Search Results (94)

In this paper, time series of length T are seen as frequency distributions. Each distribution is defined with respect to a statistical variable having T observed values. A methodological system based on Gini’s approach is put forward, so the statistical model through which time series are handled is a frequency distribution studied inside a linear system. In addition to the starting frequency distributions that are observed, other frequency distributions are treated. Thus, marginal distributions based on the notion of proportionality are introduced together with joint distributions. Both distributions are statistical models. A fundamental invariance property related to marginal distributions is made explicit in this research work, so one can focus on collections of marginal frequency distributions, identifying multiple frequency distributions. For this reason, the latter is studied via a tensor. As frequency distributions are practical realizations of nonparametric probability distributions over $\mathbb{R}$, one passes from frequency distributions to discrete random variables. In this paper, a mathematical model that generates time series is put forward. It is a stochastic process based on subjective previsions of random variables. A subdivision of the exchangeability of variables of a statistical nature is shown, so a reinterpretation of principal component analysis that is based on the notion of proportionality also characterizes this research work. Full article

Monitoring land cover/use dynamics and wildfire occurrences is very important for land management planning and risk mitigation practices. In this research, moderate-resolution imaging spectroradiometer (MODIS) annual land cover images for the period 2001–2023 are utilized for the twenty administrative regions of Italy. Monthly MODIS burned area images are utilized for the period 2001–2020 to study wildfire occurrences across these regions. In addition, monthly Global Precipitation Measurement images for the period 2001–2020 are employed to estimate correlations between precipitation and burned areas annually and seasonally. Boxplots are produced to show the distributions of each land cover/use type within the regions. The non-parametric Mann–Kendall trend test and Sen’s slope are applied to estimate a linear trend, with statistical significance being evaluated for each land cover/use time series of size 23. Pearson’s correlation method is applied for correlation analysis. It is found that grasslands and woodlands have been declining and increasing in most regions, respectively, most significantly in Abruzzo (−0.88%/year for grasslands and 0.71%/year for grassy woodlands). The most significant and frequent wildfires have been observed in southern Italy, particularly in Basilicata, Apulia, and Sicily, mainly in grasslands. The years 2007 and 2017 experienced severe wildfires in the southern regions, mainly during July and August, due to very hot and dry conditions. Negative Pearson’s correlations are estimated between precipitation and burnt areas, with the most significant one being for Basilicata during the fire season (r = −0.43). Most of the burned areas were mainly within the elevation range of 0–500 m and the lowlands of Apulia. In addition, for the 2001–2020 period, a high positive correlation (r > 0.7) is observed between vegetation and land surface temperature, while significant negative correlations between these variables are observed for Apulia (r ≈ −0.59), Sicily (r ≈ −0.69), and Sardinia (r ≈ −0.74), and positive correlations (r > 0.25) are observed between vegetation and precipitation in these three regions. This study’s findings can guide land managers and policymakers in developing or maintaining a sustainable environment. Full article

Introduced as a complementary concept to Shannon entropy, extropy provides an alternative perspective for measuring uncertainty. While useful in areas such as reliability theory and scoring rules, extropy in its original form treats all outcomes equally, which can limit its applicability in real-world settings where different outcomes have varying degrees of importance. To address this, the weighted extropy measure incorporates a weight function that reflects the relative significance of outcomes, thereby increasing the flexibility and sensitivity of uncertainty quantification. In this paper, we propose a novel recursive non-parametric kernel estimator for weighted extropy based on $\alpha$-mixing dependent observations, a common setting in time series and stochastic processes. The recursive formulation allows for efficient updating with sequential data, making it particularly suitable for real-time analysis. We establish several theoretical properties of the estimator, including its recursive structure, consistency, and asymptotic behavior under mild regularity conditions. A comprehensive simulation study and data application demonstrate the practical performance of the estimator and validate its superiority over the non-recursive kernel estimator in terms of accuracy and computational efficiency. The results confirm the relevance of the method for dynamic, dependent, and weighted systems. Full article

Accurate mapping of rubber plantation stand age is essential for forest inventory, land use monitoring, and carbon stock estimation. This study proposes a pixel-based approach that integrates the Bare Soil Index (BSI) with Normalized Difference Vegetation Index (NDVI) time series to detect land clearance events and predict stand age. The methodology involves feature engineering, selection, and evaluation of three tree-based and one non-parametric supervised machine learning models. Predictive features were extracted from interannual spectral index profiles, with an optimal subset selected using Recursive Feature Elimination (RFE). The best-performing model, optimized using a grid search matrix, was trained and applied to stacked images for pixel-level land clearance prediction over 37 years of NDVI and BSI time series. By aggregating predictions and performing post-classification analysis, a spatially explicit stand-age map was generated. The result was validated using secondary rubber farmer registration data, achieving an overall prediction accuracy of 84.5% and a root mean squared error (RMSE) of 1.86 years. The findings highlight the effectiveness of machine learning with NDVI and BSI time series for stand-age estimation, contributing to advancing remote sensing methodologies for forest inventory and support furfure high-precision carbon stock assessments. Full article

This paper examined the cyclical patterns of mergers and acquisitions (M&A) in the global water sector from 1982 to 2024, with a focus on both linear and nonlinear dynamics in M&A waves. Through a univariate analysis using ARFIMA models, we found that the data exhibited stationary behavior, meaning that in response to an exogenous shock, the series is likely to revert to its original trend over time. Additionally, the non-parametric Brock, Dechert, and Scheinkman (BDS) test revealed the complex and irregular nature of M&A cycles within the sector. To account for this complexity, we applied the Markov-switching dynamic regression (MS-DR) model, which shows that once the industry enters a high-activity regime, it tends to persist in this state for extended periods. This suggests that external shocks or trends—such as regulatory reforms or global water scarcity concerns—are key drivers that trigger and sustain waves of M&A activity in the sector. Full article

A new predictor in functional time series (FTS ) is considered. It is based on the asymmetric weighting function of quantile regression. More precisely, we assume that FTS is generated from a single-index model that permits the observation of endogenous–exogenous variables by combining the nonparametric model with a linear one. In parallel, the $L^1$-modal predictor is estimated using the M-estimation of the derivative of the conditional quantile of the generated FTS. In the mathematical part, we prove the complete convergence of the constructed estimator, and we determine its convergence rate. An empirical analysis is performed to prove the applicability of the estimator and to evaluate the impact of different structures involved in the smoothing approach. This analysis is carried out using simulated and real data. Finally, the regressive nature of the constructed predictor allows it to provide a robust instantaneous predictor for environmental data. Full article

Estimating the Probability Density Function (PDF) of observed data is crucial as a problem in its own right, and also for diverse engineering applications. This paper utilizes two powerful mathematical tools, the concept of moments and the relatively little-known Padé approximation to achieve this. On the one hand, moments encapsulate crucial information that is central to both the “time-” and “frequency-”domain representations of the data. On the other hand, the Padé approximation provides an effective means of obtaining a convergent series from the data. In this paper, we invoke these established tools to estimate the PDF. As far as we know, the theoretical results that we have proven, and the experimental results that confirm them, are novel and rather pioneering. The method we propose is nonparametric. It leverages the concept of using the moments of the sample data—drawn from the unknown PDF that we aim to estimate—to reconstruct the original PDF. This is achieved through the application of the Padé approximation. Apart from the theoretical analysis, we have also experimentally evaluated the validity and efficiency of our scheme. The Padé approximation is asymmetric. The most unique facet of our work is that we have utilized this asymmetry to our advantage by working with two mirrored versions of the data to obtain two different versions of the PDF. We have then effectively “superimposed” them to yield the final composite PDF. We are not aware of any other research that utilizes such a composite strategy, in any signal processing domain. To evaluate the performance of the proposed method, we have employed synthetic samples obtained from various well-known distributions, including mixture densities. The accuracy of the proposed method has also been compared with that gleaned by several State-Of-The-Art (SOTA) approaches. The results that we have obtained underscore the robustness and effectiveness of our method, particularly in scenarios where the sample sizes are considerably reduced. Thus, this research confirms how the SOTA of estimating nonparametric PDFs can be enhanced by the Padé approximation, offering notable advantages over existing methods in terms of accuracy when faced with limited data. Full article

This research focuses on biological systems with sexual reproduction in which female and male individuals coexist together, forming female–male couples with the purpose of procreation. The couples can originate new females and males according to a certain probability law. Consequently, in this type of biological systems, two biological phases are involved: a mating phase in which the couples are formed, and a reproduction phase in which the couples, independently of the others, originate new offspring of both sexes. Due to several environmental factors of a random nature, these phases usually develop over time in a non-predictable (random) environment, frequently influenced by the numbers of females and males in the population and by the number of couples participating in the reproduction phase. In order to investigate the probabilistic evolution of these biological systems, in previous papers, by using a methodology based on branching processes, we had introduced a new class of two-sex mathematical models. Some probabilistic properties and limiting results were then established. Additionally, under a non-parametric statistical framework, namely, not assuming to have known the functional form of the offspring law, estimates for the main parameters affecting the reproduction phase were determined. We now continue this research line focusing the attention on the estimation of such reproductive parameters under a parametric statistical setting. In fact, we consider offspring probability laws belonging to the family of bivariate power series distributions. This general family includes the main probability distributions used to describe the offspring dynamic in biological populations with sexual reproduction. Under this parametric context, we propose accurate estimates for the parameters involved in the reproduction phase. With the aim of assessing the quality of the proposed estimates, we also determined optimal credibility intervals. For these purposes, we apply the Bayesian estimation methodology. As an illustration of the methodology developed, we present a simulated study about the demographic dynamics of Labord’s chameleon populations, where a sensitivity analysis on the prior density is included. Full article

Singular spectrum analysis is a powerful nonparametric technique used to decompose the original time series into a set of components that can be interpreted as trend, seasonal, and noise. For their part, neural networks are a family of information-processing techniques capable of approximating highly nonlinear functions. This study proposes to improve the precision in the prediction of air quality. For this purpose, a hybrid adaptation is considered. It is based on an integration of the singular spectrum analysis and the recurrent neural network long short-term memory; the SSA is applied to the original time series to split signal and noise, which are then predicted separately and added together to obtain the final forecasts. This hybrid method provided better performance when compared with other methods. Full article

U-statistics are fundamental in modeling statistical measures that involve responses from multiple subjects. They generalize the concept of the empirical mean of a random variable X to include summations over each m-tuple of distinct observations of X. W. Stute introduced conditional U-statistics, extending the Nadaraya–Watson estimates for regression functions. Stute demonstrated their strong pointwise consistency with the conditional expectation $r^{\left(m\right)}(\phi ,\mathbf{t})$, defined as $\mathbb{E}\left[\phi (Y_1,\dots ,Y_m)\right|(X_1,\dots ,X_m)=\mathbf{t}]$ for $\mathbf{t}\in {\mathcal{X}}^m$. This paper focuses on estimating functional single index (FSI) conditional U-processes for regular time series data. We propose a novel, automatic, and location-adaptive procedure for estimating these processes based on k-Nearest Neighbor (kNN) principles. Our asymptotic analysis includes data-driven neighbor selection, making the method highly practical. The local nature of the kNN approach improves predictive power compared to traditional kernel estimates. Additionally, we establish new uniform results in bandwidth selection for kernel estimates in FSI conditional U-processes, including almost complete convergence rates and weak convergence under general conditions. These results apply to both bounded and unbounded function classes, satisfying certain moment conditions, and are proven under standard Vapnik–Chervonenkis structural conditions and mild model assumptions. Furthermore, we demonstrate uniform consistency for the nonparametric inverse probability of censoring weighted (I.P.C.W.) estimators of the regression function under random censorship. This result is independently valuable and has potential applications in areas such as set-indexed conditional U-statistics, the Kendall rank correlation coefficient, and discrimination problems. Full article

Bitcoin (BTC-USD) is a virtual currency that has grown in popularity after its inception in 2008. BTC-USD is an internet communication network that makes using digital money, including digital payments, easy. It offers decentralized clearing of transactions and money supply. This study attempts to accurately anticipate the BTC-USD prices (Close) using data from September 2023 to September 2024, comprising 390 observations. Four machine learning models—Multi-layer Perceptron, Extreme Learning Machine, Neural Network AutoRegression, and Extreme-Gradient Boost—as well as four time series models—Auto-Regressive Integrated Moving Average, Auto-Regressive, Non-Parametric Auto-Regressive, and Simple Exponential Smoothing models—are used to achieve this end. Various hybrid models are then proposed utilizing these models, which are based on simple averaging of these models. The data-splitting technique, commonly used in comparative analysis, splits the data into training and testing data sets. Through comparison testing with training data sets consisting of 30%, 20%, and 10%, the present work demonstrated that the suggested hybrid model outperforms the individual approaches in terms of error metrics, such as the MAE, RMSE, MAPE, SMAPE, and direction accuracy, such as correlation and the MDA of BTC. Furthermore, the DM test is utilized in this study to measure the differences in model performance, and a graphical evaluation of the models is also provided. The practical implication of this study is that financial analysts have a tool (the proposed model) that can yield insightful information about potential investments. Full article

In this paper, nonlinear system identification using Bayesian network has been implemented to discover open-loop lateral-directional aerodynamic model parameters of an agile aircraft using a grey box modelling structure. Our novel technique has been demonstrated on simulated flight data from an F-16 nonlinear simulation of its Flight Dynamic Model (FDM). A mathematical model has been obtained using time series analysis of a Box–Jenkins (BJ) model structure, and parameter refinement has been performed using Bayesian mechanics. The aircraft nonlinear Flight Dynamic Model is adequately excited with doublet inputs, as per the dictates of its natural frequency, in accordance with non-parametric modelling (Finite Impulse Response) estimates. Time histories of optimized doublet inputs in the form of aileron and rudder deflections, and outputs in the form of roll and yaw rates are recorded. Dataset is pre-processed by implementing de-trending, smoothing, and filtering techniques. Blend of System Identification time-domain grey box modelling structures to include Output Error (OE) and Box–Jenkins (BJ) Models are stage-wise implemented in multiple flight conditions under varied stochastic models. Furthermore, a reduced order parsimonious model is obtained using Akaike information Criteria (AIC). Parameter error minimization activity is conducted using the Levenberg–Marquardt (L-M) Algorithm, and parameter refinement is performed using the Bayesian Algorithm due to its natural connection with grey box modelling. Comparative analysis of different nonlinear estimators is performed to obtain best estimates for the lateral–directional aerodynamic model of supersonic aircraft. Model Quality Assessment is conducted through statistical techniques namely: Residual Analysis, Best Fit Percentage, Fit Percentage Error, Mean Squared Error, and Model order. Results have shown promising one-step model predictions with an accuracy of 96.25%. Being a sequel to our previous research work for postulating longitudinal aerodynamic model of supersonic aircraft, this work completes the overall aerodynamic model, further leading towards insight to its flight control laws and subsequent simulator design. Full article

In order to consider the impact of source-load uncertainty on traditional power system planning methods, a medium- and long-term optimization planning method based on source-load uncertainty modeling and time-series production simulation is proposed. First, a new energy output probability model is developed using non-parametric kernel density estimation, and the spatial correlation of the new energy output is described using pair-copula theory to model the uncertainty analysis of the new energy output. Secondly, a large number of source-load scenarios are generated using the Markov chain Monte Carlo simulation method, and the optimal selection method for discrete state numbers is provided, and then the scenario reduction is carried out using the fast forward elimination technology. Finally, the typical time-series curves of the source-load uncertainty characteristics obtained are incorporated into the optimization planning method together with various flexible resources, such as the demand-side response and energy storage, and the rationality of the planning scheme is judged and optimized based on key indicators such as the cost, wind–light abandonment rate, and loss-of-load rate. Based on the above methods, this paper offers an example of the power supply planning scheme for a certain region in the next 30 years, providing effective guidance for the development of new energy in the region. Full article

Background: Repetitive transcranial magnetic stimulation (rTMS) has shown therapeutic effects in neurological patients by inducing neural plasticity. In this pilot study, we analyzed the modifying effects of high-frequency (HF-)rTMS applied to the dorsolateral prefrontal cortex (DLPFC) of patients with mild cognitive impairment (MCI) using an advanced approach of functional connectome analysis based on network control theory (NCT). Methods: Using local-to-global functional parcellation, average and modal controllability (AC/MC) were estimated for DLPFC nodes of prefrontal-lateral control networks (R/LH_Cont_PFCl_3/4) from a resting-state fMRI series acquired at three time points (T0 = baseline, T1 = T0 + 4 weeks, T2 = T1 + 20 weeks) in MCI patients receiving regular daily sessions of 10 Hz HF-rTMS (n = 10, 68.00 ± 8.16 y, 4 males) or sham (n = 10, 63.80 ± 9.95 y, 5 males) stimulation, between T0 and T1. Longitudinal (group) effects on AC/MC were assessed with non-parametric statistics. Spearman correlations (ρ) of AC/MC vs. neuropsychological (RBANS) score %change (at T1, T2 vs. T0) were calculated. Results: AC median was reduced in MCI-rTMS, compared to the control group, for RH_Cont_PFCl_3/4 at T1 and T2 (vs. T0). In MCI-rTMS patients, for RH_Cont_PFCl_3, AC % change at T1 (vs. T0) was negatively correlated with semantic fluency (ρ = −0.7939, p = 0.045) and MC % change at T2 (vs. T0) was positively correlated with story memory (ρ = 0.7416, p = 0.045). Conclusions: HF-rTMS stimulation of DLFC nodes significantly affects the controllability of the functional connectome in MCI patients. Emerging correlations between AC/MC controllability and cognitive performance changes, immediately (T1 vs. T0) and six months (T2 vs. T0) after treatment, suggest NCT could help explain the HF-rTMS impact on prefrontal-lateral control network, monitoring induced neural plasticity effects in MCI patients. Full article

We propose a new methodology to transform a time series into an ordered sequence of any entropic and information functionals, providing a novel tool for data analysis. To achieve this, a new algorithm has been designed to optimize the Probability Density Function (PDF) associated with a time signal in the context of non-parametric Kernel Density Estimation (KDE). We illustrate the applicability of this method for anomaly detection in time signals. Specifically, our approach combines a non-parametric kernel density estimator with overlapping windows of various scales. Regarding the parameters involved in the KDE, it is well-known that bandwidth tuning is crucial for the kernel density estimator. To optimize it for time-series data, we introduce an adaptive solution based on Jensen–Shannon divergence, which adjusts the bandwidth for each window length to balance overfitting and underfitting. This solution selects unique bandwidth parameters for each window scale. Furthermore, it is implemented offline, eliminating the need for online optimization for each time-series window. To validate our methodology, we designed a synthetic experiment using a non-stationary signal generated by the composition of two stationary signals and a modulation function that controls the transitions between a normal and an abnormal state, allowing for the arbitrary design of various anomaly transitions. Additionally, we tested the methodology on real scalp-EEG data to detect epileptic crises. The results show our approach effectively detects and characterizes anomaly transitions. The use of overlapping windows at various scales significantly enhances detection ability, allowing for the simultaneous analysis of phenomena at different scales. Full article