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This article extends recent asymptotic theory developed for the Hodrick Prescott (HP) filter and boosted HP (bHP) filter to long-range dependent time series that have fractional Brownian motion (fBM) limit processes after suitable standardization. Under general conditions, it is shown that the asymptotic form of the HP filter is a smooth curve, analogous to the finding in Phillips and Jin for integrated time series and series with deterministic drifts. Boosting the filter using the iterative procedure suggested in Phillips and Shi leads under well-defined rate conditions to a consistent estimate of the fBM limit process or the fBM limit process with an accompanying deterministic drift when that is present. A stopping criterion is used to automate the boosting algorithm, giving a data-determined method for practical implementation. The theory is illustrated in simulations and two real data examples that highlight the differences between simple HP filtering and the use of boosting. The analysis is assisted by employing a uniformly and almost surely convergent trigonometric series representation of fBM. [ABSTRACT FROM AUTHOR]

In this article, we study a common break point in means for panel data with cross‐sectional dependence through unobservable common factors, in which the observations are long‐range dependent over time and are heteroscedastic and may have different degrees of dependence across panels. First, we adopt the least squares method without taking the data features into account to estimate the common break point and to see how the data features affect the asymptotic behaviors of the estimator. Then, an iterative least squares estimator of the common break point which accounts for the common factors in the estimation procedure is examined. Our theoretical results reveal that: (1) There is a trade‐off between the overall break magnitude of the panel data and the long‐range dependence for both estimators. (2) The second estimation procedure can eliminate the effects of common factors from the asymptotic behaviors of the estimator successfully, but it cannot improve the rate of convergence of the estimator in most cases. Moreover, Monte Carlo simulations are given to illustrate the theoretical results on finite‐sample performance. [ABSTRACT FROM AUTHOR]

Fractional Brownian motion has become a standard tool to address long-range dependence in financial time series. However, a constant memory parameter is too restrictive to address different market conditions. Here, we model the price fluctuations using a multifractional Brownian motion assuming that the Hurst exponent is a time-deterministic function. Through the multifractional Itô calculus, both the related transition density function and the analytical European Call option pricing formula are obtained. The empirical performance of the multifractional Black–Scholes model is tested by calibration of option market quotes for the SPX index and offers best fit than its counterparts based on standard and fractional Brownian motions. [ABSTRACT FROM AUTHOR]

Current research on human pose estimation often focuses on using complex structures to improve task accuracy, while overlooking resource consumption and inference speed during actual deployment. Based on the LitePose pose estimation architecture, this paper proposes a lightweight bottom-up pose estimation model, WLitePose, designed to better handle complex scenes. Specifically, to address the limitations of the MSE loss function, a heatmap weighted loss function is proposed to enable the model to focus more on the areas surrounding the true keypoint locations during training. To enhance the model's ability to handle variations in human scale, a lightweight deconvolution module is used after the main architecture to generate higher-resolution heatmaps. During the inference phase, heatmaps of different resolutions are aggregated. Additionally, the DFC-bottleneck block is proposed to enhance the backbone network's ability to capture long-range dependence between different spatial pixels. Experimental results on the COCO and CrowdPose datasets demonstrate that the proposed model achieves a good balance between task accuracy and computational complexity. [ABSTRACT FROM AUTHOR]

The valuation of equity-linked annuity (EIA) has been extensively studied, while few papers consider the impact of long-range dependence (LRD) features on financial and mortality dynamics in EIAs' valuation. To characterise the LRD feature, we adopt the fractional Brownian motion (FBM) in modelling the dynamics of asset prices and mortality intensities, in which clustering jumps are captured by the compound Hawkes process. Besides, the interest rate dynamic is driven by the FBM and correlates to the asset price dynamic. Numerical analyses show that ignorance of the LRD feature and the jump component in the modelling framework could lead to a potential deficiency in the reserve and solvency capital of EIA policies. [ABSTRACT FROM AUTHOR]

This study investigates the volatility of the Euro-to-US Dollar exchange rate, specifically focusing on identifying long-memory characteristics. Through the analysis of daily data spanning from January 1, 2018, to January 10, 2023, the study uncovers a robust long-memory feature. Supporting this exploration, the study endorses the use of sophisticated models such as Fractionally Integrated Generalized Autoregressive Conditionally Heteroskedastic (FIGARCH) and Hyperbolic Generalized Autoregressive Conditionally Heteroskedastic (HYGARCH), incorporating both student and skewed student innovation distributions. The results underscore the superior performance of FIGARCH and HYGARCH models, particularly when coupled with a skewed student distribution. This collaborative approach enhances the predictability of crucial financial metrics, including Value at Risk (VaR) and Expected Shortfall (ESF), for both long and short trading positions. Significantly, the FIGARCH model, when utilizing a skewed student distribution, demonstrates exceptional predictive power. This outcome challenges the efficient market hypothesis and suggests the potential for generating outstanding returns. In light of these findings, this research contributes valuable insights for comprehending and navigating the intricacies of the Euro-to-US Dollar exchange rate, providing a forward-looking perspective for financial practitioners and researchers alike. [ABSTRACT FROM AUTHOR]

We consider a class of stationary processes exhibiting both long-range dependence and heavy tails. Separate limit theorems for sums and for extremes have been established recently in the literature with novel objects appearing in the limits. In this article, we establish the joint sum-and-max limit theorems for this class of processes. In the finite-variance case, the limit consists of two independent components: a fractional Brownian motion arising from the sum and a long-range dependent random sup measure arising from the maximum. In the infinite-variance case, we obtain in the limit two dependent components: a stable process and a random sup measure whose dependence structure is described through the local time and range of a stable subordinator. For establishing the limit theorem in the latter case, we also develop a joint convergence result for the local time and range of subordinators, which may be of independent interest. [ABSTRACT FROM AUTHOR]

Fractional Brownian motion approximation of queueing networks has been studied extensively. In the existing results related to this topic, the Hurst parameter of multidimensional fractional Brownian motion is only a constant H (0 < H < 1). However, just as pointed out by many scholars and practitioners, various Hurst parameters may be more appropriate. On the other hand, as a multivariate extension of fractional Brownian motion, operator fractional Brownian motion has operator self-similarity, and the dependence structure across the components of it is determined by the Hurst matrix. Moreover, it has also many potential applications in queueing theory. Inspired by these facts, we consider a queueing network with ON/OFF sources, and show that the workload process can be approximated by a reflected operator fractional Brownian motion under a heavy traffic condition. With this fact, it is important to consider stationarity. However, except for some special cases, there is no literature related to this topic. In our work, we construct an explicit stationary process associated with a two-dimensional reflected operator fractional Brownian motion. [ABSTRACT FROM AUTHOR]

In the context of functional time series, we propose a significance test to distinguish between short memory with a change point and long range dependence. The test is based on coefficients of projections onto an optimal direction that captures the dependence structure of the latent stationary functions that are not observable due to a potential change point. The optimal direction must be estimated as well. The test statistic is constructed using the local Whittle estimator applied to these coefficients. It has standard normal distribution under the null hypothesis (change point) and diverges to infinity under the alternative (long range dependence). The article includes asymptotic theory, a simulation study and an application to curve‐valued time series derived from intraday asset prices. [ABSTRACT FROM AUTHOR]

Electromyographic (EMG) signals exhibit complex interference patterns that comprise several single motor unit action potentials (SMUAPs). Evidence of a model that can generate EMG signals and considers intrinsic characteristics, such as long-range dependence (LRD) or shortrange dependence (SRD), or that supports the study of pathology-related signals is lacking. Therefore, the present study aimed to develop an EMG signal generator based on SRD or LRD derived from firing patterns. We used a dynamic model to parameterize up to 15 SMUAP waveforms of real EMG signals extracted from a database. Then, we used relative appearance rates for some signals based on the number of SMUAPs to generate the latter randomly. Furthermore, we complemented our model by generating a random firing pattern. The synthetic reconstruction of the signals indicated a displacement compared with their respective firing patterns, with the highest error rate being 4.1%. The model of the EMG signal generator in its current state could be useful for a specialist who intends to study the behavior of the signals, starting with the exploration of synthetic signals and then proceeding to the real signals. [ABSTRACT FROM AUTHOR]

We consider fractional integral operators (I − T) d , d ∈ (− 1 , 1) acting on functions g : Z ν → R , ν ≥ 1 , where T is the transition operator of a random walk on Z ν . We obtain the sufficient and necessary conditions for the existence, invertibility, and square summability of kernels τ (s ; d) , s ∈ Z ν of (I − T) d . The asymptotic behavior of τ (s ; d) as | s | → ∞ is identified following the local limit theorem for random walks. A class of fractionally integrated random fields X on Z ν solving the difference equation (I − T) d X = ε with white noise on the right-hand side is discussed and their scaling limits. Several examples, including fractional lattice Laplace and heat operators, are studied in detail. [ABSTRACT FROM AUTHOR]

We consider INAR(1) processes modulated by an unobserved strongly dependent 0 - 1 process. The observed process exhibits zero inflation and long memory. A simple method is proposed for estimating the INAR-parameters without modelling the unobserved modulating process. Asymptotic results for the estimators are derived, and a zero-inflation test is introduced. Asymptotic rejection regions and asymptotic power under long-memory alternatives are derived. A small simulation study illustrates the asymptotic results. [ABSTRACT FROM AUTHOR]

In the power system, failure interruption hugely compromises the power system reliability. Therefore, an efficient method to correctly predict how long the power outage last would significantly improve the efficiency. To address this problem, we propose a method based on a suitable stochastic motion. First, we introduce linear multifractional Lévy stable motion (LMLSM). Then, by computing the global and local fractal characteristics we show that the LMLSM is multifractal and possesses the long-range dependence (LRD) property. Besides, the non-Gaussian characteristics of the LMLSM are analyzed, which means it can better describe the constant peak values in the stochastic time series. Furthermore, a discrete iterative prediction model is derived with fractional Black-Scholes differential equation. At last, a case study is provided based on the real failure interruption duration (FID) dataset in the power grid, by illustrating the validity of the proposed prediction method for power grid reliability. • A prediction method of power outage length is provided. • A multifractal model is derived to describe the local irregularity of the multifractal Levy stable motion. • The expression of the increment distribution of the multifractal Levy stable motion is derived. • Compared with existing models of time series prediction model, the prediction accuracy is better. [Display omitted] [ABSTRACT FROM AUTHOR]

Reflection in the image not only significantly reduces the image quality, but also seriously affects the subsequent computer vision tasks. So proposed a single image reflection removal cascaded algorithm using non local correlation and contrast constraint. This algorithm utilizes a dual-branch approach for LSTM-based information propagation across cascades. It employs reflection and background features to complement each other and iteratively refine prediction accuracy, ensuring mutual enhancement of the two branches' prediction results. To facilitate training for multiple cascade steps, a positivenegative contrastive regularization loss is introduced. This loss treats background images and original images' features as positive and negative samples, respectively. This ensures that the target image is brought closer to the background image while moving away from the original image in the representation space, narrowing the prediction range and effectively alleviating the ill-posed problem. Additionally, an efficient, low-computational-cost non-local correlation prediction module is proposed, capable of capturing contextual information for all pixels along cross paths. Through further cascade operations, each pixel captures long-distance dependencies across the entire image, enabling the use of surrounding point information to predict background information obscured by strong reflections. Experimental results demonstrate that, compared to current algorithms, the proposed algorithm achieves superior results and exhibits robust performance. [ABSTRACT FROM AUTHOR]

Understanding the long-range dependence and self-similarity of global sea surface chlorophyll concentration (SSCC) will enrich its characteristics description and analysis with global change patterns. The satellite SSCC products were collected from the European Space Agency during the period from 29 July 1998 to 31 December2020. After resampling the SSCC products into the spatial resolution of 1°, the missing values were interpolated by Bayesian maximum entropy with mean absolute error of cross validation equaling to 0.1295 mg/m[sup 3]. Generalized Cauchy model was employed to quantitatively determine the long-range dependence and self-similarity of SSCC at a global scale by using the Hurst parameter and fractal dimension. Good fitted results were achieved with an averaged R[sup 2] of 0.9141 and a standard deviation of 0.0518 across the 32,281 spatial locations of the entire ocean; the averaged values of Hurst parameter and fractal dimension were 0.8667 and 1.2506, respectively, suggesting strong long-range dependence and weak self-similarity of SSCC in the entire oceans. Univariate and multivariate generalized addictive models (GAM) were introduced to depict the influence of sea surface height anomaly, sea surface salinity, sea surface temperature and sea surface wind on the Hurst parameter and fractal dimension of SSCC; and smaller mean absolute error were achieved for the GAM of Hurst parameter than that of fractal dimension. Sea surface height anomaly showed the strongest influence for the Hurst parameter than the other three factors, and sea surface wind depicted similar influence; the sea surface temperature owned opposite influence on Hurst parameter compared to sea surface salinity. [ABSTRACT FROM AUTHOR]

Roller bearing degradation features fractal characteristics such as self-similarity and long-range dependence (LRD). However, the existing remaining useful life (RUL) prediction models are memoryless or short-range dependent. To this end, we propose a RUL prediction model based on fractional Brownian motion (FBM). Bearing faults can happen in different places, and thus their degradation features are difficult to extract accurately. Through variational mode decomposition (VMD), the original degradation feature is decomposed into several components of different frequencies. The monotonicity, robustness and trends of the different components are calculated. The frequency component with the best metric values is selected as the training data. In this way, the performance of the prediction model is hugely improved. The unknown parameters in the degradation model are estimated by the maximum likelihood algorithm. The Monte Carlo method is applied to predict the RUL. A case study of a bearing is presented and the prediction performance is evaluated using multiple indicators. [ABSTRACT FROM AUTHOR]

We propose a new time series model called Rational Gaussian Noise (rGn) to describe a pattern of long-range dependence. The rGn model is shown to be an extension of the traditional fractional Gaussian noise (fGn). Theoretical formulas such as autocorrelation function, and some properties of rGn are derived and compared to that of fGn. Transformed S&P500 daily excessive return data is used as a case study where parameters for both the rGn and fGn models are estimated. [ABSTRACT FROM AUTHOR]

To enhance the economic viability of wind energy in cold regions and ensure the safe operational management of wind farms, this paper proposes a short-term wind turbine blade icing wind power prediction method that combines principal component analysis (PCA) and fractional Lévy stable motion (fLsm). By applying supervisory control and data acquisition (SCADA) data from wind turbines experiencing icing in a mountainous area of Yunnan Province, China, the model comprehensively considers long-range dependence (LRD) and self-similar features. Adopting a combined pattern of previous-day predictions and actual measurement data, the model predicts the power under near-icing conditions, thereby enhancing the credibility and accuracy of icing forecasts. After validation and comparison with other prediction models (fBm, CNN-Attention-GRU, XGBoost), the model demonstrates a remarkable advantage in accuracy, achieving an accuracy rate and F1 score of 96.86% and 97.13%, respectively. This study proves the feasibility and wide applicability of the proposed model, providing robust data support for reducing wind turbine efficiency losses and minimizing operational risks. [ABSTRACT FROM AUTHOR]

Understanding the long-range dependence and self-similarity of global sea surface chlorophyll concentration (SSCC) will enrich its characteristics description and analysis with global change patterns. The satellite SSCC products were collected from the European Space Agency during the period from 29 July 1998 to 31 December2020. After resampling the SSCC products into the spatial resolution of 1°, the missing values were interpolated by Bayesian maximum entropy with mean absolute error of cross validation equaling to 0.1295 mg/m3. Generalized Cauchy model was employed to quantitatively determine the long-range dependence and self-similarity of SSCC at a global scale by using the Hurst parameter and fractal dimension. Good fitted results were achieved with an averaged R2 of 0.9141 and a standard deviation of 0.0518 across the 32,281 spatial locations of the entire ocean; the averaged values of Hurst parameter and fractal dimension were 0.8667 and 1.2506, respectively, suggesting strong long-range dependence and weak self-similarity of SSCC in the entire oceans. Univariate and multivariate generalized addictive models (GAM) were introduced to depict the influence of sea surface height anomaly, sea surface salinity, sea surface temperature and sea surface wind on the Hurst parameter and fractal dimension of SSCC; and smaller mean absolute error were achieved for the GAM of Hurst parameter than that of fractal dimension. Sea surface height anomaly showed the strongest influence for the Hurst parameter than the other three factors, and sea surface wind depicted similar influence; the sea surface temperature owned opposite influence on Hurst parameter compared to sea surface salinity.

Remaining useful life prediction guarantees a reliable and safe operation of turbofan engines. Long-range dependence (LRD) and heavy-tailed characteristics of degradation modeling make this method advantageous for the prediction of RUL. In this study, we propose fractional Lévy stable motion for degradation modeling. First, we define fractional Lévy stable motion simulation algorithms. Then, we demonstrate the LRD and heavy-tailed property of fLsm to provide support for the model. The proposed method is validated with the C-MAPSS dataset obtained from the turbofan engine. Principle components analysis (PCA) is conducted to extract sources of variance. Experimental data show that the predictive model based on fLsm with exponential drift exhibits superior accuracy relative to the existing methods. [ABSTRACT FROM AUTHOR]

In this paper, a fractional Weibull process is utilized in a predictive stochastic differential equation model to allow for skewness and heavy-tailed characteristics. To this aim, a fractional Weibull process with non-Gaussian characteristics and a long memory effect is proposed to drive the predictive stochastic differential equation. The difference iterative forecasting model is proposed as its stochastic difference scheme. The consistency, stability, and convergence of the model are analyzed. In the proposed model, variational mode decomposition is utilized as the data preprocessing approach to separate the stationary and non-stationary components. Actual wind speed data and stock price data are employed in two separate case studies. [ABSTRACT FROM AUTHOR]

We consider the Gaussian Volterra process X θ = { X θ (t) , t ∈ [ 0 , T ] } , θ = (α , β , γ) introduced in Mishura and Shklyar [Theory and Applications 2022a, 431–452] We specify the parameters θ for which X θ is non Markovian, semimartingale, and exhibits long-range dependence. Finally, by using its Paley–Wiener–Zygmund representation we establish its continuity in θ, uniformly in t. [ABSTRACT FROM AUTHOR]

We study the limit of fluctuations of the rescaled occupation time process of a branching particle system in Rd, where the particles are subject to symmetric a-stable migration (0 < a = 2), critical binary branching, and general non-lattice lifetime distribution. We focus on two different regimes: lifetime distributions having finite expectation, and Pareto-type lifetime distributions, i.e. distributions belonging to the normal domain of attraction of a γ-stable law with γ ∈ (0, 1). In the latter case we show that, for dimensions aγ < d < a(1 + γ), the fluctuations of the rescaled occupation time converge weakly to a centered Gaussian process whose covariance function is explicitly calculated, and we call it weighted sub-fractional Brownian motion. Moreover, in the case of lifetimes with finite mean, we show that for a < d < 2a the fluctuation limit turns out to be the same as in the case of exponentially distributed lifetimes studied by Bojdecki et al. (2004, 2006a,b). We also investigate the maximal parameter range allowing existence of the weighted sub-fractional Brownian motion and provide some of its fundamental properties, such as path continuity, long-range dependence, self-similarity and the lack of Markov property. [ABSTRACT FROM AUTHOR]

The paper investigates long memory, structural breaks, and spurious long memory in the daily trading volume of the largest and most active cryptocurrencies and stablecoins, namely, Bitcoin, Ethereum, Tether, USD coin, Binance coin, Binance USD, Ripple, Cardano, Solana, Dogecoin and Bitcoin cash. The overall results show that both long memory and structural breaks are present in the cryptocurrencies trading volume, and the detected long memory property is not driven by structural breaks but rather true and thus not spurious. Given this, we conduct out-of-sample forecasting and indicate that the ARFIMA model, which accounts for long-range dependence, has a superior forecasting performance over the standard ARIMA model for four cryptocurrencies, namely, Binance coin, Ripple, Cardano, and Dogecoin at most forecasting horizons ahead and the shorter forecasting horizon (1-day ahead) for most cryptocurrencies under investigation. [ABSTRACT FROM AUTHOR]

The so-called multi-mixed fractional Brownian motions (mmfBm) and multi-mixed fractional Ornstein–Uhlenbeck (mmfOU) processes are studied. These processes are constructed by mixing by superimposing or mixing (infinitely many) independent fractional Brownian motions (fBm) and fractional Ornstein–Uhlenbeck processes (fOU), respectively. Their existence as ${L^{2}}$ processes is proved, and their path properties, viz. long-range and short-range dependence, Hölder continuity, p-variation, and conditional full support, are studied.

In this paper we discuss the details, limitations, and difficulties of the implementation in hardware of a memristor-based random number generator that exhibits monofractal/multifractal behavior. To do so, the components and selection criteria of a reference memristor and one proposed by the authors, the chaotic circuit leveraging them, and the processing that is performed on the chaotic signals to achieve the random discrete sequences are described. After applying the estimation tools, findings indicate that more than 60% of the proposed combinations allow generating random discrete sequences, with long-range dependence, and that both monofractal and multifractal behaviors can also be obtained. Consequently, a hardware system was achieved that can be used as a source of entropy in future synthetic biological signal generators.

The authors consider a class of periodogram estimates of unknown parameters of the nonlinear regression model "signal plus noise" and prove asymptotic normality, provided that the regression function is almost periodic, and the noise is a functional of a strongly dependent Gaussian random process. [ABSTRACT FROM AUTHOR]

In this article, one class of periodogram estimates of unknown parameters of the nonlinear regression model “signal plus noise” is considered. The asymptotic normality is proved, provided that the regression function is almost periodic, and the noise is a functional of a strongly dependent Gaussian random process. [ABSTRACT FROM AUTHOR]

We study the large deviation behaviors of a stochastic fluid queue with an input being a generalized Riemann–Liouville (R–L) fractional Brownian motion (FBM), referred to as GFBM. The GFBM is a continuous mean-zero Gaussian process with non-stationary increments, extending the standard FBM with stationary increments. We first derive the large deviation principle for the GFBM by using the weak convergence approach. We then obtain the large deviation principle for the stochastic fluid queue with the GFBM as the input process as well as for an associated running maximum process. Finally, we study the long-time behavior of these two processes; in particular, we show that a steady-state distribution exists and derives the exact tail asymptotics using the aforementioned large deviation principle together with some maximal inequality and modulus of continuity estimates for the GFBM. [ABSTRACT FROM AUTHOR]

The so-calledmulti-mixed fractional Brownianmotions (mmfBm) and multi-mixed fractional Ornstein--Uhlenbeck (mmfOU) processes are studied. These processes are constructed by mixing by superimposing or mixing (infinitely many) independent fractional Brownian motions (fBm) and fractional Ornstein--Uhlenbeck processes (fOU), respectively. Their existence as L² processes is proved, and their path properties, viz. long-range and short-range dependence, Hölder continuity, p-variation, and conditional full support, are studied. [ABSTRACT FROM AUTHOR]

The generalized mixed fractional Brownian motion (gmfBm) is a Gaussian process with stationary increments that exhibits long-range dependence controlled by its Hurst indices. It is defined by taking linear combinations of a finite number of independent fractional Brownian motions with different Hurst indices. In this paper, we investigate the long-time behavior of gmfBm when it is time-changed by a tempered stable subordinator or a gamma process. As a main result, we show that the time-changed process exhibits a long-range dependence property under some conditions on the Hurst indices. The time-changed gmfBm can be used to model natural phenomena that exhibit long-range dependence, even when the underlying process is not itself long-range dependent. [ABSTRACT FROM AUTHOR]

We consider a change-point test based on the Hill estimator to test for structural changes in the tail index of long memory stochastic volatility time series. In order to determine the asymptotic distribution of the corresponding test statistic, we prove a uniform reduction principle for the tail empirical process in a two-parameter Skorohod space. It is shown that such a process displays a dichotomous behavior according to an interplay between the Hurst parameter, that is, a parameter characterizing the dependence in the data, and the tail index. Our theoretical results are accompanied by simulation studies and an analysis of financial time series with regard to structural changes in the tail index. [ABSTRACT FROM AUTHOR]

In this article, we show that the nth-order fractional Brownian motions (fBm) introduced by Perrin et al. are non Markovian special semimartingales. Their infinite mixtures are also presented and shown to be semimartingales satisfying mixed self-similarity property and accounting for long-range dependence phenomena. As result, they are alternative to mixed fBm in modeling stock prices in arbitrage-free financial markets. [ABSTRACT FROM AUTHOR]

Knowable moments, abbreviated as K-moments, are redefined as expectations of maxima or minima of a number of stochastic variables that are a sample of the variable of interest. The new definition enables applicability of the concept to any type of variable, continuous or discrete, and generalization for transformations thereof. While K-moments share some characteristics with classical and other moments, as well as with order statistics, they also have some unique features, which make them useful in relevant applications. These include the fact that they are knowable, i.e., reliably estimated from a sample for high orders. Moreover, unlike other moment types, K-moment values can be assigned values of distribution function by making optimal use of the entire dataset. In addition, K-moments offer the unique advantage of considering the estimation bias when the data are not an independent sample but a time series from a process with dependence. Both for samples and time series, the K-moment concept offers a strategy of model fitting, including its visualization, that is not shared with other methods. This enables utilization of the highest possible moment orders, which are particularly useful in modelling extremes that are closely associated with high-order moments. [ABSTRACT FROM AUTHOR]

Automated anomaly detection is the prerequisite to minimize human errors and costs caused by manual inspection. Recently, image-based anomaly detections have gained more attention by widely adopting machine vision systems and computer-aided detections. We propose a classification method using spectral features based on 2D discrete wavelet packet transform under the hierarchical structure of wavelet energies. By capturing the self-similar and long-range dependent characteristics of 2D fractional Brownian field (fBf), wavelet packet spectra are derived to construct a linear model representing the relationship between wavelet energies and resolution levels. 2D DWPT-based energy features effectively preserve irregular oscillations in original images at high-frequency domains as well as at low-frequency domains under a pyramidal structure. In comparison with the existing 2D discrete wavelet transform method, the proposed method shows a potential in efficiently classifying normal and abnormal image data in a numerical example and a real industrial application. [ABSTRACT FROM AUTHOR]

We prove existence and uniqueness for the solution of a class of mixed fractional stochastic differential equations with discontinuous drift driven by both standard and fractional Brownian motion. Additionally, we establish a generalized Itô rule valid for functions with an absolutely continuous derivative and applicable to solutions of mixed fractional stochastic differential equations with Lipschitz coefficients, which plays a key role in our proof of existence and uniqueness. The proof of such a formula is new and relies on showing the existence of a density of the law under mild assumptions on the diffusion coefficient. [ABSTRACT FROM AUTHOR]

Lane detection is a common task in computer vision that involves identifying the boundaries of lanes on a road from an image or a video. Improving the accuracy of lane detection is of great help to advanced driver assistance systems and autonomous driving that help cars to identify and keep in the correct lane. Current high-accuracy models of lane detection are mainly based on artificial neural networks. Among them, CLRNet is the latest famous model, which attains high lane detection accuracy. However, in some scenarios, CLRNet attains lower lane detection accuracy, and we revealed that this is caused by insufficient global dependence information. In this study, we enhanced CLRNet and proposed a new model called NonLocal CLRNet (NLNet). NonLocal is an algorithmic mechanism that captures long-range dependence. NLNet employs NonLocal to acquire more long-range dependence information or global information and then applies the acquired information to a Feature Pyramid Network (FPN) in CLRNet for improving lane detection accuracy. Using the CULane dataset, we trained NLNet. The experimental results showed that NLNet outperformed state-of-the-art models in terms of accuracy in most scenarios, particularly in the no-line scenario and night scenario. This study is very helpful for developing more accurate lane detection models. [ABSTRACT FROM AUTHOR]

Recently, the growth of blockchain technology and the economic benefits of cryptocurrencies have led to a proliferation of malicious cryptomining activities on the internet, resulting in significant losses for companies and institutions. Therefore, accurately detecting and identifying these behaviors has become essential. To address low accuracy in detecting and identifying cryptomining behaviors in encrypted traffic, a technique for identifying cryptomining behavior traffic is proposed. This technique is based on the time series characteristics of network traffic and introduces the feature of long-range dependence, and the recognition effect is not easily affected by the encryption algorithm. First, 48-dimensional features are extracted from the network traffic using statistical methods and the rescaled range method, of which 47 dimensions are statistical features and 1 dimension is a long-range dependence feature. Second, because there is much less cryptomining traffic information than normal network traffic information in the dataset, the dataset is processed using oversampling to make the two types of traffic data balanced. Finally, a random forest model is used to identify the type of traffic based on its features. Experiments demonstrate that this approach achieves good detection performance and provides an effective solution for identifying encrypted network traffic with malicious cryptomining behavior. The long-range dependence features introduced therein together with the statistical features describe a more comprehensive flow characteristics, and the preprocessing of the dataset improves the performance of the identification model.

Hydroclimatic processes such as precipitation, temperature, wind speed and dew point are usually considered to be independent of each other. In this study, the cross–correlations between key hydrological-cycle processes are examined, initially by conducting statistical tests, then adding the impact of long-range dependence, which is shown to govern all these processes. Subsequently, an innovative stochastic test that can validate the significance of the cross–correlation among these processes is introduced based on Monte-Carlo simulations. The test works as follows: observations obtained from numerous global-scale timeseries were used for application to, and a comparison of, the traditional methods of validation of statistical significance, such as the t-test, after filtering the data based on length and quality, and then by estimating the cross–correlations on an annual-scale. The proposed method has two main benefits: it negates the need of the pre-whitening data series which could disrupt the stochastic properties of hydroclimatic processes, and indicates tighter limits for upper and lower boundaries of statistical significance when analyzing cross–correlations of processes that exhibit long-range dependence, compared to classical statistical tests. The results of this analysis highlight the need to acquire cross–correlations between processes, which may be significant in the case of long-range dependence behavior.

We examine the impact of the Bank of Japan's exchange traded fund (ETF) purchases on two aspects of market efficiency—long-range dependence and price delay—of the TOPIX and Nikkei 225 indices. An increase in ETF purchases results in lower long-range dependence for both indices while the impact on the price delay varies according to index and measure. A sub-period analysis shows that the impact on market efficiency varies over time, with the dominant pattern being a delayed harmful effect, followed by a positive impact and thereafter a negative effect. The implications of these findings are discussed. [ABSTRACT FROM AUTHOR]

In this paper, an adaptive remaining useful life prediction model is proposed for electric vehicle lithium batteries. Capacity degradation of the electric car lithium batteries is modeled by the multi-fractal Weibull motion. The varying degree of long-range dependence and the 1/f characteristics in the frequency domain are also analyzed. The age and state-dependent degradation model is derived, with the associated adaptive drift and diffusion coefficients. The adaptive mechanism considers the quantitative relations between the drift and diffusion coefficients. The unit-to-unit variability is considered a random variable. To facilitate the application, the convergence of the RUL prediction model is proved. Replacement of the lithium battery in the electric car is recommended according to the remaining useful life prediction results. The effectiveness of the proposed model is shown in the case study. [ABSTRACT FROM AUTHOR]

This paper investigates the time-consistent mean-variance reinsurance-investment (RI) problem faced by life insurers. Inspired by recent findings that mortality rates exhibit long-range dependence (LRD), we examine the effect of LRD on RI strategies. We adopt the Volterra mortality model proposed in Wang et al. [(2021). Volterra mortality model: actuarial valuation and risk management with long-range dependence. Insurance: Mathematics and Economics96, 1–14] to incorporate LRD into the mortality rate process and describe insurance claims using a compound Poisson process with intensity represented by the stochastic mortality rate. Under the open-loop equilibrium mean-variance criterion, we derive explicit equilibrium RI controls and study the uniqueness of these controls in cases of constant and state-dependent risk aversion. We simultaneously resolve difficulties arising from unbounded non-Markovian parameters and sudden increases in the insurer's wealth process. While the exiting literature suggests that LRD has a significant effect on longevity hedging, we find that reinsurance is a risk management strategy that is robust to LRD. [ABSTRACT FROM AUTHOR]

In this paper, a new concept for some stochastic process called fractional G-Brownian motion (fGBm) is developed. The fGBm can exhibit long-range dependence and consider volatility uncertainty simultaneously, compared to the standard Brownian motion, fractional Brownian motion and G-Brownian motion. Thus it generalizes the concepts of the latter three processes, and can be a better alternative stochastic process in real applications. The existence, representation and some intrinsic properties for the fGBm are discussed, and some partial differential equations related to fGBm are also present. Finally, some numerical simulations for the distributions of G-normally distributed random variable and sample paths of fGBm are carried out, which shows that fGBm can be better to describe the amplitudes of the randomness. [ABSTRACT FROM AUTHOR]