Utilizing the Vector Autoregression Model (VAR) for Short-Term Solar Irradiance Forecasting

Forecasting solar irradiance is a critical task in the renewable energy sector, as it provides essential information regarding the potential energy production from solar panels. This study aims to utilize the Vector Autoregression (VAR) model to forecast solar irradiance levels and weather characteristics in the San Francisco Bay Area. The results demonstrate a correlation between predicted and actual solar irradiance, indicating the effectiveness of the VAR model for this task. However, the model may not be sufficient for this region due to the requirement of additional weather features to reduce disparities between predictions and actual observations. Additionally, the current lag order in the model is relatively low, limiting its ability to capture all relevant information from past observations. As a result, the model’s forecasting capability is limited to short-term horizons, with a maximum horizon of four hours.

Threshold autoregression models for forecasting El Nino events

-In this paper, monthly mean SST data in a large area are used. After the spacial average of the data is carried out and the secular monthly means are substracted, a time series (Jan. 1951-Dec. 1985) of SST anomalies of the cold tongue water area in the eastern tropical Pacific Ocean is obtained. On the basis of the time series, an autoregression model, a self-exciting threshold autoregression model and an open loop autoregression model are developed respectively. The interannual variations are simulated by means of those models. The simulation results show that all the three models have made very good hindcasting for the nine El Nino events since 1951. In order to test the reliability of the open loop threshold model, extrapolated forecast was made for the period of Jan. 1986-Feb. 1987. It can be seen from the forecasting that the model could forecast well the beginning and strengthening stages of the recent El Nino event (1986-1987). Correlation coefficients of the estimations to observations are respectively 0. 84, 0. 88 and 0. 89. It is obvious that all the models work well and the open loop threshold one is the best. So the open loop threshold autoregression model is a useful tool for monitoring the SSTinterannual variation of the cold tongue water area in the Eastern Equatorial Pacific Ocean and for estimating the El Nino strength.

Asymptotic normality of error density estimator in stationary and explosive autoregressive models

In this paper,we consider the limit distribution of the error density function estima-tor in the rst-order autoregressive models with negatively associated and positively associated random errors.Under mild regularity assumptions,some asymptotic normality results of the residual density estimator are obtained when the autoregressive models are stationary process and explosive process.In order to illustrate these results,some simulations such as con dence intervals and mean integrated square errors are provided in this paper.It shows that the residual density estimator can replace the density\estimator"which contains errors.

Deep Learning-Based Stock Price Prediction Using LSTM Model

The stock market is a vital component of the broader financial system,with its dynamics closely linked to economic growth.The challenges associated with analyzing and forecasting stock prices have persisted since the inception of financial markets.By examining historical transaction data,latent opportunities for profit can be uncovered,providing valuable insights for both institutional and individual investors to make more informed decisions.This study focuses on analyzing historical transaction data from four banks to predict closing price trends.Various models,including decision trees,random forests,and Long Short-Term Memory(LSTM)networks,are employed to forecast stock price movements.Historical stock transaction data serves as the input for training these models,which are then used to predict upward or downward stock price trends.The study’s empirical results indicate that these methods are effective to a degree in predicting stock price movements.The LSTM-based deep neural network model,in particular,demonstrates a commendable level of predictive accuracy.This conclusion is reached following a thorough evaluation of model performance,highlighting the potential of LSTM models in stock market forecasting.The findings offer significant implications for advancing financial forecasting approaches,thereby improving the decision-making capabilities of investors and financial institutions.

THE LIMIT THEOREM FOR DEPENDENT RANDOM VARIABLES WITH APPLICATIONS TO AUTOREGRESSION MODELS

This paper studies the autoregression models of order one, in a general time series setting that allows for weakly dependent innovations. Let {Xt} be a linear process defined by Xt =∑k=0^∞ψ kεt-k, where {ψk, k ≥ 0} is a sequence of real numbers and {εk, k = 0, ±1, ±2,...} is a sequence of random variables. Two results are proved in this paper. In the first result, assuming that {εk, k ≥ 1} is a sequence of asymptotically linear negative quadrant dependent （ALNQD） random variables, the authors find the limiting distributions of the least squares estimator and the associated regression t statistic. It is interesting that the limiting distributions are similar to the one found in earlier work under the assumption of i.i.d, innovations. In the second result the authors prove that the least squares estimator is not a strong consistency estimator of the autoregressive parameter a when {εk, k ≥ 1} is a sequence of negatively associated （NA） random variables, and ψ0 = 1, ψk = 0, k ≥ 1.

Trend Autoregressive Model Exact Run Length Evaluation on a Two-Sided Extended EWMA Chart

The Extended Exponentially Weighted Moving Average(extended EWMA)control chart is one of the control charts and can be used to quickly detect a small shift.The performance of control charts can be evaluated with the average run length(ARL).Due to the deriving explicit formulas for the ARL on a two-sided extended EWMA control chart for trend autoregressive or trend AR(p)model has not been reported previously.The aim of this study is to derive the explicit formulas for the ARL on a two-sided extended EWMA con-trol chart for the trend AR(p)model as well as the trend AR(1)and trend AR(2)models with exponential white noise.The analytical solution accuracy was obtained with the extended EWMA control chart and was compared to the numer-ical integral equation(NIE)method.The results show that the ARL obtained by the explicit formula and the NIE method is hardly different,but the explicit for-mula can help decrease the computational(CPU)time.Furthermore,this is also expanded to comparative performance with the Exponentially Weighted Moving Average(EWMA)control chart.The performance of the extended EWMA control chart is better than the EWMA control chart for all situations,both the trend AR(1)and trend AR(2)models.Finally,the analytical solution of ARL is applied to real-world data in the healthfield,such as COVID-19 data in the United Kingdom and Sweden,to demonstrate the efficacy of the proposed method.

Constructing Confidence Regions for Autoregressive-Model Parameters

We discuss formulas and techniques for finding maximum-likelihood estimators of parameters of autoregressive (with particular emphasis on Markov and Yule) models, computing their asymptotic variance-covariance matrix and displaying the resulting confidence regions;Monte Carlo simulation is then used to establish the accuracy of the corresponding level of confidence. The results indicate that a direct application of the Central Limit Theorem yields errors too large to be acceptable;instead, we recommend using a technique based directly on the natural logarithm of the likelihood function, verifying its substantially higher accuracy. Our study is then extended to the case of estimating only a subset of a model’s parameters, when the remaining ones (called nuisance) are of no interest to us.

Modelling COVID-19 Cumulative Number of Cases in Kenya Using a Negative Binomial INAR (1) Model

In this paper, a Negative Binomial (NB) Integer-valued Autoregressive model of order 1, INAR (1), is used to model and forecast the cumulative number of confirmed COVID-19 infected cases in Kenya independently for the three waves starting from 14th March 2020 to 1st February 2021. The first wave was experienced from 14th March 2020 to 15th September 2020, the second wave from around 15th September 2020 to 1st February 2021 and the third wave was experienced from 1st February 2021 to 3rd June 2021. 5, 10, and 15-day-ahead forecasts are obtained for these three waves and the performance of the NB-INAR (1) model analysed.

River channel flood forecasting method of coupling wavelet neural network with autoregressive model

Based on analyzing the limitations of the commonly used back-propagation neural network （BPNN）, a wavelet neural network （WNN） is adopted as the nonlinear river channel flood forecasting method replacing the BPNN. The WNN has the characteristics of fast convergence and improved capability of nonlinear approximation. For the purpose of adapting the timevarying characteristics of flood routing, the WNN is coupled with an AR real-time correction model. The AR model is utilized to calculate the forecast error. The coefficients of the AR real-time correction model are dynamically updated by an adaptive fading factor recursive least square（RLS） method. The application of the flood forecasting method in the cross section of Xijiang River at Gaoyao shows its effectiveness.

Modeling groundwater nitrate concentrations using spatial and non-spatial regression models in a semi-arid environment

Nitrate nitrogen(NO_(3)^(-)N)from agricultural activities and in industrial wastewater has become the main source of groundwater pollution,which has raised widespread concerns,particularly in arid and semi-arid river basins with little water that meets relevant standards.This study aimed to investigate the performance of spatial and non-spatial regression models in modeling nitrate pollution in a semi-intensive farming region of Iran.To perform the modeling of the groundwater's NO_(3)^(-)N concentration,both natural and anthropogenic factors affecting groundwater NO_(3)^(-)N were selected.The results of Moran's I test showed that groundwater nitrate concentration had a significant spatial dependence on the density of wells,distance from streams,total annual precipitation,and distance from roads in the study area.This study provided a way to estimate nitrate pollution using both natural and anthropogenic factors in arid and semi-arid areas where only a few factors are available.Spatial regression methods with spatial correlation structures are effective tools to support spatial decision-making in water pollution control.

Influencing Factors and Prediction of Risk of Returning to Ecological Poverty in Liupan Mountain Region,China

China has resolved its overall regional poverty in 2020 by attaining moderate societal prosperity.The country has entered a new development stage designed to achieve its second centenary goal.However,ecological fragility and risk susceptibility have increased the risk of returning to ecological poverty.In this paper,the Liupan Mountain Region of China was used as a case study,and the counties were used as the scale to reveal the spatiotempora differentiation and influcing factors of the risk of returning to poverty in study area.The indicator data for returning to ecological poverty from 2011-2020 were collected and summarized in three dimensions:ecological,economic and social.The autoregressive integrated moving average model(ARIMA)time series and exponential smoothing method(ES)were used to predict the multidimensional indicators of returning to ecological poverty for 61 counties(districts)in the Liupan Mountain Region for 2021-2030.The back propagation neural network(BPNN)and geographic information system(GIS)were used to generate the spatial distribution and time variation for the index of the risk of returning to ecological poverty(RREP index).The results show that 1)ecological factors were the main factors in the risk of returning to ecological poverty in Liupan Mountain Region.2)The RREP index for the 61 counties(districts)exhibited a downward trend from 2021-2030.The RREP index declined more in medium-and high-risk areas than in low-risk areas.From 2021 to 2025,the RREP index exhibited a slight downward trend.From 2026 to2030,the RREP index was expected to decline faster,especially from 2029-2030.3)Based on the RREP index,it can be roughly divided into three types,namely,the high-risk areas,the medium-risk areas,and the low-risk areas.The natural resource conditions in lowrisk areas of returning to ecological poverty,were better than those in medium-and high-risk areas.

JUMP DETECTION BY WAVELET IN NONLINEAR AUTOREGRESSIVE MODELS

Wavelets are applied to detection of the jump points of a regression function in nonlinear autoregressive model x(t) = T(x(t-1)) + epsilon t. By checking the empirical wavelet coefficients of the data,which have significantly large absolute values across fine scale levels, the number of the jump points and locations where the jumps occur are estimated. The jump heights are also estimated. All estimators are shown to be consistent. Wavelet method ia also applied to the threshold AR(1) model(TAR(1)). The simple estimators of the thresholds are given,which are shown to be consistent.

Empirical likelihood for first-order mixed integer-valued autoregressive model

In this paper, we not only construct the confidence region for parameters in a mixed integer-valued autoregressive process using the empirical likelihood method, but also establish the empirical log-likelihood ratio statistic and obtain its limiting distribution. And then, via simulation studies we give coverage probabilities for the parameters of interest. The results show that the empirical likelihood method performs very well.

AUTOREGRESSIVE MODEL AND POWER SPECTRUM CHARATERISTICS OF CURRENT SIGNAL IN HIGH FREQUENCY GROUP PULSE MICRO-ELECTROCHEMICAL MACHINING

The identification of the inter-electrode gap size in the high frequency group pulse micro-electrochemical machining （HGPECM） is mainly discussed. The auto-regressive（AR） model of group pulse current flowing across the cathode and the anode are created under different situations with different processing parameters and inter-electrode gap size. The AR model based on the current signals indicates that the order of the AR model is obviously different relating to the different processing conditions and the inter-electrode gap size; Moreover, it is different about the stability of the dynamic system, i.e. the white noise response of the Green＇s function of the dynamic system is diverse. In addition, power spectrum method is used in the analysis of the dynamic time series about the current signals with different inter-electrode gap size, the results show that there exists a strongest power spectrum peak, characteristic power spectrum（CPS）, to the current signals related to the different inter-electrode gap size in the range of 0～5 kHz. Therefore, the CPS of current signals can implement the identification of the inter-electrode gap.

Iterative learning control of SOFC based on ARX identification model

This paper presents an application of iterative learning control (ILC) technique to the voltage control of solid oxide fuel cell (SOFC) stack. To meet the demands of the control system design, an autoregressive model with exogenous input (ARX) is established. Firstly, by regulating the variation of the hydrogen flow rate proportional to that of the current, the fuel utilization of the SOFC is kept within its admissible range. Then, based on the ARX model, three kinds of ILC controllers, i.e. P-, PI- and PD-type are designed to keep the voltage at a desired level. Simulation results demonstrate the potential of the ARX model applied to the control of the SOFC, and prove the excellence of the ILC controllers for the voltage control of the SOFC.

PARTICLE FILTERING BASED AUTOREGRESSIVE CHANNEL PREDICTION MODEL

A particle filtering based AutoRegressive (AR) channel prediction model is presented for cognitive radio systems. Firstly, this paper introduces the particle filtering and the system model. Secondly, the AR model of order p is used to approximate the flat Rayleigh fading channels; its stability is discussed, and an algorithm for solving the AR model parameters is also given. Finally, an AR channel prediction model based on particle filtering and second-order AR model is presented. Simulation results show that the performance of the proposed AR channel prediction model based on particle filtering is better than that of Kalman filtering.

Multivariate Generalized Autoregressive Conditional Heteroscedastic Model

In this paper, by making use of the Hadamard product of matrices, a natural and reasonable generalization of the univariate GARCH (Generalized Autoregressive Conditional heteroscedastic) process introduced by Bollerslev (J. Econometrics 31(1986), 307-327) to the multivariate case is proposed. The conditions for the existence of strictly stationary and ergodic solutions and the existence of higher-order moments for this class of parametric models are derived.

Asymptotic Normality of Pseudo-LS Estimator of Error Variance in Partly Linear Autoregressive Models

Consider the model Yt = βYt-1＋g（Yt-2）＋εt for 3 〈 t 〈 T. Hereg is anunknown function, β is an unknown parameter, εt are i.i.d, random errors with mean 0 andvariance σ2 and the fourth moment α4, and α4 are independent of Y8 for all t ≥ 3 and s = 1, 2.Pseudo-LS estimators σ, σ2T α4τ and D2T of σ^2,α4 and Var（ε2↑3） are respectively constructedbased on piecewise polynomial approximator of g. The weak consistency of α4T and D2T are proved. The asymptotic normality of σ2T is given, i.e., √T（σ2T -σ^2）/DT converges indistribution to N（0, 1）. The result can be used to establish large sample interval estimatesof σ^2 or to make large sample tests for σ^2.

Noise reduction of acoustic Doppler velocimeter data based on Kalman filtering and autoregressive moving average models

Oceanic turbulence measurements made by an acoustic Doppler velocimeter(ADV)suffer from noise that potentially affects the estimates of turbulence statistics.This study examines the abilities of Kalman filtering and autoregressive moving average models to eliminate noise in ADV velocity datasets of laboratory experiments and offshore observations.Results show that the two methods have similar performance in ADV de-noising,and both effectively reduce noise in ADV velocities,even in cases of high noise.They eliminate the noise floor at high frequencies of the velocity spectra,leading to a longer range that effectively fits the Kolmogorov-5/3 slope at midrange frequencies.After de-noising adopting the two methods,the values of the mean velocity are almost unchanged,while the root-mean-square horizontal velocities and thus turbulent kinetic energy decrease appreciably in these experiments.The Reynolds stress is also affected by high noise levels,and de-noising thus reduces uncertainties in estimating the Reynolds stress.

The m-delay Autoregressive Model with Application

The classical autoregressive(AR)model has been widely applied to predict future data usingmpast observations over five decades.As the classical AR model required m unknown parameters,this paper implements the AR model by reducing m parameters to two parameters to obtain a new model with an optimal delay called as the m-delay AR model.We derive the m-delay AR formula for approximating two unknown parameters based on the least squares method and develop an algorithm to determine optimal delay based on a brute-force technique.The performance of them-delay AR model was tested by comparing with the classical AR model.The results,obtained from Monte Carlo simulation using the monthly mean minimum temperature in PerthWestern Australia from the Bureau of Meteorology,are no significant difference compared to those obtained from the classical AR model.This confirms that the m-delay AR model is an effective model for time series analysis.