Autoregressive Function Research Articles

البرمجة الضبابية وتحسين أداء الخوارزميات في بيئة متعددة المتغيرات الرتيبة

In many situations of daily life, when we start statistical analysis, we encounter data that we suffer from inaccuracy in its measurement, either due to observation or measurement errors or the lack of appropriate conditions for collecting this data, such as failure times of machines, equipment, electrical devices, medical, engineering and economic data. In many medical studies, the researcher may have a strong conviction that the regression function used to describe the relationship between two variables has a certain form or formula that can be characterized by certain ordering restrictions such as monotonicity; monotonic regression has important applications in statistics, operations research, and signal processing, and these applications are often characterized by a very large value of n. For such large-scale problems, it is of great practical importance to develop algorithms whose complexity does not increase rapidly with increasing n. It is a nonparametric regression technique that preserves order. In this thesis, the proposed fuzzy autoregressive monotonic method, fuzzy autoregressive monotonic least squares (FILSR), fuzzy autoregressive M estimator (FIM), and fuzzy autoregressive maximum likelihood estimator (FIML) were proposed. The best method for estimating the autoregressive function is the fuzzy autoregressive maximum likelihood method with a mean square error of (0.51455).

Using a linear dynamic system to measure functional connectivity from M/EEG

Objective. Measures of functional connectivity (FC) can elucidate which cortical regions work together in order to complete a variety of behavioral tasks. This study’s primary objective was to expand a previously published model of measuring FC to include multiple subjects and several regions of interest. While FC has been more extensively investigated in vision and other sensorimotor tasks, it is not as well understood in audition. The secondary objective of this study was to investigate how auditory regions are functionally connected to other cortical regions when attention is directed to different distinct auditory stimuli. Approach. This study implements a linear dynamic system (LDS) to measure the structured time-lagged dependence across several cortical regions in order to estimate their FC during a dual-stream auditory attention task. Results. The model’s output shows consistent functionally connected regions across different listening conditions, indicative of an auditory attention network that engages regardless of endogenous switching of attention or different auditory cues being attended. Significance. The LDS implemented in this study implements a multivariate autoregression to infer FC across cortical regions during an auditory attention task. This study shows how a first-order autoregressive function can reliably measure functional connectivity from M/EEG data. Additionally, the study shows how auditory regions engage with the supramodal attention network outlined in the visual attention literature.

Joint Component Estimation for Electricity Price Forecasting Using Functional Models

This work considers the issue of modeling and forecasting electricity prices within the functional time series approach. As this is often performed by estimating and predicting the different components of the price dynamics, we study whether jointly modeling the components, able to account for their inter-relations, could improve prediction with respect to a separate instance of modeling. To investigate this issue, we consider and compare the predictive performance of four different predictors. The first two, namely Smoothing Splines-Seasonal Autoregressive (SS-SAR) and Smoothing Splines-Functional Autoregressive (SS-FAR) are based on separate modeling while the third one is derived from a single-step procedure that jointly estimates all the components by suitably including exogenous variables. It is called Functional Autoregressive with eXogenous variables (FARX) model. The fourth one is a combination of the SS-FAR and FARX predictors. The predictive performances of the models are tested using electricity price data from the northern zone of the Italian electricity market (IPEX), both in terms of forecasting error indicators (MAE, MAPE and RMSE) and by means of the Diebold and Mariano test. The results point out that jointly estimating the components leads to significantly more accurate predictions than using a separate instance of modeling. In particular, the MAE, MAPE, and RMSE values for the best predictor, based on the FARX(3,0,4) model, are 4.25, 9.28, and 5.38, respectively. The percentage error reduction is about 20% with respect to SS-SAR(3,1) and about 10% with respect to SS-FAR(5). Finally, this study suggests that the forecasting errors are generally higher on Sunday and Monday, from hours 3 to 6 in the morning and 14 to 15 in the afternoon, and in June and December. On the other hand, prices are relatively lower on Wednesday, Thursday, and Friday, from hour 20 to 1 a.m., and in January and February.

Measuring the productivity of urban commercial banks in China

This paper contributes to the productivity analysis literature by measuring the productivity of 76 urban commercial banks operating in China's 27 regions from 2013 to 2018. A spatial total factor productivity index is constructed using a spatial autoregressive production function. The index is decomposed into the efficiency change and the returns to scale change, and it identifies both spatial direct (feedback) and spatial indirect (spillovers) components. The result confirms positive spatial dependence in the production of urban commercial banks. Additionally, productivity of China's urban commercial banks increases, which is mainly contributed to by the returns to scale change.

Bootstrapping Long-Run Covariance of Stationary Functional Time Series

A key summary statistic in a stationary functional time series is the long-run covariance function that measures serial dependence. It can be consistently estimated via a kernel sandwich estimator, which is the core of dynamic functional principal component regression for forecasting functional time series. To measure the uncertainty of the long-run covariance estimation, we consider sieve and functional autoregressive (FAR) bootstrap methods to generate pseudo-functional time series and study variability associated with the long-run covariance. The sieve bootstrap method is nonparametric (i.e., model-free), while the FAR bootstrap method is semi-parametric. The sieve bootstrap method relies on functional principal component analysis to decompose a functional time series into a set of estimated functional principal components and their associated scores. The scores can be bootstrapped via a vector autoregressive representation. The bootstrapped functional time series are obtained by multiplying the bootstrapped scores by the estimated functional principal components. The FAR bootstrap method relies on the FAR of order 1 to model the conditional mean of a functional time series, while residual functions can be bootstrapped via independent and identically distributed resampling. Through a series of Monte Carlo simulations, we evaluate and compare the finite-sample accuracy between the sieve and FAR bootstrap methods for quantifying the estimation uncertainty of the long-run covariance of a stationary functional time series.

Vibration-Based SHM in the Synthetic Mooring Lines of the Semisubmersible OO-Star Wind Floater under Varying Environmental and Operational Conditions.

As the industry transitions toward Floating Offshore Wind Turbines (FOWT) in greater depths, conventional chain mooring lines become impractical, prompting the adoption of synthetic fiber ropes. Despite their advantages, these mooring lines present challenges in inspection due to their exterior jacket, which prevents visual assessment. The current study focuses on vibration-based Structural Health Monitoring (SHM) in FOWT synthetic mooring lines under uncertainty arising from varying Environmental and Operational Conditions (EOCs). Six damage detection methods are assessed, utilizing either multiple models or a single functional model. The methods are based on Vector Autoregressive (VAR) or Transmittance Function Autoregressive with exogenous input (TF-ARX) models. All methods are evaluated through a Monte Carlo study involving 1100 simulations, utilizing acceleration signals generated from a finite element model of the OO-Star Wind Floater Semi 10 MW wind turbine. With signals from only two measuring positions, the methods demonstrate excellent results, detecting the stiffness reduction of a mooring line at levels 10% through 50%. The methods are also tested for healthy cases, with those utilizing TF-ARX models achieving zero false alarms, even for EOCs not encountered in the training data.

Agricultural credit guarantee scheme fund and oil palm production in Nigeria: A vector autoregressive (VAR) approach

Oil palm has been identified as one of the key agricultural products that can diversify Nigeria’s economy. However, its production and export have been hampered by capital constraints. Consequently, the Agricultural Credit Guarantee Scheme Fund (ACGSF) was introduced to encourage lending to farmers and agro-processors to enhance agricultural productivity. Therefore, this study aims to determine the effectiveness of ACGSF allocations to the oil palm production subsector. Time series data on oil palm production, as well as data on ACGSF allocations to oil palm and cash crop production, prime lending rate and commercial banks' loans to agriculture were obtained from FAOSTAT and the Central Bank of Nigeria. Vector autoregression, Granger causality and impulse response functions were used to estimate the short-run relationship. The results reveal that ACGSF allocations to the oil palm subsector and commercial banks’ loans to agriculture have negative and positive effects, respectively, on oil palm production. There was unidirectional causality from ACGSF and commercial banks to agriculture to oil palm production. The findings suggest expansion and close monitoring of the ACGSF scheme, and the intensification and esterification of oil palm production. The study shows that estimating the effect of ACGSF on overall agricultural productivity does not provide deep insight into commodity-specific credit packages.

On Limit Theorems for Functional Autoregressive Processes with Random Coefficients

On Limit Theorems for Functional Autoregressive Processes with Random Coefficients

An Improved grey wolf optimizer with weighting functions and its application to Unmanned Aerial Vehicles path planning

The grey wolf optimizer (GWO) is an optimization algorithm that draws inspiration from nature. It is an optimization algorithm based on population that iteratively searches for the optimal solution by simulating the social behavior and hunting behavior of grey wolves. It has recently been shown that GWO can be improved by the introduction of initializing, movement, selecting and updating. In this paper, we extend an improved grey wolf optimizer with weighting functions (IGWO-WFs), which include multi-modal adaptive function, sigmoid function and autoregressive function. The IGWO-WFs has 74% improved to the conventional algorithms. It can be resolved the instability and convergence issues of GWO and investigate the effectiveness of the methods through numerical simulations and the path planning of Unmanned Aerial Vehicles (UAVs).

Self-Supervised Graph Completion for Incomplete Multi-View Clustering

Incomplete multi-view clustering (IMVC) is challenging, as it requires adequately exploring complementary and consistency information under the incompleteness of data. Most existing approaches attempt to overcome the incompleteness at instance-level. In this work, we develop a new approach to facilitate IMVC from a new perspective. Specifically, we transfer the issue of missing instances to a similarity graph completion problem for incomplete views, and propose a self-supervised multi-view graph completion algorithm to infer the associated missing entries. Further, by incorporating constrained feature learning, the inferred graph can be naturally leveraged in representation learning. We theoretically show that our feature learning process performs an Auto-Regressive filter function by encoding the learned similarity graph, which could yield discriminative representation for a clustering task. Extensive experiments demonstrate the effectiveness of the proposed method in comparison with state-of-the-art methods. The source code of our method is available at the <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">GitHub</b> : <uri xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">https://github.com/CLiu272/SGC-IMVC</uri> .

ОЦІНКА ВПЛИВУ ІННОВАЦІЙНОГО ПОТЕНЦІАЛУ РЕСУРСОЗАБЕЗПЕЧЕННЯ НА ФІНАНСОВУ ЕФЕКТИВНІСТЬ АГРАРНОГО СЕКТОРА ЕКОНОМІКИ УКРАЇНИ

The purpose of the study is to improve the methodological support for the assessment of the financial efficiency of the agricultural sector of Ukraine under the influence of the innovative potential management of its resource provision. The main scientific methods used in the study are fundamental provisions of the theory of innovation and finance, correlation and multifactor regression analysis, mathematical programming, etc. According to the results of the conducted research the parameter of technological progress as an indicator of the level of innovation development of the agrarian sector of the Ukrainian economy was obtained after modelling of autoregressive multiplicative Tinbergen-Solow production function. The numerical value of the technological progress parameter indicates a potential for additional growth in agricultural output of +0.142%, while other conditions remain unchanged. 23 indicators of the state of the resource provision of the agricultural sector were systematized in 4 groups: the results of the production activity of the agricultural sector (6 indicators), the resource supply of the agricultural sector (8 indicators), the efficiency of the use of resources by agricultural enterprises (4 indicators), and sustainability of the financial condition of agricultural enterprises (5 indicators). A power-law four-factor regression model of the impact of the output volume of the agricultural sector, the value of current assets, return on capital and the current liquidity ratio on the volume of net profit of agricultural enterprises of Ukraine was obtained. It is proved that the elasticity of net profit for agricultural output is 0.01%, for the value of current assets - 1.46%, for capital accumulation - 0.72%, for current liquidity - 3.2%. We constructed the target functions of maximization of the agricultural production output on the basis of the Tinbergen-Solow production function, net profit on the basis of the four-factor power model of net profit, return on equity on the basis of the two-factor DuPont model for the short term. The solving of target functions allowed for maximization of the return on equity of agrarian enterprises of Ukraine only at the expense of the existing innovation potential of production resources and will be used in further research by the authors.

Conformal prediction bands for two-dimensional functional time series

Time evolving surfaces can be modeled as two-dimensional Functional time series, exploiting the tools of Functional data analysis. Leveraging this approach, a forecasting framework for such complex data is developed. The main focus revolves around Conformal Prediction, a versatile nonparametric paradigm used to quantify uncertainty in prediction problems. Building upon recent variations of Conformal Prediction for Functional time series, a probabilistic forecasting scheme for two-dimensional functional time series is presented, while providing an extension of Functional Autoregressive Processes of order one to this setting. Estimation techniques for the latter process are introduced, and their performance are compared in terms of the resulting prediction regions. Finally, the proposed forecasting procedure and the uncertainty quantification technique are applied to a real dataset, collecting daily observations of Sea Level Anomalies of the Black Sea.

Causal Relationship Between Spot Price &amp; Future Derivative Prices – Case of Crude Oil

This research aims to examine the theoretical and empirical connections between current and future crude oil prices using cutting-edge econometric methods. It surveys existing literature and theoretical frameworks, exploring theories like arbitrage, market efficiency, and risk management techniques. The study then conducts a comprehensive empirical investigation using a large dataset, including data from extreme market volatility and other significant events in the financial world. Time series econometric methods like Granger causality tests, Vector Autoregression (VAR), and impulse response functions are used to capture the causal connections between spot and future prices. The analysis uncovers insights on lead-lag dynamics, volatility spillovers, and both short- and long-term causal impacts between current and future crude oil prices. Market fundamentals, geopolitical developments, and speculative behavior are also highlighted as influencing the causal relationships studied. The findings shed light on the link between future and current crude oil prices and provide valuable insights into the factors influencing these prices. This paper examines the relationship between future and spot crude oil prices, offering valuable insights for energy policy, risk management, hedging techniques, investment allocation, and governmental interventions.

Learning CHARME models with neural networks

In this paper, we consider a model called CHARME (Conditional Heteroscedastic Autoregressive Mixture of Experts), a class of generalized mixture of nonlinear (non)parametric AR-ARCH time series. The main objective of this paper is to learn the autoregressive and volatility functions of this model with neural networks (NN). This approach is justified thanks to the universal approximation capacity of neural networks. On the other hand, in order to build the learning theory, it is necessary first to prove the ergodicity of the CHARME model. We therefore show in a general nonparametric framework that under certain Lipschitz-type conditions on the autoregressive and volatility functions, this model is stationary, ergodic and $$\tau $$ -weakly dependent. These conditions are much weaker than those in the existing literature. Moreover, this result forms the theoretical basis for deriving an asymptotic theory of the underlying parametric estimation, which we present for this model in a general parametric framework. Altogether, this allows to develop a learning theory for the NN-based autoregressive and volatility functions of the CHARME model, where strong consistency and asymptotic normality of the considered estimator of the NN weights and biases are guaranteed under weak conditions. Numerical experiments are reported to support our theoretical findings.

УЧЕТ СКОРРЕЛИРОВАННОСТИ ОШИБОК СПУТНИКОВЫХ ДАННЫХ НАБЛЮДЕНИЙ AMV В АНСАМБЛЕВОЙ СИСТЕМЕ УСВОЕНИЯ ДАННЫХ

The effect of considering correlated errors in AMV (Atmospheric Motion Vectors) satellite observations of wind in the local ensemble transform Kalman filter data assimilation system is studied. It is customary to use a diagonal covariance matrix of errors in observations taking part in assimilation. When assimilating satellite data with correlated errors, the data are thinned, and the values of diagonal elements of the error covariance matrix are often overestimated. This is accompanied by the loss of useful information about the correlation between the errors. The present study uses a different method: the elements of the error covariance matrix for AMV satellite observations are simulated using a second-order autoregressive function. It is shown that such approach reduces the root-mean-square error in initial data for a numerical weather prediction model, in particular on small scales, and improves the forecast quality. It is found that the application of the non-diagonal AMV observation error covariance matrix increases the accuracy of analysis and forecast fields.

On consistency and sparsity for high-dimensional functional time series with application to autoregressions

Modelling a large collection of functional time series arises in a broad spectral of real applications. Under such a scenario, not only the number of functional variables can be diverging with, or even larger than the number of temporally dependent functional observations, but each function itself is an infinite-dimensional object, posing a challenging task. In this paper, we propose a three-step procedure to estimate high-dimensional functional time series models. To provide theoretical guarantees for the three-step procedure, we focus on multivariate stationary processes and propose a novel functional stability measure based on their spectral properties. Such stability measure facilitates the development of some useful concentration bounds on sample (auto)covariance functions, which serve as a fundamental tool for further convergence analysis in high-dimensional settings. As functional principal component analysis (FPCA) is one of the key dimension reduction techniques in the first step, we also investigate the non-asymptotic properties of the relevant estimated terms under a FPCA framework. To illustrate with an important application, we consider vector functional autoregressive models and develop a regularization approach to estimate autoregressive coefficient functions under the sparsity constraint. Using our derived non-asymptotic results, we investigate convergence properties of the regularized estimate under high-dimensional scaling. Finally, the finite-sample performance of the proposed method is examined through both simulations and a public financial dataset.

Hedging role of stablecoins

Wild price fluctuations of cryptocurrencies make it difficult for investors to maintain stable asset values. This study investigates the hedging properties of US dollar (USD)-pegged stablecoins against bitcoin returns. We analyzed the hedging abilities of the three largest stablecoins—namely, Tether, USD Coin, and Binance USD—using the dynamic conditional correlation–generalized autoregressive conditional heteroskedasticity, dummy variable regression, vector autoregression, and impulse response functions. We found that stablecoins are generally negatively correlated with bitcoin returns, indicating that they can be effective hedging instruments against high-volatility crypto assets. Among the stablecoins, Binance USD offers the largest risk reduction, and Tether was a weak safe haven during the COVID-19 crisis period. Crypto investors can diversify their portfolios by holding stablecoins.

Forecasting Day-Ahead Traffic Flow Using Functional Time Series Approach

Nowadays, short-term traffic flow forecasting has gained increasing attention from researchers due to traffic congestion in many large and medium-sized cities that pose a serious threat to sustainable urban development. To this end, this research examines the forecasting performance of functional time series modeling to forecast traffic flow in the ultra-short term. An appealing feature of the functional approach is that unlike other methods, it provides information over the whole day, and thus, forecasts can be obtained for any time within a day. Within this approach, a Functional AutoRegressive (FAR) model is used to forecast the next-day traffic flow. For empirical analysis, the traffic flow data of Dublin airport link road, Ireland, collected at a fifteen-minute interval from 1 January 2016 to 30 April 2017, are used. The first twelve months are used for model estimation, while the remaining four months are for the one-day-ahead out-of-sample forecast. For comparison purposes, a widely used model, namely AutoRegressive Integrated Moving Average (ARIMA), is also used to obtain the forecasts. Finally, the models’ performances are compared based on different accuracy statistics. The study results suggested that the functional time series model outperforms the traditional time series models. As the proposed method can produce traffic flow forecasts for the entire next day with satisfactory results, it can be used in decision making by transportation policymakers and city planners.

Quantitative Easing and Macroeconomic Performance in the United States

Abstract This scientific paper examines the relationship between macroeconomic variables whose performance is measured under the implementation of Quantitative Easing in the US, by estimating vector autoregression (VAR) and Impulse Response Function with monthly data from US Federal Reserve, observed during the period January 1994-January 2022. Variables include: Consumer Price Index (CPIAUCSL); Industrial Production (INDPRO); Unemployment Rate (UNRATE); Interest Rates, Government Securities, Government Bonds (INTGSBUSM193N); Volatility Index (VIXCLS), Real Broad Effective Exchange Rate (RBUSBIS), Federal Surplus or Deficit (MTSDS133FMS), Money Supply M1 (WM1NS), M2 (WMNS), M3 (MABMM301USM189S). An evidence on macroeconomic variables of Consumer Price Index and Industrial Production when evaluating the effectiveness of QE is provided.

An Implication of Impulse Response Function in the Perspective of Green Revolution, Credit Disbursement, and Fossil Fuel Utilization in Pakistan

Recently, credit disbursement and fossil fuel utilization increased to enhance wheat production so peasants could benefit from the green revolution. To look at the impact of credit disbursement, fossil fuel utilization, and the determinants of the green revolution were arranged to investigate the association among them. For this purpose, the study employed the time series in the perspective of Pakistan, spanning 1971 to 2019. Modern econometrics techniques like Johansen cointegration, vector autoregressive and impulse response function were employed along with a number of diagnostics tests. Evidence of the Johansen model shows significant long-run cointegration among the green revolution, credit disbursement, fossil fuel, and total wheat production. The Johansen test elaborates that 1% increase in credit disbursement and fossil fuel increases the total wheat production by 0.57% and 0.04 % respectively. Moreover, the determinants of the green revolution also positively affect wheat production. While the coefficient, residual and stability diagnostic tests are in favor of the study. The findings of the impulse response function state that all the concerned variables positively affect the total wheat production in the coming years. The study suggested that the government and private sector should invest in research and development to introduce the organic chemical and forming to avoid soil fertility and environmental degradation.