk of apprehension induced by police presence acts as a powerful deterrent against homicides. [ABSTRACT FROM AUTHOR]

In this paper, we study the regularity properties of solutions of dynamic evolution problems in perfect plasticity. We prove that for any space dimension and for any closed convex set of constraints containing zero as an interior point, the solutions are regular in space during a short time interval if the data are smooth and compactly supported. The result is based on the hyperbolic structure of the model, namely the finite speed propagation property. [ABSTRACT FROM AUTHOR]

In this study, a semi-varying coefficient error-in-variable model with surrogate data and validation sample is proposed. Without specifying any error structure, we firstly use the local linear kernel smoothing technique to define the estimators and the proposed estimators are proved to be asymptotically normal. Then, we conduct generalized likelihood ratio (GLR) test on varying coefficient function. The data–driven bandwidth selection method is discussed. Finally, simulated studies are conducted to illustrate the finite sample properties of the proposed estimators and efficiency of the GLR methodology. [ABSTRACT FROM AUTHOR]

We present local biplots, an extension of the classic principal component biplot to multidimensional scaling. Noticing that principal component biplots have an interpretation as the Jacobian of a map from data space to the principal subspace, we define local biplots as the Jacobian of the analogous map for multidimensional scaling. In the process, we show a close relationship between our local biplot axes, generalized Euclidean distances, and generalized principal components. In simulations and real data we show how local biplots can shed light on what variables or combinations of variables are important for the low-dimensional embedding provided by multidimensional scaling. They give particular insight into a class of phylogenetically-informed distances commonly used in the analysis of microbiome data, showing that different variants of these distances can be interpreted as implicitly smoothing the data along the phylogenetic tree and that the extent of this smoothing is variable. [ABSTRACT FROM AUTHOR]

This paper investigates the discrete-time problem of the regularized Schrödinger equation with fractional Laplacian term in bounded domains. We proved the exponential stability and the Kato smoothing effect of the discrete-time Crank–Nicolson scheme. The proofs are based on uniform estimates of the semi-discrete resolvent obtained by the Z-Transformation. We constructed a well-posed approximation scheme and carried out numerical simulations to verify numerically the exponential stability and the smoothing effect. [ABSTRACT FROM AUTHOR]

In many real-world applications of monitoring multivariate spatio-temporal data that are non-stationary over time, one is often interested in detecting hot-spots with spatial sparsity and temporal consistency, instead of detecting system-wise changes as in traditional statistical process control (SPC) literature. In this paper, we propose an efficient method to detect hot-spots through tensor decomposition, and our method has three steps. First, we fit the observed data into a Smooth Sparse Decomposition Tensor (SSD-Tensor) model that serves as a dimension reduction and de-noising technique: it is an additive model decomposing the original data into: smooth but non-stationary global mean, sparse local anomalies, and random noises. Next, we estimate model parameters by the penalized framework that includes Least Absolute Shrinkage and Selection Operator (LASSO) and fused LASSO penalty. An efficient recursive optimization algorithm is developed based on Fast Iterative Shrinkage Thresholding Algorithm (FISTA). Finally, we apply a Cumulative Sum (CUSUM) Control Chart to monitor model residuals after removing global means, which helps to detect when and where hot-spots occur. To demonstrate the usefulness of our proposed SSD-Tensor method, we compare it with several other methods including scan statistics, LASSO-based, PCA-based, T2-based control chart in extensive numerical simulation studies and a real crime rate dataset. [ABSTRACT FROM AUTHOR]

Exponential smoothing is one of the most commonly used prediction methods. When the data has obvious periodicity and seasonality, Holt–Winters usually has a good prediction performance. However, the predicted results often do not meet our expectations when the trend of the original data is not clear. To further reduce the randomness of time series, a new method combining grey generating operator with the traditional Holt–Winters is proposed. The accumulated sequence by grey generating operator can have obvious variation law. Three practical examples were selected to evaluate the forecasting performance of this proposed method. The results indicate that the proposed model can substantially have the better forecasting capability than traditional Holt–Winters method. [ABSTRACT FROM AUTHOR]

Fractional diffusion equations (FDEs) were shown to provide very competitive descriptions of challenging phenomena of anomalously diffusive transport or long-range interactions. However, FDEs introduce mathematical issues that are not common in the context of integer-order diffusion equations. For instance, the homogeneous Dirichlet boundary-value problems of linear elliptic FDEs with smooth data in one space dimension may generate solutions with singularities that do not seem physically relevant, which are in sharp contrast to their integer-order analogues do. We prove the wellposedness of the Dirichlet boundary-value problem of one dimensional variable-order linear space-fractional diffusion equations (sFDEs). We further prove that their solutions have the similar regularities as their integer-order analogues if the order has an integer limit at the boundary or have the same singularity near the boundary as their constant-order sFDE analogues if the order has a non-integer limit at the boundary. In particular, we prove that constant-order sFDEs with a variable-order modification indeed generate solutions with significantly improved regularities. [ABSTRACT FROM AUTHOR]

We performed two simulation studies that investigated dimensionality recovery in NPD tetrachoric correlation matrices using parallel analysis. In each study, the NPD matrices were rehabilitated by three smoothing algorithms. In Study 1, we replicated the work by Debelak and Tran on the assessment of dimensionality in one- or two-dimensional common factor models. In Study 2, we extended the Debelak and Tran design in three important ways. Specifically, we investigated: (a) a wider range of factors; (b) models with varying amounts of model error; and (c) models generated from more realistic population item parameters. Our results indicated that matrix smoothing of NPD tetrachoric correlation matrices improves the performance of parallel analysis with binary data. However, these improvements were modest and often of trivial size. To demonstrate the effect of matrix smoothing on an empirical data set, we applied parallel analysis and factor analysis to Adjective Checklist data from the California Twin Registry. [ABSTRACT FROM AUTHOR]

Time series modeling has entered an era of unprecedented growth in the size and complexity of data which require new modeling approaches. While many new general purpose machine learning approaches have emerged, they remain poorly understand and irreconcilable with more traditional statistical modeling approaches. We present a general class of exponential smoothed recurrent neural networks (RNNs) which are well suited to modeling nonstationary dynamical systems arising in industrial applications. In particular, we analyze their capacity to characterize the nonlinear partial autocorrelation structure of time series and directly capture dynamic effects such as seasonality and trends. Application of exponentially smoothed RNNs to forecasting electricity load, weather data, and stock prices highlight the efficacy of exponential smoothing of the hidden state for multistep time series forecasting. The results also suggest that popular, but more complicated neural network architectures originally designed for speech processing are likely over-engineered for industrial forecasting and light-weight exponentially smoothed architectures, trained in a fraction of the time, capture the salient features while being superior and more robust than simple RNNs and autoregressive models. Additionally, uncertainty quantification of Bayesian exponential smoothed RNNs is shown to provide improved coverage. [ABSTRACT FROM AUTHOR]

Recent developments of advanced imaging systems spur their applications in many areas, ranging from satellite remote sensing for geographic information to thermal imaging analysis for manufacturing process monitoring and control. Due to different specifications of imaging systems, the resulting image stream data (videos) have different spatial and temporal resolutions. This proposed work is based on the image stream data captured by multiple imaging systems for the same object with different but complementary spatial and temporal resolutions. For example, one system has high spatial but low temporal resolutions while the other one has opposite resolutions. The goal of this article is to develop a new super resolution method that integrates these different types of image stream data to improve both spatial and temporal resolutions, which is critical to obtaining more insightful information for more effective quality control of targeted processes or systems. To fulfill this goal, a new tensor completion model is developed by considering both smooth and sparse features simultaneously and is thus termed smooth and sparse tensor completion (SSTC). The results of the extensive case studies illustrate the superiority of our method over the elaborately selected benchmark methods. [ABSTRACT FROM AUTHOR]

Forecasting hierarchical or grouped time series using a reconciliation approach involves two steps: computing base forecasts and reconciling the forecasts. Base forecasts can be computed by popular time series forecasting methods such as exponential smoothing (ETS) and Autoregressive Integrated Moving Average (ARIMA) models. The reconciliation step is a linear process that adjusts the base forecasts to ensure they are coherent. However, using ETS or ARIMA for base forecasts can be computationally challenging when there are a large number of series to forecast, as each model must be numerically optimized for each series. We propose a linear model that avoids this computational problem and handles the forecasting and reconciliation in a single step. The proposed method is very flexible in incorporating external data. We illustrate our approach using a dataset on monthly Australian domestic tourism, as well as a simulated dataset. We compare our approach to reconciliation using ETS and ARIMA, and show that our approach is much faster while providing similar levels of forecast accuracy. Supplementary files for this article are available online. [ABSTRACT FROM AUTHOR]

Unemployment hysteresis of Middle East and North African (MENA) countries is investigated under a battery of unit root testing frameworks in the extant literature, including a recently proposed Panel SUR Dickey-Fuller-like unit root test with Fourier and Exponential Smooth Transition Regression (ESTR) nonlinearities. The Fourier function allows for smooth nonlinear breaks, while the ESTR nonlinearity allows for instantaneous breaks. The two nonlinearity types make the recent approach quite appealing. It has, however, been scarcely applied to empirically test the unemployment hysteresis hypothesis. Although we find conflicting stances from ADF, FADF and ADF-SB testing frameworks, evidence of unemployment hysteresis effect in Lebanon is consistent across all three tests. The ADF and FADF tests confirmed the hysteresis hypothesis in Kuwait and Lebanon, while FADF-SB rejected the unemployment hysteresis hypothesis across all the 19 MENA countries. The results from the KSS and FKSS unit root testing frameworks consistently affirmed the hysteresis effect in Oman and Turkey, while there are mixed stances for Kuwait and Lebanon. The results from SURADF and SURKSS only supported the hysteresis hypothesis in Turkey, while the same was confirmed only for Bahrain under the SURFADF and SURFKSS testing frameworks. The unemployment hysteresis hypothesis is confirmed for 12 (about 63.15% of the total number considered) MENA economies. [ABSTRACT FROM AUTHOR]

We prove that the half-wave maps problem on R 4 + 1 with target S2 is globally well-posed for smooth initial data which are small in the critical l1 based Besov space. This is a formal analogue of the result proved by Tataru for wave maps. [ABSTRACT FROM AUTHOR]

Forecasting is a crucial step in almost all scientific research and is essential in many areas of industrial, commercial, clinical and economic activity. There are many forecasting methods in the literature; but exponential smoothing stands out due to its simplicity and accuracy. Despite the facts that exponential smoothing is widely used and has been in the literature for a long time, it suffers from some problems that potentially affect the model's forecast accuracy. An alternative forecasting framework, called Ata, was recently proposed to overcome these problems and to provide improved forecasts. In this study, the forecast accuracy of Ata and exponential smoothing will be compared among data sets with no or linear trend. The results of this study are obtained using simulated data sets with different sample sizes, variances. Forecast errors are compared within both short and long term forecasting horizons. The results show that the proposed approach outperforms exponential smoothing for both types of time series data when forecasting the near and distant future. The methods are implemented on the U.S. annualized monthly interest rates for services data and their forecasting performance are also compared for this data set. [ABSTRACT FROM AUTHOR]

A three-level implicit difference scheme is developed for a inviscid Burgers' equation with time delay. It is proved that the proposed scheme is uniquely solvable, stable, and unconditionally convergent with order O (τ 2 + h 2) in the maximal norm based on an assumption of monotone initial data and smooth solutions, where τ is the temporal step size and h is the spatial step size. Finally, numerical experiments are applied to illustrate the effectiveness of theoretical results. [ABSTRACT FROM AUTHOR]

This study compared the accuracy of automatic time series forecasting methods in predicting the results of the 2018 Swedish general election using data from the Party Preference Survey opinion poll collected during the years 1984–2018. The general exponential smoothing state space (ETS) model performed best, outperforming even the exit poll collected at the time of the election, while the complex seasonal autoregressive integrated moving average (ARIMA) model was beaten by the simple exponential smoothing method. Holt's linear trend method performed worse than even the naïve method. The results of this study show the usefulness of easily applied automatic forecasting methods. [ABSTRACT FROM AUTHOR]

Adaptive penalized splines via radial basis are constructed to estimate regression functions and their derivatives. A weight vector based on the range of observations is embedded into the penalty matrix, which remarkably improves the adaptability of the penalized spline smoothing model. Fast computation and comparison with traditional spline models are studied, and the empirical results and simulations show that the new method outperforms smoothing splines, traditional penalized splines and local polynomial smoothing when estimating regression functions and their derivatives, particularly when the observations have inhomogeneous variation. [ABSTRACT FROM AUTHOR]

It is proved recently that partially dissipative hyperbolic systems converge globally-in-time to parabolic systems in a slow time scaling, when initial data are smooth and sufficiently close to constant equilibrium states. Based on this result, we establish error estimates between the smooth solutions of the hyperbolic systems of balance laws and those of the parabolic limit systems in one space dimension. The proof of the error estimates uses a stream function technique together with energy estimates. As applications of the results, we give five examples arising from physical models. [ABSTRACT FROM AUTHOR]

Soil visible-near-infrared reflection (Vis-NIR; 350 to 2500 nm) spectra is a comprehensive reflection of various soil physical and chemical properties, resulting in significant differences of hyperspectral characteristics and diversity of soil property prediction models. Calcium carbonate regulates several soil properties that were widely used to describe soil types and to quantify vulnerability to erosion. Therefore, spectral-based determination of soil calcium carbonate content is essential for agricultural management and environmental evaluation. Based on their reflectance similarity, the soil Vis-NIR spectra data itself can be classified into different spectral groups to predict soil calcium carbonate. To obtain the best hyperspectral quantitative prediction model for soil calcium carbonate based on soil group spectral data and spectral group data, a total of 246 soil samples were collected from seven soil types in Shaanxi province, China, and the soil Vis-NIR spectra were measured. All the soil spectral data were smoothed using Savitzky-Golay and continuum removal method. In this paper, we combined spectral angle cosine (SAC) algorithm with spectral correlation coefficient (SCC) algorithm to classify soil spectra. The results indicated that the coefficient of correlations between measured and predicted soil properties for seven prediction models based on random regression forest (RFR) were low (Ratio of performance to deviation, RPD < 2.00). When soil spectra were classified into three types based on the SAC-SCC spectral similarity measurement method, accuracy of all the prediction models increased significantly (R2 ≥ 0.96; RPD > 2.00) compared with the individual soil type models. These results provide a novel method for soil spectral classification and soil attribute estimation. [ABSTRACT FROM AUTHOR]

In this paper, we study a boundary value problem of fractional convection–diffusion equation with general two-sided fractional derivative. The well-posedness of the variation formulation is investigated under some properly assumptions. A Petrov-Galerkin method is developed, which employs the Jacobi poly-fractonomials for the trial and test space. The new approach allows the derivation of optimal error estimates in properly weighted Sobolev space and the matrix of the leading term is diagonal. We show that even for smooth data, we only obtain algebraic convergence due to the regularity of the solution. Some numerical examples are presented to demonstrate the validity of our theoretical results. [ABSTRACT FROM AUTHOR]

The present paper proposes an alternative procedure to test for cointegration in asymmetric exponential smooth transition autoregressive (AESTAR) model. The proposed new F-statistics test the null hypothesis of no cointegration against the alternative hypothesis of cointegration with asymmetric ESTAR adjustment. We derive the nonstandard limit distributions analytically via Monte Carlo simulations. We also study the finite sample properties and the power of proposed tests with Monte Carlo simulations and find that the empirical sizes of two tests are quite close to the nominal one and the proposed tests do not lead to over-rejections of the null hypothesis of no cointegration. [ABSTRACT FROM AUTHOR]

The development of sustainable energy systems is crucial to addressing the environmental, economical, and social pressures of the energy sector. Energy sustainability, as one of the most important factors powering modern economies, is a complex concept related to important technological, environmental, and socio-economic issues. This paper proposes a framework for defining and measuring the sustainability of national energy systems. It is based on several energy sustainability indicators that cover three major dimensions: environment, human system, and energy system. The proposed framework includes data smoothing, normalization and imputation, and application of the PROMETHEE method to evaluate the sustainability performance of 43 European countries. The results show that geographical and income groupings are strongly related to energy sustainability performance. In particular, high-income Scandinavian and Western European countries are highly ranked in terms of energy sustainability. A sensitivity analysis regarding the main parameters of the PROMETHEE method justifies the robustness of rankings, while a comparison with other barometers shows that the presented results are consistent with alternative energy sustainability approaches. [ABSTRACT FROM AUTHOR]

Dynamic visualization of multidimensional hydrometeorological data is vital for decision-makers to catch situational awareness and command an emergency response in natural disasters. Nevertheless, few software tools can comprehensively visualize hydrometeorological data in different scales, dimensions, and time. In this paper, an interactive 4D spatio-temporal visualization system based on a virtual globe is proposed. Voxel-based data model and multi-level index are adopted to organize the field data in a unified data structure. Meanwhile, it is resampled in both spatial and temporal dimensions in memory to prepare smooth data stream for rendering. Ten field models, including large-scale volume rendering and adaptive streamline rendering, are accelerated and integrated to display the field data collaboratively. The profile analysis and eddy tracking improve user experience in interactively exploring specific scenes. The system is tested against both large-scale meteorological data in the atmosphere and small-scale hydrological data at the surface, using typhoon landfall and riverine flood, respectively. The results demonstrate the applicability and efficiency of the system to dynamically visualize hydrometeorological data. [ABSTRACT FROM AUTHOR]

Assume that, in a parabolic or hyperbolic equation, the right-hand side is analytic in time and the coefficients are analytic in time at each fixed point of the space. We show that the infinitely differentiable solution to this equation is also analytic in time at each fixed point of the space. This solution is given in the form of the Taylor expansion with respect to time t with coefficients depending on x. The coefficients of the expansion are defined by recursion relations, which are obtained from the condition of compatibility of order k = ∞. The value of the solution on the boundary is defined by the right-hand side and initial data, so that it is not prescribed. We show that exact regular and weak solutions to the initial–boundary value problems for parabolic and hyperbolic equations can be determined as the sum of a function that satisfies the boundary conditions and the limit of the infinitely differentiable solutions for smooth approximations of the data of the corresponding problem with zero boundary conditions. These solutions are represented in the form of the Taylor expansion with respect to t. The suggested method can be considered as an alternative to numerical methods of solution of parabolic and hyperbolic equations. [ABSTRACT FROM AUTHOR]

Missing data is a common problem in the analysis of geospatial information. Existing methods introduce spatiotemporal dependencies to reduce imputing errors yet ignore ease of use in practice. Classical interpolation models are easy to build and apply; however, their imputation accuracy is limited due to their inability to capture spatiotemporal characteristics of geospatial data. Consequently, a lightweight ensemble model was constructed by modelling the spatiotemporal dependencies in a classical interpolation model. Temporally, the average correlation coefficients were introduced into a simple exponential smoothing model to automatically select the time window which ensured that the sample data had the strongest correlation to missing data. Spatially, the Gaussian equivalent and correlation distances were introduced in an inverse distance-weighting model, to assign weights to each spatial neighbor and sufficiently reflect changes in the spatiotemporal pattern. Finally, estimations of the missing values from temporal and spatial were aggregated into the final results with an extreme learning machine. Compared to existing models, the proposed model achieves higher imputation accuracy by lowering the mean absolute error by 10.93 to 52.48% in the road network dataset and by 23.35 to 72.18% in the air quality station dataset and exhibits robust performance in spatiotemporal mutations. [ABSTRACT FROM AUTHOR]

Abstract–In functional data analysis, data are commonly assumed to be smooth functions on a fixed interval of the real line. In this work, we introduce a comprehensive framework for the analysis of functional data, whose domain is a two-dimensional manifold and the domain itself is subject to variability from sample to sample. We formulate a statistical model for such data, here called functions on surfaces, which enables a joint representation of the geometric and functional aspects, and propose an associated estimation framework. We assess the validity of the framework by performing a simulation study and we finally apply it to the analysis of neuroimaging data of cortical thickness, acquired from the brains of different subjects, and thus lying on domains with different geometries. for this article are available online. [ABSTRACT FROM AUTHOR]

We propose a new class of filtering and smoothing methods for inference in high-dimensional, nonlinear, non-Gaussian, spatio-temporal state-space models. The main idea is to combine the ensemble Kalman filter and smoother, developed in the geophysics literature, with state-space algorithms from the statistics literature. Our algorithms address a variety of estimation scenarios, including online and off-line state and parameter estimation. We take a Bayesian perspective, for which the goal is to generate samples from the joint posterior distribution of states and parameters. The key benefit of our approach is the use of ensemble Kalman methods for dimension reduction, which allows inference for high-dimensional state vectors. We compare our methods to existing ones, including ensemble Kalman filters, particle filters, and particle MCMC. Using a real data example of cloud motion and data simulated under a number of nonlinear and non-Gaussian scenarios, we show that our approaches outperform these existing methods. for this article are available online. [ABSTRACT FROM AUTHOR]

Separation properties of the local extrema of best piecewise monotonic approximations to measurements of a real univariate function are of fundamental importance to the development of efficient algorithms that calculate these approximations. Piecewise monotonic approximation to n data is expressed as the minimization of some strictly convex function of the data errors subject to the restriction that the piecewise linear interpolant to the approximated values consists of at most k monotonic sections, where k is a prescribed positive integer. The major task is to determine automatically the positions of the joins of these sections, which is a combinatorial problem that can require about O (n k − 1) combinations in order to find an optimal one. We state theorems which prove the remarkable property that the local maxima of optimal approximations with k−1 monotonic sections are separated by the local maxima of optimal approximations with k monotonic sections, and local minima are separated similarly. We describe briefly a suitable technique that makes use of this property and gives the global solution in O (n 2 + k n log 2 ⁡ n) computer operations. Some numerical results show large gains in efficiency over existing methods. Further, as an illustration, we apply the technique to 39,082 observations of daily sunspots. [ABSTRACT FROM AUTHOR]

The main purpose of this paper is the development of data-driven iterative plug-in algorithms for local polynomial estimation of the trend and its derivatives under dependent errors. Furthermore, a data-driven lag-window estimator for the variance factor in the bandwidth is proposed so that the nonparametric stage is carried out without any parametric assumption on the stationary errors. Analysis of the residuals using an ARMA model is further discussed. Moreover, some computational features of the data-driven algorithms are discussed in detail. Practical performance of the proposals is confirmed by a simulation study and a comparative study, and illustrated by quarterly US GDP and labour force data. An R package called 'smoots' (smoothing time series) for smoothing the trend and its derivatives in short-memory time series is developed based on the proposals of this paper. [ABSTRACT FROM AUTHOR]