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Because of the uncertainty and randomness of wind speed, wind power has characteristics such as nonlinearity and multiple frequencies. Accurate prediction of wind power is one effective means of improving wind power integration. Because the traditional single model cannot fully characterize the fluctuating characteristics of wind power, scholars have attempted to build other prediction models based on empirical mode decomposition (EMD) or ensemble empirical mode decomposition (EEMD) to tackle this problem. However, the prediction accuracy of these models is affected by modal aliasing and illusive components. Aimed at these defects, this paper proposes a multi-frequency combination prediction model based on variational mode decomposition (VMD). We use a back propagation neural network (BPNN), autoregressive moving average (ARMA) model, and least squares support vector machine (LS-SVM) to predict high, intermediate, and low frequency components, respectively. Based on the predicted values of each component, the BPNN is applied to combine them into a final wind power prediction value. Finally, the prediction performance of the single prediction models (ARMA, BPNN, LS-SVM) and the decomposition prediction models (EMD and EEMD) are used to compare with the proposed VMD model according to the evaluation indices such as average absolute error, mean square error, and root mean square error to validate its feasibility and accuracy. The results show that the prediction accuracy of the proposed VMD model is higher.

Accurate and reliable air quality predictions are critical to the ecological environment and public health. For the traditional model fails to make full use of the high and low frequency information obtained after wavelet decomposition, which easily leads to poor prediction performance of the model. This paper proposes a hybrid prediction model based on data decomposition, choosing wavelet decomposition (WD) to generate high-frequency detail sequences WD(D) and low-frequency approximate sequences WD(A), using sliding window high-frequency detail sequences WD(D) for reconstruction processing, and long short-term memory (LSTM) neural network and autoregressive moving average (ARMA) model for WD(D) and WD(A) sequences for prediction. The final prediction results of air quality can be obtained by accumulating the predicted values of each sub-sequence, which reduces the root mean square error (RMSE) by 52%, mean absolute error (MAE) by 47%, and increases the goodness of fit (R2) by 18% compared with the single prediction model. Compared with the mixed model, reduced the RMSE by 3%, reduced the MAE by 3%, and increased the R2 by 0.5%. The experimental verification found that the proposed prediction model solves the problem of lagging prediction results of single prediction model, which is a feasible air quality prediction method.

Highly public anti-Black violence in the United States may cause widely experienced distress for Black Americans. This study identifies 49 publicized incidents of racial violence and quantifies national interest based on Google searches; incidents include police killings of Black individuals, decisions not to indict or convict the officer involved, and hate crime murders. Weekly time series of population mental health are produced for 2012 through 2017 using two sources: 1) Google Trends as national search volume for psychological distress terms and 2) the Behavioral Risk Factor Surveillance System (BRFSS) as average poor mental health days in the past 30 d among Black respondents (mean weekly sample size of 696). Autoregressive moving average (ARMA) models accounted for autocorrelation, monthly unemployment, season and year effects, 52-wk lags, news-related searches for suicide (for Google Trends), and depression prevalence and percent female (for BRFSS). National search interest varied more than 100-fold between racial violence incidents. Black BRFSS respondents reported 0.26more poormental health days during weekswith two or more racial incidents relative to none, and 0.13 more days with each log10 increase in national interest. Estimates were robust to sensitivity tests, including controlling for monthly number of Black homicide victims and weekly search interest in riots. As expected, racial incidents did not predict average poor mental health days among White BRFSS respondents. Results with national psychological distress from Google Trends were mixed but generally unsupportive of hypotheses. Reducing anti-Black violence may benefit Black Americans’ mental health nationally.

In linear time series analysis, the incorporation of the moving-average term in autoregressive models yields parsimony while retaining flexibility; in particular, the first order autoregressive moving-average model, ARMA(1,1) is notable since it retains a good approximating capability with just two parameters. In the same spirit, we assess empirically whether a similar result holds for threshold processes. First, we show that the first order threshold autoregressive moving-average process, TARMA(1,1) exhibits complex, high-dimensional, behaviour with parsimony, by comparing it with threshold autoregressive processes, TAR( p ), with possibly large autoregressive order p . Second, we study the descriptive power of the TARMA(1,1) model with respect to the class of autoregressive models, seen as universal approximators: in several situations, the TARMA(1,1) model outperforms AR( p ) models even when p is large. Lastly, we analyze two real world data sets: the sunspot number and the male US unemployment rate time series. In both cases, we show that TARMA models provide a better fit with respect to the best TAR models proposed in literature.

Benzene is a pollutant which is very harmful to our health, so models are necessary to predict its concentration and relationship with other air pollutants. The data collected by eight stations in Madrid (Spain) over nine years were analyzed using the following regression-based machine learning models: multivariate linear regression (MLR), multivariate adaptive regression splines (MARS), multilayer perceptron neural network (MLP), support vector machines (SVM), autoregressive integrated moving-average (ARIMA) and vector autoregressive moving-average (VARMA) models. Benzene concentration predictions were made from the concentration of four environmental pollutants: nitrogen dioxide (NO2), nitrogen oxides (NOx), particulate matter (PM10) and toluene (C7H8), and the performance measures of the model were studied from the proposed models. In general, regression-based machine learning models are more effective at predicting than time series models.

In this paper, we reconsider the mixture vector autoregressive model, which was proposed in the literature for modelling non-linear time series. We complete and extend the stationarity conditions, derive a matrix formula in closed form for the autocovariance function of the process and prove a result on stable vector autoregressive moving-average representations of mixture vector autoregressive models. For these results, we apply techniques related to a Markovian representation of vector autoregressive moving-average processes. Furthermore, we analyse maximum likelihood estimation of model parameters by using the expectation-maximization algorithm and propose a new iterative algorithm for getting the maximum likelihood estimates. Finally, we study the model selection problem and testing procedures. Several examples, simulation experiments and an empirical application based on monthly financial returns illustrate the proposed procedures.

In view of the large output noise and low precision of the Micro-electro-mechanical Systems (MEMS) gyroscope, the virtual gyroscope technology was used to fuse the data of the MEMS gyroscope to improve its output precision. Random error model in the conventional virtual gyroscopes contained an angular rate random walk and angle random walk ignoring other noise items and the virtual gyroscope technology can not compensate all random errors of MEMS gyroscope. So, the improved virtual gyroscope technology based on the autoregressive moving average (ARMA) model was proposed. First, the conventional virtual gyroscope technology was used to model the random error of three MEMS gyroscopes, and the data fusion was carried out by a Kalman filter to get the output of the virtual gyroscope. After that, the ARMA model was used to model the output of the virtual gyroscope, the random error model was improved with the ARMA model, and the Kalman filter was designed based on the improved random error model for data fusion of the MEMS gyroscopes. The experimental results showed that the 1σ standard deviation of the output of the virtual gyroscope based on the ARMA model was 1.4 times lower than that of the conventional virtual gyroscope output.

Atmospheric particulate matter (PM) is one of the pollutants that may have a significant impact on human health. Data collected over 7 years from the air quality monitoring station at the LD-III steelworks, belonging to the Arcelor-Mittal Steel Company, located in the metropolitan area of Avilés (Principality of Asturias, Northern Spain), is analyzed using four different mathematical models: vector autoregressive moving-average, autoregressive integrated moving-average (ARIMA), multilayer perceptron neural networks and support vector machines with regression. Measured monthly, the average concentration of pollutants (SO2, NO and NO2) and PM10 (particles with a diameter less than  10 μm) is used as input to forecast the monthly average concentration of PM10 from one to 7 months ahead. Simulations showed that the ARIMA model performs better than the other models when forecasting 1 month ahead, while in the forecast from one to 9 months ahead the best performance is given by the support vector regression.

Wind speed prediction of the wind power plant has an important influence on the stability and safe operation of the power system. Because the wind speed series is intermittent and random, a combination model of EEMD-ARIMA is proposed to predict ultra-short-term wind speed. The advantage of the prediction model mentioned in this paper is to deal with the problem of large prediction errors caused by the instability of the original wind speed series. First, the ensemble empirical mode decomposition (EEMD) is used to decompose the series, and then the autoregressive moving average (ARIMA) is used to predict the components. Through the example analysis, it can be seen that the prediction model mentioned in this paper is more accurate than the traditional ARIMA model in predicting short-term wind speed.

Wind energy, as one of the renewable energies with the most potential for development, has been widely concerned by many countries. However, due to the great volatility and uncertainty of natural wind, wind power also fluctuates, seriously affecting the reliability of wind power system and bringing challenges to large-scale grid connection of wind power. Wind speed prediction is very important to ensure the safety and stability of wind power generation system. In this paper, a new wind speed prediction scheme is proposed. First, improved hybrid mode decomposition is used to decompose the wind speed data into the trend part and the fluctuation part, and the noise is decomposed twice. Then wavelet analysis is used to decompose the trend part and the fluctuation part for the third time. The decomposed data are classified. The long- and short-term memory neural network optimized by the improved particle swarm optimization algorithm is used to train the nonlinear sequence and noise sequence, and the autoregressive moving average model is used to train the linear sequence. Finally, the final prediction results were reconstructed. This paper uses this system to predict the wind speed data of China’s Changma wind farm and Spain’s Sotavento wind farm. By experimenting with the real data from two different wind farms and comparing with other predictive models, we found that (1) by improving the mode number selection in the variational mode decomposition, the characteristics of wind speed data can be better extracted. (2) According to the different characteristics of component data, the combination method is selected to predict modal components, which makes full use of the advantages of different algorithms and has good prediction effect. (3) The optimization algorithm is used to optimize the neural network, which solves the problem of parameter setting when establishing the prediction model. (4) The combination forecasting model proposed in this paper has clear structure and accurate prediction results. The research work in this paper will help to promote the development of wind energy prediction field, help wind farms formulate wind power regulation strategies, and further promote the construction of green energy structure.