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Introduction: Functional magnetic resonance imaging (fMRI) has become a fundamental tool for studying brain function. However, the presence of serial correlations in fMRI data complicates data analysis, violates the statistical assumptions of analyses methods, and can lead to incorrect conclusions in fMRI studies. Methods: In this paper, we show that conventional whitening procedures designed for data with longer repetition times (TRs) (>2 s) are inadequate for the increasing use of short-TR fMRI data. Furthermore, we comprehensively investigate the shortcomings of existing whitening methods and introduce an iterative whitening approach named "IDAR" (Iterative Data-adaptive Autoregressivemodel) to address these shortcomings. IDAR employs high-order autoregressive (AR) models with flexible and data-driven orders, offering the capability to model complex serial correlation structures in both short-TR and long-TR fMRI datasets. Results: Conventional whiteningmethods, such as AR(1), ARMA(1,1), and higher-order AR, were effective in reducing serial correlation in long-TR data but were largely ineffective in even reducing serial correlation in short-TR data. In contrast, IDAR significantly outperformed conventional methods in addressing serial correlation, power, and Type-I error for both long-TR and especially short-TR data. However, IDAR could not simultaneously address residual correlations and inflated Type-I error effectively. Discussion: This study highlights the urgent need to address the problem of serial correlation in short-TR (<1 s) fMRI data, which are increasingly used in the field. Although IDAR can address this issue for a wide range of applications and datasets, the complexity of short-TR data necessitates continued exploration and innovative approaches. These efforts are essential to simultaneously reduce serial correlations and control Type-I error rates without compromising analytical power. [ABSTRACT FROM AUTHOR]

Independent vector analysis (IVA) can be viewed as an extension of independent component analysis (ICA) to multiple datasets. It exploits the statistical dependency between different datasets through mutual information. In the context of motor imagery classification based on electroencephalogram (EEG) signals for the brain–computer interface (BCI), several methods have been proposed to extract features efficiently, mainly based on common spatial patterns, filter banks, and deep learning. However, most methods use only one dataset at a time, which may not be sufficient for dealing with a multi-source retrieving problem in certain scenarios. From this perspective, this paper proposes an original approach for feature extraction through multiple datasets based on IVA to improve the classification of EEG-based motor imagery movements. The IVA components were used as features to classify imagined movements using consolidated classifiers (support vector machines and K-nearest neighbors) and deep classifiers (EEGNet and EEGInception). The results show an interesting performance concerning the clustering of MI-based BCI patients, and the proposed method reached an average accuracy of 86.7 % . [ABSTRACT FROM AUTHOR]

Each states play pivotal roles in contributing to the economic performance of the nation. They have their own unique economic strengths, resources, and industries that contribute to the overall economic development. Terengganu, an east coast state in Malaysia has historically faced economic challenges, marked by a lag in development compared to other regions. The fundamental problem addressed is the potential correlation between educational attainment and the region's economic growth, aiming to understand how advancements in education might serve as a catalyst for economic progress. The objective of this research is to empirically analyze the impact of educational achievement on the economic development in Terengganu. Utilizing secondary data sourced from the Department of Statistics Malaysia and Economy Planning Unit Terengganu spanning from 2006 to 2022, Autoregressive Distributed Lag (ARDL) model has been employed to estimate and understand the relationship between educational attainment and economic development. The findings suggested that educational achievement plays positive impact in heightening the economic development within the region. Education contributes to the development of human capital, fostering a skilled and knowledgeable populace capable of engaging in diverse economic activities. This, in turn, attracts investments and facilitates the emergence of industries and sectors that rely on a knowledgeable and skilled labour force. This study would provide valuable insights for policymakers and academicians to formulate targeted policies and initiatives, ultimately enhancing the economic development of the states, thus contribute to a prosperous Malaysia. [ABSTRACT FROM AUTHOR]

Power conversion systems for wireless power transfer (WPT) applications have demanding requirements for continuity of service, besides being operated with stressing environmental conditions. Diagnostic and prognostic programs are thus quite useful and this work shows a novel approach based on the analysis of spectra of an autoregressive (AR) model to recognize a wide range of faulty devices, including incipient faults, when deviations from nominal parameters begin to manifest. AR modeling provides cleaner and easier to interpret spectra, where only the salient features remain, and they are more sensitive to variations in the corresponding time domain waveforms. A log spectral distance is calculated that successfully separates healthy and faulty states of the feeding single-phase inverter, even in challenging scenarios of poor signal-to-noise ratio. [ABSTRACT FROM AUTHOR]

Diagnostic checking is an important predefined step before using autoregressive models. Although many portmanteau tests were proposed for diagnostic checking, they still struggle with the issue of significant size distortion. In this paper, we develop new diagnostic checking methods based on jackknife empirical likelihood. It is demonstrated that the suggested testing statistics asymptotically have a typical chi-squared distribution. To verify the performance of the finite sample, some simulations are constructed. Additionally, a real example of five agricultural futures is provided to illustrate the merits of our diagnostic checking procedure. [ABSTRACT FROM AUTHOR]

This paper proposes a novel censored autoregressive conditional Fréchet (CAcF) model with a flexible evolution scheme for the time-varying parameters, which allows deciphering tail risk dynamics constrained by price limits from the viewpoints of different risk preferences. The proposed model can well accommodate many important empirical characteristics of financial data, such as heavy-tailedness, volatility clustering, extreme event clustering, and price limits. We then investigate tail risk dynamics via the CAcF model in the price-limited stock markets, taking entropic value at risk (EVaR) as a risk measurement. Our findings suggest that tail risk will be seriously underestimated in price-limited stock markets when the censored property of limit prices is ignored. Additionally, the evidence from the Chinese Taiwan stock market shows that widening price limits would lead to a decrease in the incidence of extreme events (hitting limit-down) but a significant increase in tail risk. Moreover, we find that investors with different risk preferences may make opposing decisions about an extreme event. In summary, the empirical results reveal the effectiveness of our model in interpreting and predicting time-varying tail behaviors in price-limited stock markets, providing a new tool for financial risk management. [ABSTRACT FROM AUTHOR]

Uncertain time series models constitute a pivotal tool for analyzing phenomena evolving over time. However, most of the prevailing research centers on parameter models, which exhibit limitations in addressing intricate temporal dynamics. To address this gap, this paper introduces a non-parametric uncertain time series model. Primarily, we propose the definition of the non-parametric uncertain time series models. Subsequently, tailored to the non-parametric uncertain additive autoregressive model, we propose a non-parametric estimation method based on linear polynomial splines. Following this, the effectiveness of these estimations is verified through residual analysis and uncertain hypothesis tests. Finally, we apply the introduced non-parametric estimation approach to the Brent crude oil spot price. [ABSTRACT FROM AUTHOR]

It has long been an open problem to provide a unified test for the intercept of autoregressive (AR) models. In this paper, we use the empirical likelihood method to solve this issue. It turns out that the resulting test statistic always converges in distribution to a standard chi-squared distribution under the null hypothesis, whether the AR process is stationary or nonstationary, and with or without an intercept. The asymptotic distribution under the local alternative hypothesis is also derived under some mild conditions. Several simulations as well as a real data example are used to show how well the suggested test performs in terms of size and power on a finite sample. [ABSTRACT FROM AUTHOR]

Vector autoregressive (VAR) modelling is widely employed in psychology for time series analyses of dynamic processes. However, the typically short time series in psychological studies can lead to overfitting of VAR models, impairing their predictive ability on unseen samples. Cross‐validation (CV) methods are commonly recommended for assessing the predictive ability of statistical models. However, it is unclear how the performance of CV is affected by characteristics of time series data and the fitted models. In this simulation study, we examine the ability of two CV methods, namely,10‐fold CV and blocked CV, in estimating the prediction errors of three time series models with increasing complexity (person‐mean, AR, and VAR), and evaluate how their performance is affected by data characteristics. We then compare these CV methods to the traditional methods using the Akaike (AIC) and Bayesian (BIC) information criteria in their accuracy of selecting the most predictive models. We find that CV methods tend to underestimate prediction errors of simpler models, but overestimate prediction errors of VAR models, particularly when the number of observations is small. Nonetheless, CV methods, especially blocked CV, generally outperform the AIC and BIC. We conclude our study with a discussion on the implications of the findings and provide helpful guidelines for practice. [ABSTRACT FROM AUTHOR]

In this article, the M-estimator of the moderate deviations from a unit root model with possibly infinite variance errors is proposed. When the autoregressive coefficients are located on both sides of stationary and explosion, the asymptotic normal properties of the corresponding estimators for unknown parameters are proved, respectively. The asymptotic properties of the M-estimators are obtained in both the mildly integrated case and the mildly explosive case. [ABSTRACT FROM AUTHOR]

Since OpenAI opened access to ChatGPT, large language models (LLMs) become an increasingly popular topic attracting researchers' attention from abundant domains. However, public researchers meet some problems when developing LLMs given that most of the LLMs are produced by industries and the training details are typically unrevealed. Since datasets are an important setup of LLMs, this paper does a holistic survey on the training datasets used in both the pre-train and fine-tune processes. The paper first summarizes 16 pre-train datasets and 16 fine-tune datasets used in the state-of-the-art LLMs. Secondly, based on the properties of the pre-train and fine-tune processes, it comments on pre-train datasets from quality, quantity, and relation with models, and comments on fine-tune datasets from quality, quantity, and concerns. This study then critically figures out the problems and research trends that exist in current LLM datasets. The study helps public researchers train and investigate LLMs by visual cases and provides useful comments to the research community regarding data development. To the best of our knowledge, this paper is the first to summarize and discuss datasets used in both autoregressive and chat LLMs. The survey offers insights and suggestions to researchers and LLM developers as they build their models, and contributes to the LLM study by pointing out the existing problems of LLM studies from the perspective of data. [ABSTRACT FROM AUTHOR]

Social relations models allow the identification of cluster, actor, partner, and relationship effects when analysing clustered dyadic data on interactions between individuals or other units of analysis. We propose an extension of this model which handles longitudinal data and incorporates dynamic structure, where the response may be continuous, binary, or ordinal. This allows the disentangling of the relationship effects from temporal fluctuation and measurement error and the investigation of whether individuals respond to their partner's behaviour at the previous observation. We motivate and illustrate the model with an application to Canadian data on pairs of individuals within families observed working together on a conflict discussion task. [ABSTRACT FROM AUTHOR]

Control charts are one of the most frequently used tools in statistical process control. They are used to monitor, measure, regulate, improve quality, and identify issues in processes across a variety of industries. The modified exponentially weighted moving average (MEWMA) control chart is frequently used to detect early shifts in the process. Herein, the aim of this study is to adjust a modified exponentially weighted moving average (MEWMA) control chart and derive the explicit formula of the ARL for the autoregressive with trend and quadratic trend models with exponential white noise. The results of the numerical integral equation (NIE) technique and the ARLs produced with the explicit formula were compared. Findings indicated that, in terms of calculation time, the explicit formula using the ARL defeated the NIE technique. The performance of the traditional EWMA, MEWMA, and adjusted MEWMA control charts based on simulation and real-world data was compared using the average run length (ARL) and the standard deviation run length (SDRL). These findings were confirmed by the average extra-quadratic loss (AEQL). Lastly, real-world data on stock prices from Thailand's SET50 and the United States' Nasdag100 index is presented to illustrate how this idea might be used. [ABSTRACT FROM AUTHOR]

Companies are trying to harness the potential of the current stage of development of the digital industry and make it cost-effective, which requires not only technological innovation but also the transformation of many existing business models. Based on an analysis of examples of digital subscription companies, this article provides additional explanations, including definitions and constituent characteristics of digital subscription business models. The aim of the article was to identify trends in the development of digital subscription services by analysing the number of active subscribers and the impact of COVID-19 on this indicator. Autoregression and analysis methods were used in the study, and the implementation of the selected models was carried out using the Python-3 programming language. The article describes a theoretical basis that determine the feasibility of using the subscription model for the company under non-deterministic critical conditions. The main approaches to forecasting the company’s performance indicators are identified. The type of data to be forecasted is determined, and the necessity of using autoregressive models for further analysis is declared. Factors associated with the COVID-2019 incidence that should be considered as exogenous variables were identified. The multicriteria selection problem was constructed by restricting the family of autoregressive models and determining the criteria for forecasting and data preparation time, forecast accuracy, and the possibility of considering external factors in determining the algorithm efficiency. It is found that moving average autoregression is the most effective. Given the further application of this algorithm to predict the number of subscribers, the expediency of implementing a subscription strategy for the company under non-deterministic critical conditions is declared. It is possible to effectively apply the selected mathematical model to predict the performance of a subscription company. The practical significance of the work lies in the possibility of creating certain benchmarks for the development of the market and a business strategy for product promotion, which will be based on an understanding of the potential benefits and threats of the market for digital subscription products and services

The assessment of the effect of the informal use of a foreign currency on the corresponding FX rates toward the national currency is a very difficult task, requiring direct calculation and modeling. It comes mostly because of the unknown quantity of foreign money used in the informal sector, but also because of the lack of quantitative calculation models. To overcome this gap and to realize a qualitative description of this effect in a concrete economic environment, we propose herein a comparative analysis between the behavior of two typical FX rate series recorded in the Albanian currency market, the Euro-ALL and USD-ALL, providing that the Euro is used commonly as a national currency substitute in the informal economy and the USD is not. So, we have evidenced that the un-stationarity degree of the Bid and Ask spread distribution for the Euro-ALL FX series is higher than for the corresponding USD-ALL case, but with a lower variance. Those features occurring simultaneously can be explained by assuming that informal use of the Euro acts as an additional perturbation on the FX system, imposing high nonstationary, but at the same time it provides reservoir or source features for the money disbalances, reducing the average fluctuations. Next, the depth of the market measured by the average Bid-Ask Spread has resulted in a smaller price for the Euro currency, indicating a lower cost of the transactions and reinforcing the assumption regarding the distribution’s in-stationarity features. Based on those indicatory findings, we propose to realize indirect evidence for our assumptions by comparing the reproduction of the corresponding distribution using autoregressive models. In this case, we have evidenced that the distribution of the FX Euro-ALL spread can be reproduced better if we include in standard ARCHX (m, n, p) models a term that mimics the informality measure. When applying the same procedure for the USD-ALL spread, the resulting distribution has not matched equally well with the original ones. Those findings have been discussed in the framework of an alternative description of the effect of the informal use of foreign currency in a small economy with a sizeable informal sector, which convene our current system under analysis, but we believe that they can be applicable for similar economic environments. Doi: 10.28991/HEF-2024-05-01-02 Full Text: PDF

Generating dance movements from music has been considered a highly challenging task, as it requires the model to comprehend concepts from two different modalities: audio and video. However, recently, research on dance generation based on deep learning has been actively conducted. Existing dance generation researches tend to focus on generating dances in limited genres or for single dancer, so when K-pop music that mixes multiple genres was applied to existing methods, they failed to generate dances of various genres or group dances. In this paper, we propose the K-pop dance generation model in an autoregressive manner, a system designed to generate two-person synchronous dances based on K-pop music. To achieve this, we created a dataset by collecting videos of multiple dancers simultaneously dancing to K-pop music and dancing in various genres. Generating synchronous dances has two meanings: one is to generate a dance that goes well with the input music and dance when both are given, and the other is to simultaneously generate multiple dances that match the given music. We call them secondary dance generation and group dance generation, respectively, and designed the proposed model, which can perform both two generation methods. In addition, we would like to propose additional learning methods to make a model that better generates synchronous dances. To assess the performance of the proposed model, both qualitative and quantitative evaluations are conducted, proving the effectiveness and suitability of the proposed model when generating synchronous dances for K-pop music.

This study delves into the domain of dynamical systems, specifically the forecasting of dynamical time series defined through an evolution function. Traditional approaches in this area predict the future behavior of dynamical systems by inferring the evolution function. However, these methods may confront obstacles due to the presence of missing variables, which are usually attributed to challenges in measurement and a partial understanding of the system of interest. To overcome this obstacle, we introduce the autoregressive with slack time series (ARS) model, that simultaneously estimates the evolution function and imputes missing variables as a slack time series. Assuming time-invariance and linearity in the (underlying) entire dynamical time series, our experiments demonstrate the ARS model’s capability to forecast future time series. From a theoretical perspective, we prove that a 2-dimensional time-invariant and linear system can be reconstructed by utilizing observations from a single, partially observed dimension of the system.

This study focuses on real-time model predictive control (MPC) implementation for a point-absorber-type wave energy converter (WEC) to achieve maximum wave power extraction. To address the MPC dependence on current and future wave excitation force knowledge, the control framework includes a square-root unscented Kalman filter (SR-UKF) to estimate the wave excitation force, whereas an autoregressive (AR) model forecasts the excitation force over the prediction horizon. The MPC utilizes a linear model of the point absorber, and its cost function is formulated as a quadratic programming (QP) problem with the objective of maximizing the wave energy extraction subject to physical limitations and constraints. A set of Laguerre functions was used to reduce the MPC computational complexity by decreasing the number of decision variables in the QP problem. The MATLAB/Simulink simulation results showed that the embodiment of point absorber nonlinearities by the SR-UKF enhanced the estimation accuracy compared with that of linear Kalman filters in terms of maximum error, root mean square error, and goodness of fit. Moreover, an AR model of order 100 provided satisfactory prediction performance for a 4 s prediction. The MPC strategy was simulated to evaluate its efficiency with respect to the absorbed wave power and generated electrical power under different sea-state conditions and disturbance uncertainties. Depending on sea state, it was found that the proposed MPC strategy generated 27.8% to 80% more electrical power than resistive loading control. Finally, a hardware-in-the-loop experimental setup was used to validate the computational viability of the proposed control framework in real-time WEC applications.

Nitrogen dioxide (NO2) is one of the pollutants that can cause potential damage to the ecosystem. NO2 emitted from vehicles forms the primary precursor for ground-level ozone. In this study, an analysis of the daily average of NO2 concentration with meteorology measured for two years 2021 and 2022 is being carried out. It is evident from the analysis that NO2 concentration followed an apparent diurnal pattern with a maximum value in the morning hours and a minimum during the afternoon hours. Summer months recorded the highest, and North East Monsoon (NEM) recorded the lowest values of NO2. A statistically significant positive correlation was found between NO2 and Temperature. An autoregressive model was formulated to forecast the daily average values of NO2 concentration. Unit root test was performed to check the stationarity of the data points, which is important in determining trends and seasonal changes. From the model procedure, the order that best fits the data was identified as AR (4), in which the process has the current value based on the previous three values. The Akaike Information Criterion (AIC) and Schwartz Criterion (SC), which are estimators of prediction error for AR (4), are low. The Jarque confirmed the normal distribution-Bera test, which again approves the satisfactoriness of the model.. [ABSTRACT FROM AUTHOR]

Several new models based on item response theory have recently been suggested to analyse intensive longitudinal data. One of these new models is the time‐varying dynamic partial credit model (TV‐DPCM; Castro‐Alvarez et al., Multivariate Behavioral Research, 2023, 1), which is a combination of the partial credit model and the time‐varying autoregressive model. The model allows the study of the psychometric properties of the items and the modelling of nonlinear trends at the latent state level. However, there is a severe lack of tools to assess the fit of the TV‐DPCM. In this paper, we propose and develop several test statistics and discrepancy measures based on the posterior predictive model checking (PPMC) method (PPMC; Rubin, The Annals of Statistics, 1984, 12, 1151) to assess the fit of the TV‐DPCM. Simulated and empirical data are used to study the performance of and illustrate the effectiveness of the PPMC method. [ABSTRACT FROM AUTHOR]

This paper firstly studies the coefficients estimation of the AR model with normal innovation by proposing an asymptotically honest generalized fiducial (AHGF) method. Furthermore, the AHGF method is introduced to skew-normal setting. Simulation results show that the AHGF method shows more advantages than traditional methods. Specifically, the AHGF method often has a smaller mean square error for point estimation. And for interval estimation, the AHGF method behaves closer to the nominal level than other methods while maintaining comparable or shorter lengths. Finally, a temperature dataset and a sunspot series are applied to illustrate the proposed AHGF methodology. [ABSTRACT FROM AUTHOR]

Accurate prediction models of thermal errors are very useful for improving the machining accuracy of machine tools; it is also the core of thermal error compensation technology. Often, it is preferable to predict thermal deformation using a dynamic model, as opposed to computational inaccuracy and non-robustness existing in the static model. Autoregressive models are one of the most commonly used dynamic models. However, the autoregressive model needs to measure the thermal error online, which can be intrusive to the production process and reduce production efficiency. This paper presents a new exogenous input autoregressive modeling approach based on mixed variables (MV-ARX) in CNC Swiss lathes. In addition, offline prediction is achieved by replacing online measurements with estimates of thermal errors. The effects of factors on thermal error, such as ambient temperature and spindle speed, are analyzed through thermal characteristic experiments. The K-means clustering method was used to select the thermal critical point, and the exogenous input autoregressive prediction model was optimized by combining the selected temperature variables with the spindle speed to improve the accuracy and robustness of offline prediction. Compared with the model based on temperature-variable autoregression (TV-ARX) and multivariate linear regression (MLR), the proposed model shows better prediction performance. The offline prediction of thermal errors also showed good performance under non-training conditions, with an offline prediction accuracy of up to 83.52%. The modeling method proposed in this work may pave the way for improving the prediction of other errors with similar nonlinear hysteresis dynamical systems. [ABSTRACT FROM AUTHOR]

The future values of the expected claims are very important for the insurance companies for avoiding the big losses under uncertainty which may be produced from future claims. In this paper, we define a new size-of-loss distribution for the negatively skewed insurance claims data. Four key risk indicators are defined and analyzed under four estimation methods: maximum likelihood, ordinary least squares, weighted least squares, and Anderson Darling. The insurance claims data are modeled using many competitive models and comprehensive comparison is performed under nine statistical tests. The autoregressive model is proposed to analyze the insurance claims data and estimate the future values of the expected claims. The value-at-risk estimation and the peaks-over random threshold mean-of-order-p methodology are considered. [ABSTRACT FROM AUTHOR]

Decreases in the diversity of farmland communities reported at various scales and across taxonomic groups have fueled searches for ultimate reasons, primarily focusing on aspects of agricultural land use. However, the importance of individual external factors as drivers of population dynamics may vary across populations. We used density estimates of the European hare (Lepus europaeus) from a study site near Czempiń, western Poland, covering a time series of 50 years, to analyse long-term trends in overwinter survival. We employed an autoregressive population model to test associations between cereals yields (as a proxy for agricultural land use), fox predation, winter climate and hare density, and compared our results to those reported for a Danish population exposed to an oceanic climate and a Czech population exposed to a more continental climate. We found that at the Polish study site, hare density was negatively associated with fox density, but there were no associations with cereals yield or winter climate. Using generalized additive models, we found nonlinear trends in autumn and spring hare densities also showing a gradual increase in overwinter survival from the 1970s to 2009. We did not detect any decreased juvenile productivity over the study period. We conclude that survival during the breeding season was the most significant demographic trait driving hare dynamics. Our study provides evidence of strong spatial variability in the importance of individual extrinsic factors as drivers of hare population trends. [ABSTRACT FROM AUTHOR]

We present a new set of equations for tree level volume and aboveground biomass estimation for ocote pine (Pinus oocarpa Schiede ex Schltdl). These equation systems are the first developed for this species in Nicaragua. The first system includes a taper function, a merchantable volume equation, and volume equations for stem, coarse branches, and whole trees. The second system estimates whole tree and individual tree component biomass (stem wood, bark, branches, and needles). Data from 112 sampled trees were used for models' development. Seemingly Unrelated Iterative Regression and the Generalized Method of Moments were used to simultaneously fit the volume and biomass equations systems, respectively; both methods ensure additivity and compatibility between equations. Weighted regression and a second-order continuous autoregressive error structure were used to correct heteroscedasticity and autocorrelation within the hierarchical dataset. The predictive power of the new proposed equations is higher than the currently used models for P. oocarpa in the country. These equation systems represent a scientific advancement that will enhance forest inventories, optimize timber management of the species, and facilitate accurate monitoring of forest carbon dynamics. Additionally, the new equations will contribute to a more precise accounting of CO2 emissions from the country's forestry sector. [ABSTRACT FROM AUTHOR]

In this study, researchers examine a nonlinear autoregressive (NLAR) time-series model with regression function and dependent innovations in which the errors of the model follow the two-piece scale mixtures of normal (TP-SMN) distributions. Robustness and atypical forms of the proposed class of two-piece distributions along with the flexibility of the nonlinear autoregressive model develop desirable properties which can be applied to several types of datasets. The nonlinear regression function part of the autoregressive time-series model is estimated via the semiparametric and nonparametric curve estimation based on the conditional least square method and nonparametric kernel approach. The maximum likelihood (ML) estimates of the model parameters, using a suitable hierarchical representation of the TP-SMN family on the model are obtained via an expectation maximization (EM)-type algorithm. Performances and usefulness of the proposed model and estimates are shown via simulation studies and a real dataset. [ABSTRACT FROM AUTHOR]

A generalized autoregressive (GNAR) model fusing both linearity and nonlinearity is proposed to solve the complex nonlinear time series modeling problem. First, the mathematical model of the GNAR model is established while the mathematical mechanism and physical meaning of the GNAR model are both expounded from the two aspects of Weierstrass theory and Volterra theory. Then, an improved least squares parameter estimation method, namely robust Residuals Adjusted Least Squares (RALS) method, is introduced and its process is successionally proposed to improve the anti-outlier performance of the GNAR model. Next, the mathematical model of the computational complexity for the GNAR model is established and the complexity model is introduced into the AIC to propose an improved AIC (iAIC). Finally, a dataset containing 23 records is established and experiments are carried out. The results show that the GNAR model with RALS estimator has high fitting accuracy. The Mean Square Error (MSE) of the series predicted by the GNAR model with Least Squares (LS) estimator is 325.3% higher than that of the series predicted by the GNAR model with RALS estimator at most. The effectiveness of order determination method reaches 82.61%. Therefore, the GNAR model together with its parameter estimation method and order determination method proposed in this paper are effective. [ABSTRACT FROM AUTHOR]

Independent vector analysis (IVA) can be viewed as an extension of independent component analysis (ICA) to multiple datasets. It exploits the statistical dependency between different datasets through mutual information. In the context of motor imagery classification based on electroencephalogram (EEG) signals for the brain–computer interface (BCI), several methods have been proposed to extract features efficiently, mainly based on common spatial patterns, filter banks, and deep learning. However, most methods use only one dataset at a time, which may not be sufficient for dealing with a multi-source retrieving problem in certain scenarios. From this perspective, this paper proposes an original approach for feature extraction through multiple datasets based on IVA to improve the classification of EEG-based motor imagery movements. The IVA components were used as features to classify imagined movements using consolidated classifiers (support vector machines and K-nearest neighbors) and deep classifiers (EEGNet and EEGInception). The results show an interesting performance concerning the clustering of MI-based BCI patients, and the proposed method reached an average accuracy of 86.7%.

This research aims to derive the average run length (ARL) evaluation of the double exponentially weighted moving average (double EWMA) control chart for observation data that follows exponential white noise in a time series model with an autoregressive model. Since most real-world data is automatically correlated, autoregressive models are available. Comparisons were made between the ARLs obtained using the explicit formula and the numerical integral equation (NIE) approach. The results showed that the explicit formula's use of the ARL outperformed the NIE approach in terms of computation time. After that, the efficacy of the exponentially weighted moving average (EWMA) and double EWMA charts is then compared using the suggested explicit ARL formula. The ARL of the double EWMA chart was found to perform better than the ARL of the EWMA chart in all situations. It also uses natural gas and diesel prices on stock exchanges around the world as cases studies. The results show that the double EWMA chart has better detection sensitivity than the EWMA chart, and the results are consistent with the experimental results. As a result, the sensitivity of the double EWMA chart in detecting changes makes it a good alternative for monitoring processes with real-world data. [ABSTRACT FROM AUTHOR]

This paper proposes a P ositional- E ncoded A synchronous Auto R egression (PEAR) method for satellite anomaly detection. We empirically observe that a single classification model can hardly detect unknown anomalous situations and neglect the Markov nature of temporal satellite data. To address this, we adopt an autoregressive model to deal with the prediction of unknown anomaly for satellite data. We further propose a non-uniform temporal encoding method for asynchronous data and a median filtering method for more accurate detection. To reduce the effect of outliers, we employ an adaptive threshold selection method to achieve a more robust classification boundary. We test the proposed method on the time series prediction models including LSTM and transformers and we further employ the positional encoding strategy to improve the modeling capabilities of the Transformer model on high-frequency information. Experiments on real satellite data demonstrate that the proposed PEAR method outperforms the baseline method by 55.79%. • We propose an autoregressive model to predict the unknown satellite anomaly. • We employ the positional encoding strategy to fit high-frequency information. • Extensive experiments demonstrate the superior performances of PEAR. [ABSTRACT FROM AUTHOR]

The study of multivariate time series forecasting (MTSF) problems has high significance in many areas, such as industrial forecasting and traffic flow forecasting. Traditional forecasting models pay more attention to the temporal features of variables and lack depth in extracting spatial and spatiotemporal features between variables. In this paper, a novel model based on the Transformer, convolutional neural network (CNN), and long short-term memory (LSTM) network is proposed to address the issues. The model first extracts the spatial feature vectors through the proposed Multi-kernel CNN. Then it fully extracts the temporal information by the Encoder layer that consists of the Transformer encoder layer and the LSTM network, which can also obtain the potential spatiotemporal correlation. To extract more feature information, we stack multiple Encoder layers. Finally, the output is decoded by the Decoder layer composed of the ReLU activation function and the Linear layer. To further improve the model's robustness, we also integrate an autoregressive model. In model evaluation, the proposed model achieves significant performance improvements over the current benchmark methods for MTSF tasks on four datasets. Further experiments demonstrate that the model can be used for long-horizon forecasting and achieve satisfactory results on the yield forecasting of test items (our private dataset, TIOB). [ABSTRACT FROM AUTHOR]

In economic and financial applications, there is often the need for analysing multivariate time series, comprising of time series for a range of quantities. In some applications, such complex systems can be associated with some underlying network describing pairwise relationships among the quantities. Accounting for the underlying network structure for the analysis of this type of multivariate time series is required for assessing estimation error and can be particularly informative for forecasting. Our work is motivated by a dataset consisting of time series of industry-to-industry transactions. In this example, pairwise relationships between Standard Industrial Classification (SIC) codes can be represented using a network, with SIC codes as nodes and pairwise transactions between SIC codes as edges, while the observed time series of the amounts of the transactions for each pair of SIC codes can be regarded as time-varying weights on the edges. Inspired by Knight et al. (2020, J. Stat. Softw. , 96, 1–36), we introduce the GNAR-edge model which allows modelling of multiple time series utilizing the network structure, assuming that each edge weight depends not only on its past values, but also on past values of its neighbouring edges, for a range of neighbourhood stages. The method is validated through simulations. Results from the implementation of the GNAR-edge model on the real industry-to-industry data show good fitting and predictive performance of the model. The predictive performance is improved when sparsifying the network using a lead–lag analysis and thresholding edges according to a lead–lag score. [ABSTRACT FROM AUTHOR]

Energy costs represent a significant share of the total cost of ownership in high-performance computing systems. Using a unique data set collected by massive sensor networks in a petascale national supercomputing center, we first present an explanatory model to identify key factors affecting energy consumption in supercomputing. Our analytic results show that workload distribution among the nodes has significant effects and could effectively be leveraged to improve energy efficiency. We then establish the high model performance using in-sample and out-of-sample analyses and develop prescriptive models for energy-optimal runtime workload management. We present four dynamic resource management methodologies (packing, load balancing, threshold-based switching, and energy optimization), model their application at two levels (within-rack and cross-rack resource allocation), and explore runtime resource redistribution policies for jobs under the computational steering and comparatively evaluate strategies that use computational steering with those that do not. Our experimental results lead to a threshold strategy that yields near-optimal energy efficiency under all workload conditions. We further calibrate the energy-optimal resource allocations over the full range of workloads and present a bi-criteria evaluation to consider energy consumption and job performance tradeoffs. We conclude with implementation guidelines and policy insights into energy-efficient computing resource management in large supercomputing centers. Energy costs represent a significant share of the total cost of ownership in high-performance computing (HPC) systems. Using a unique data set collected by massive sensor networks in a petascale national supercomputing center, we first present an explanatory model to identify key factors that affect energy consumption in supercomputing. Our analytic results show that, not only does computing node utilization significantly affect energy consumption, workload distribution among the nodes also has significant effects and could effectively be leveraged to improve energy efficiency. Next, we establish the high model performance using in-sample and out-of-sample analyses. We then develop prescriptive models for energy-optimal runtime workload management and extend the models to consider energy consumption and job performance tradeoffs. Specifically, we present four dynamic resource management methodologies (packing, load balancing, threshold-based switching, and energy optimization), model their application at two levels (purely within-rack and jointly cross-rack resource allocation), and explore runtime resource redistribution policies for jobs under the emergent principle of computational steering and comparatively evaluate strategies that use computational steering with those that do not. Our experimental studies show that packing is preferred when the total workload of a rack is higher than a threshold and load balancing is preferred when it is lower. These results lead to a threshold strategy that yields near-optimal energy efficiency under all workload conditions. We further calibrate the energy-optimal resource allocations over the full range of workloads and present a bicriteria evaluation to consider energy consumption and job performance tradeoffs. We demonstrate significant energy savings of our proposed strategies under various workload conditions. We conclude with implementation guidelines and policy insights into energy-efficient computing resource management in large supercomputing data centers. History: Olivia Liu Sheng, Senior Editor; Xiaobai Li, Associate Editor. Funding: The authors thank the National Supercomputing Center of Singapore for enabling and supporting this research. J. Li received support from the National Natural Science Foundation of China [Grants 71901169, 72032006, and T2293774]. Supplemental Material: The online appendices are available at https://doi.org/10.1287/isre.2023.1208. [ABSTRACT FROM AUTHOR]

Background: Policy evaluation studies that assess how state-level policies affect health-related outcomes are foundational to health and social policy research. The relative ability of newer analytic methods to address confounding, a key source of bias in observational studies, has not been closely examined. Methods: We conducted a simulation study to examine how differing magnitudes of confounding affected the performance of 4 methods used for policy evaluations: (1) the two-way fixed effects difference-in-differences model; (2) a 1-period lagged autoregressive model; (3) augmented synthetic control method; and (4) the doubly robust difference-in-differences approach with multiple time periods from Callaway-Sant'Anna. We simulated our data to have staggered policy adoption and multiple confounding scenarios (i.e., varying the magnitude and nature of confounding relationships). Results: Bias increased for each method: (1) as confounding magnitude increases; (2) when confounding is generated with respect to prior outcome trends (rather than levels), and (3) when confounding associations are nonlinear (rather than linear). The autoregressive model and augmented synthetic control method had notably lower root mean squared error than the two-way fixed effects and Callaway-Sant'Anna approaches for all scenarios; the exception is nonlinear confounding by prior trends, where Callaway-Sant'Anna excels. Coverage rates were unreasonably high for the augmented synthetic control method (e.g., 100%), reflecting large model-based standard errors and wide confidence intervals in practice. Conclusions: In our simulation study, no single method consistently outperformed the others, but a researcher's toolkit should include all methodologic options. Our simulations and associated R package can help researchers choose the most appropriate approach for their data. [ABSTRACT FROM AUTHOR]

We present an any-to-one voice conversion (VC) system, using an autoregressive model and LPCNet vocoder, aimed at enhancing the converted speech in terms of naturalness, intelligibility, and speaker similarity. As the name implies, non-parallel any-to-one voice conversion does not require paired source and target speeches and can be employed for arbitrary speech conversion tasks. Recent advancements in neural-based vocoders, such as WaveNet, have improved the efficiency of speech synthesis. However, in practice, we find that the trajectory of some generated waveforms is not consistently smooth, leading to occasional voice errors. To address this issue, we propose to use an autoregressive (AR) conversion model along with the high-fidelity LPCNet vocoder. This combination not only solves the problems of waveform fluidity but also produces more natural and clear speech, with the added capability of real-time speech generation. To precisely represent the linguistic content of a given utterance, we use speaker-independent PPG features (SI-PPG) computed from an automatic speech recognition (ASR) model trained on a multi-speaker corpus. Next, a conversion model maps the SI-PPG to the acoustic representations used as input features for the LPCNet. The proposed autoregressive structure enables our system to produce the following prediction step outputs from the acoustic features predicted in the previous step. We evaluate the effectiveness of our system by performing any-to-one conversion pairs between native English speakers. Experimental results show that the proposed method outperforms state-of-the-art systems, producing higher speech quality and greater speaker similarity. [ABSTRACT FROM AUTHOR]

The Tweedie distribution is a useful tool to model zero-inflated non-negative continuous data. However, the Tweedie dispersion relationship (DR) is not general enough to cover some important forms such as quadratic dispersion, and an easy and fast-to-implement Tweedie AR(1) model (first-order autoregressive model) needs to be developed for spatio-temporal modelling. In this research we extend the Tweedie distribution to accommodate flexible DRs, and propose a Tweedie Markov process (TMP) with the AR(1) autocorrelation structure. This TMP is simple to implement and requires only the Tweedie probability density function. Simulation studies and real data analysis are conducted to validate our new approach. [ABSTRACT FROM AUTHOR]

Damage identification plays an important role in enhancing resilience by facilitating precise detection and assessment of structural impairments, thereby strengthening the resilience of critical infrastructure. A current challenge of vibration-based damage detection methods is the difficulty of enhancing the precision of the detection results. This problem can be approached through improving the noise reduction performance of algorithms. A novel method based partially on the errors-in-variables (EIV) model and its total least-squares (LS) algorithm is proposed in this study. Compared with a classical damage detection approach involving adoption of auto-regressive (AR) models and the least-squares (LS) method, the proposed method accounts for all the observation errors as well as the relationships between them, especially in an elevated level of noise, which leads to a better accuracy. Accordingly, a shaking table test and its corresponding finite element simulation of a full-scale web steel structure were conducted. The acceleration time-series output data of the model after suffering from different seismic intensities were used to identify damage using the presented detection method. The response and identification results of the experiment and the finite element analysis are consistent. The finding of this paper indicated that the presented approach is capable of detecting damage with a higher accuracy, especially when the signal noise is high. [ABSTRACT FROM AUTHOR]

This paper analyzes the current situation of university English teaching and constructs a trinity of EGP+ESP+EIC multiple teaching innovation systems for university English based on the principles of English teaching innovation. In order to analyze this innovative teaching system of English, a stratified statistical model and a spatial autoregressive model are combined, and four ordinal stratified spatial autoregressive Probit models are innovatively constructed to model data where the dependent variable is ordinal, and there is a spatial dependency situation with a stratified structure. The analysis shows that in the process of continuous innovation of English teaching mode, the number of people who are dissatisfied with English teaching decreases by 30%, the number of people who are very satisfied increases by 35%, and the number of people who are very satisfied accounts for 42.5% of the total number of people and 90% of the total number of people who are satisfied in the final stage of innovation of English teaching in university. The English teaching innovation strategy for university students based on this study is feasible.

This paper proposes a novel censored autoregressive conditional Fréchet (CAcF) model with a flexible evolution scheme for the time-varying parameters, which allows deciphering tail risk dynamics constrained by price limits from the viewpoints of different risk preferences. The proposed model can well accommodate many important empirical characteristics of financial data, such as heavy-tailedness, volatility clustering, extreme event clustering, and price limits. We then investigate tail risk dynamics via the CAcF model in the price-limited stock markets, taking entropic value at risk (EVaR) as a risk measurement. Our findings suggest that tail risk will be seriously underestimated in price-limited stock markets when the censored property of limit prices is ignored. Additionally, the evidence from the Chinese Taiwan stock market shows that widening price limits would lead to a decrease in the incidence of extreme events (hitting limit-down) but a significant increase in tail risk. Moreover, we find that investors with different risk preferences may make opposing decisions about an extreme event. In summary, the empirical results reveal the effectiveness of our model in interpreting and predicting time-varying tail behaviors in price-limited stock markets, providing a new tool for financial risk management.

The time-inhomogeneous autoregressive model AR(1) is studied, which is the process of the form ${X_{n+1}}={\alpha _{n}}{X_{n}}+{\varepsilon _{n}}$, where ${\alpha _{n}}$ are constants, and ${\varepsilon _{n}}$ are independent random variables. Conditions on ${\alpha _{n}}$ and distributions of ${\varepsilon _{n}}$ are established that guarantee the geometric recurrence of the process. This result is applied to estimate the stability of n-steps transition probabilities for two autoregressive processes ${X^{(1)}}$ and ${X^{(2)}}$ assuming that both ${\alpha _{n}^{(i)}}$, $i\in \{1,2\}$, and distributions of ${\varepsilon _{n}^{(i)}}$, $i\in \{1,2\}$, are close enough.

Ensuring the reliability of data obtained from Wireless Sensor Networks (WSNs) deployed in farmland to monitor soil parameters is crucial for optimizing smart irrigation. These distributed sensor nodes encounter various challenges and are vulnerable to sensor faults that can significantly degrade the network's service quality. In this article, we present an innovative approach for detecting sensor faults within WSNs for smart irrigation by combining an autoregressive model with a Kalman filter. Integrating the Kalman filter and the autoregressive model combines their strengths in a synergistic manner. The algorithm is developed with consideration for the resource constraints of the sensor nodes and addresses the challenge of lacking ground truth information for the monitored area. The primary advantage of this proposed technique lies in its simplicity of implementation, requiring minimal computational complexity while enhancing the application's reliability. Through experimentation and validation, we demonstrate the effectiveness of this combined approach in detecting sensor fault detection in real-world WSNs scenarios.

Data-driven parametric reduced-order models (ROMs) in state-space form are valuable tools for rapid aeroelastic (AE) analysis and aerostructure control synthesis. However, the issue of state inconsistence (significant variations in model parameters over tradespaces) makes ROMs noninterpolatable, and therefore unable to accommodate use over broad flight parameter space. This paper presents a holistic framework that combines a system identification technique with state-consistence enforcement (SCE) and a genetic algorithm (GA) for the automated development of interpolatable AE ROMs across broad flight regimes. The SCE technique introduces a regularization term to the AutoRegressive model with eXogenous inputs (ARX) to specifically penalize model parameter variation between flight conditions. The GA autonomously guides the ROM development process toward optimal SCE-ARX hyperparameter selection that balances between model parameter variations and ROM accuracy. The GA-guided SCE-ARX approach is applied to build a parametric AE-ROM database at selected flight conditions, which, because of its state consistence, can be interpolated to create ROMs at any interstitial conditions, where training data or ROMs are not initially available, hence rapidly establishing the full coverage of the entire parameter space. The ROMs generated by the proposed method are compared with those by ARX, SCE, and GA-guided ARX in prediction accuracy. The individual and combined effects of SCE and GA on model parameter variation and ROM interpolatability are thoroughly investigated. The present method demonstrates the most accurate and robust performance for parametric ROM construction across the broad flight envelope. [ABSTRACT FROM AUTHOR]

It is known that the block-based version of the bootstrap method can be used for distributional parameter estimation of dependent data. One of the advantages of this method is that it improves mean square errors. The paper makes two contributions. First, we consider the moving blocking bootstrap method for estimation of parameters of the autoregressive model. For each block, the parameters are estimated based on the modified maximum likelihood method. Second, we provide a method for model selection, Vuong's test and tracking interval, i.e. for selecting the optimal model for the innovation's distribution. Our analysis provides analytic results on the asymptotic distribution of the bootstrap estimators and also computational results via simulations. Some properties of the moving blocking bootstrap method are investigated through Monte Carlo simulation. This simulation study shows that, sometimes, Vuong's test based on the modified maximum likelihood method is not able to distinguish between the two models; Vuong's test based on the moving blocking bootstrap selects one of the competing models as optimal model. We have studied real data, the S&P500 data, and select optimal model for this data based on the theoretical results. [ABSTRACT FROM AUTHOR]

A modified exponentially weighted moving average (EWMA) scheme is a quality control chart which can quickly detect small shifts in autocorrelated data. In this article, an explicit formula is presented to calculate the average run length (ARL) for a modified EWMA chart with an autoregressive AR(p) model involving exponential white noise. Its performance is compared with a numerical integral equation method via a simulation study to determine whether the explicit formula can help decrease the processing time. Moreover, this scheme is tested against a classical EWMA control chart using the ARL and RMI results. Finally, the explicit formula for ARL is applied to a real numerical example from the health field to demonstrate the efficacy of our method. [ABSTRACT FROM AUTHOR]

The task of comparison testing of time series power spectrum parametric estimates is considered. It is shown that an urgent problem that arises in solving it is the optimization of the parameters of spectral estimates under conditions of small samples of observations. To overcome this problem, it is proposed to use the system-wide concept of analysis through time series synthesis. Based on this concept, a regular method was developed for comparison testing of parametric estimates of the power spectrum that are obtained from a time series of finite duration. Within the method, solutions are accepted based on the results of testing statistical hypotheses about the homogeneity of two samples: the finite empirical one, compiled based on the results of observations, and an infinite virtual one, mathematically synthesized according to each individual parametric estimate in the series of spectral alternatives being examined. The principle of minimum informational divergence between samples according to the Kullback–Leibler criterion. An example of the practical application of the developed method is presented in the problem of discrete spectral modeling of speech signals. The ability of the method to identify patterns of unstable parametric estimates of the autoregressive type has been shown. The results obtained are intended for use in the field of speech acoustics, as well as technical and medical diagnostics, where parametric methods of spectral analysis are increasingly used in practice. [ABSTRACT FROM AUTHOR]

A great deal of economic problems are related to detecting the stability of time series data, where the main interest is in the unit root test. In this paper, we consider the unit root testing problem with errors being long-memory processes with the GARCH structure. A new test statistic is developed by using the random weighted bootstrap method. It turns out that the proposed statistic has a chi-squared distribution asymptotically regardless of the process being stationary or nonstationary, and with or without an intercept term. The simulation results show that the statistic has a desired finite sample performance in terms of both size and power. A real data application is also given relying on the inflation rate data of 17 countries. [ABSTRACT FROM AUTHOR]