Abstract: The use of electrical conductivity (EC) as a water quality indicator is useful for estimating the mineralization and salinity of water. The objectives of this study were to explore, for the first time, extreme learning machine (ELM) and wavelet-extreme learning machine hybrid (WA-ELM) models to forecast multi-step-ahead EC and to employ an integrated method to combine the advantages of WA-ELM models, which utilized the boosting ensemble method. For comparative purposes, an adaptive neuro-fuzzy inference system (ANFIS) model, and a WA-ANFIS model, were also developed. The study area was the Aji-Chay River at the Akhula hydrometric station in Northwestern Iran. A total of 315 monthly EC (µS/cm) datasets (1984–2011) were used, in which the first 284 datasets (90% of total datasets) were considered for training and the remaining 31 (10% of total datasets) were used for model testing. Autocorrelation function (ACF) and partial autocorrelation function (PACF) demonstrated that the 6-month lags were potential input time lags. The results illustrated that the single ELM and ANFIS models were unable to forecast the multi-step-ahead EC in terms of root mean square error (RMSE), coefficient of determination (R2) and Nash–Sutcliffe model efficiency coefficient (NSC). To develop the hybrid WA-ELM and WA-ANFIS models, the original time series of lags as inputs, and time series of 1, 2 and 3 month-step-ahead EC values as outputs, were decomposed into several sub-time series using different maximal overlap discrete wavelet transform (MODWT) functions, namely Daubechies, Symlet, Haar and Coiflet of different orders at level three. These sub-time series were then used in the ELM and ANFIS models as an input dataset to forecast the multi-step-ahead EC. The results indicated that single WA-ELM and WA-ANFIS models performed better than any ELM and ANFIS models. Also, WA-ELM models outperformed WA-ANFIS models. To develop the boosting multi-WA-ELM and multi-WA-ANFIS ensemble models, a least squares boosting (LSBoost) algorithm was used. The results showed that boosting multi-WA-ELM and multi-WA-ANFIS ensemble models outperformed the individual WA-ELM and WA-ANFIS models.

Abstract: Daily land surface temperature (LST) forecasting is of great significance for application in climate-related, agricultural, eco-environmental, or industrial studies. Hybrid data-driven prediction models using Ensemble Empirical Mode Composition (EEMD) coupled with Machine Learning (ML) algorithms are useful for achieving these purposes because they can reduce the difficulty of modeling, require less history data, are easy to develop, and are less complex than physical models. In this article, a computationally simple, less data-intensive, fast and efficient novel hybrid data-driven model called the EEMD Long Short-Term Memory (LSTM) neural network, namely EEMD-LSTM, is proposed to reduce the difficulty of modeling and to improve prediction accuracy. The daily LST data series from the Mapoling and Zhijaing stations in the Dongting Lake basin, central south China, from 1 January 2014 to 31 December 2016 is used as a case study. The EEMD is firstly employed to decompose the original daily LST data series into many Intrinsic Mode Functions (IMFs) and a single residue item. Then, the Partial Autocorrelation Function (PACF) is used to obtain the number of input data sample points for LSTM models. Next, the LSTM models are constructed to predict the decompositions. All the predicted results of the decompositions are aggregated as the final daily LST. Finally, the prediction performance of the hybrid EEMD-LSTM model is assessed in terms of the Mean Square Error (MSE), Mean Absolute Error (MAE), Mean Absolute Percentage Error (MAPE), Root Mean Square Error (RMSE), Pearson Correlation Coefficient (CC) and Nash-Sutcliffe Coefficient of Efficiency (NSCE). To validate the hybrid data-driven model, the hybrid EEMD-LSTM model is compared with the Recurrent Neural Network (RNN), LSTM and Empirical Mode Decomposition (EMD) coupled with RNN, EMD-LSTM and EEMD-RNN models, and their comparison results demonstrate that the hybrid EEMD-LSTM model performs better than the other five models. The scatterplots of the predicted results of the six models versus the original daily LST data series show that the hybrid EEMD-LSTM model is superior to the other five models. It is concluded that the proposed hybrid EEMD-LSTM model in this study is a suitable tool for temperature forecasting.

Abstract: Short-term wind speed prediction is beneficial to guarantee the safety of wind power utilization and reduce the cost of wind power generation. As a kind of the powerful artificial intelligent algorithms, support vector regression (SVR) has been successfully employed in solving forecasting problems. However, due to the intrinsic complexity and multi-patterns of wind speed fluctuations, it is regarded as one of the most challenging applications for wind speed prediction. To alleviate the influence of complexity and capture these different patterns, this study proposes a novel approach named SIE–WDA–GA–SVR for short-term wind speed prediction, which applies the seasonal information extraction (SIE) and wavelet decomposition algorithm (WDA) into hybrid model that integrates the genetic algorithm (GA) into SVR. First, the proposed approach uses SIE to decompose the original wind speed into seasonal and trend components, and the seasonal indices are calculated by SIE. Second, the proposed approach uses WDA to decompose the trend component into both the approximate and the detailed scales. Third, the proposed approach uses GA–SVR to forecast the approximated and detailed scales, respectively. Then, the prediction values of the trend component can be obtained by integrating the prediction values of the approximated scale into the prediction values of the detailed scale. By integrating the seasonal indices into the prediction values of trend component, we can obtain the final forecasting results of the original wind speed. Moreover, the partial autocorrelation function is used to determine the number of input dimension for the SVR, and the GA is used to select the parameters of the SVR. Four real wind speed datasets are used as test samples to verify the proposed approach. Experimental results indicate that the proposed approach outperforms other benchmark models in four statistical error measures, and can improve the forecasting accuracy of wind speed.

Abstract: Autocorrelation and partial autocorrelation, which provide a mathematical tool to understand repeating patterns in time series data, are often used to facilitate the identification of model orders of time series models (e.g., moving average and autoregressive models). Asymptotic methods for testing autocorrelation and partial autocorrelation such as the 1/T approximation method and the Bartlett's formula method may fail in finite samples and are vulnerable to non-normality. Resampling techniques such as the moving block bootstrap and the surrogate data method are competitive alternatives. In this study, we use a Monte Carlo simulation study and a real data example to compare asymptotic methods with the aforementioned resampling techniques. For each resampling technique, we consider both the percentile method and the bias-corrected and accelerated method for interval construction. Simulation results show that the surrogate data method with percentile intervals yields better performance than the other methods. An R package pautocorr is used to carry out tests evaluated in this study.

Abstract: In time series investigation of characteristics of production system, different competing models are generally obtained particularly in production settings with stochastic output attributable to bottleneck problems. Consequently, selecting the best model that describes a production system becomes challenging and critical because some models that fit observed data most accurately may not predict future values correctly on account to model complexities. This research desires to demonstrate the procedure for model selection in production system with random output via the use of Adjusted Coefficient of Determination (R2 ) , Akaike and Schwarz criteria tools. Production output measurements obtained serve as input data to Autocorrelation Function and Partial Autocorrelation Function to obtain the order of Autoregressive, Autoregressive Moving Average and Autoregressive Integrated Moving Average models. The model parameters were estimated and used for predictions and compared with original and transformed data to obtain Sum of Squared Error (SSE). Afterward, the models were subjected to adequacy evaluation and subsequently tested with Akaike and Schwarz criteria. Among the competing models, ARIMA (3, 1, 1) model explain 66% variance of the dataset and wielded the lowest Akaike and Schwarz values of 534.41m and 534.34m respectively and thus selected as the model that represents the production system under investigation. The approach establishes that Adjusted Coefficient of Determination in conjunction with Akaike and Schwarz criteria are adequate tools for model selection in time series investigation particularly in stochastic situation

Abstract: For a multivariate stationary process, we develop explicit representations for the finite predictor coefficient matrices, the finite prediction error covariance matrices and the partial autocorrelation function (PACF) in terms of the Fourier coefficients of its phase function in the spectral domain. The derivation is based on a novel alternating projection technique and the use of the forward and backward innovations corresponding to predictions based on the infinite past and future, respectively. We show that such representations are ideal for studying the rates of convergence of the finite predictor coefficients, prediction error covariances, and the PACF as well as for proving a multivariate version of Baxter’s inequality for a multivariate FARIMA process with a common fractional differencing order for all components of the process.

Abstract: An information-theoretic approach to numerically determine the Markov order of discrete stochastic processes defined over a finite state space is introduced. To measure statistical dependencies between different time points of symbolic time series, two information-theoretic measures are proposed. The first measure is time-lagged mutual information between the random variables $X_{n}$ and $X_{n+k}$, representing the values of the process at time points $n$ and $n+k$, respectively. The measure will be termed autoinformation, in analogy to the autocorrelation function for metric time series, but using Shannon entropy rather than linear correlation. This measure is complemented by the conditional mutual information between $X_{n}$ and $X_{n+k}$, removing the influence of the intermediate values $X_{n+k-1},\ldots,X_{n+1}$. The second measure is termed partial autoinformation, in analogy to the partial autocorrelation function in metric time series analysis. Mathematical relations with known quantities such as the entropy rate and active information storage are established. Both measures are applied to a number of examples, ranging from theoretical Markov and non-Markov processes with known stochastic properties, to models from statistical physics, and finally, to a discrete transform of an EEG data set. The combination of autoinformation and partial autoinformation yields important insights into the temporal structure of the data in all test cases. For first- and higher-order Markov processes, partial autoinformation correctly identifies the order parameter, but also suggests extended, non-Markovian effects in the examples that lack the Markov property. For three hidden Markov models, the underlying Markov order is found. The combination of both quantities may be used as an early step in the analysis of experimental, non-metric time series and can be employed to discover higher-order Markov dependencies, non-Markovianity and periodicities in symbolic time series.

Abstract: The aims of this study contribute to a new hybrid model by combining ensemble empirical mode decomposition (EEMD) with multikernel function least square support vector machine (MKLSSVM) optimized by hybrid gravitation search algorithm (HGSA) for short-term wind speed prediction. In the forecasting process, EEMD is adopted to make the original wind speed data decomposed into intrinsic mode functions (IMFs) and one residual firstly. Then, partial autocorrelation function (PACF) is applied to identify the correlation between the corresponding decomposed components. Subsequently, the MKLSSVM using multikernel function of radial basis function (RBF) and polynomial (Poly) kernel function by weight coefficient is exploited as core forecasting engine to make the short-term wind speed prediction. To improve the regression performance, the binary-value GSA (BGSA) in HGSA is utilized as feature selection approach to remove the ineffective candidates and reconstruct the most relevant feature input-matrix for the forecasting engine, while real-value GSA (RGSA) makes the parameter combination optimization of MKLSSVM model. In the end, these respective decomposed subseries forecasting results are combined into the final forecasting values by aggregate calculation. Numerical results and comparable analysis illustrate the excellent performance of the EEMD-HGSA-MKLSSVM model when applied in the short-term wind speed forecasting.

Abstract: Prediction of rainfall data by using Feed Forward Neural Network (FFNN) model is proposed. FFNN is a class of neural network which has three layers for processing. In time series prediction, including in case of rainfall data, the input layer is the past values of the same series up to certain lag and the output layer is the current value. Beside a few lagged times, the seasonal pattern also considered as an important aspect of choosing the potential input. The autocorrelation function and partial autocorrelation function patterns are used as aid of selecting the input. In the second layer called hidden layer, the logistic sigmoid is used as activation function because of the monotonic and differentiable. Processing is done by the weighted summing of the input variables and transfer process in the hidden layer. Backpropagation algorithm is applied in the training process. Some gradient based optimization methods are used to obtain the connection weights of FFNN model. The prediction is the output resulting of the process in the last layer. In each optimization method, the looping process is performed several times in order to get the most suitable result in various composition of separating data. The best one is chosen by the least mean square error (MSE) criteria. The least of in-sample and out-sample predictions from the repeating results been the base of choosing the best optimization method. In this study, the model is applied in the ten-daily rainfall data of ZOM 136 Cokrotulung Klaten. Simulation results give a consecution that the more complex architecture is not guarantee the better prediction.

Abstract: Gold investment worldwide has grown dramatically in the last few years. To be a gold investors, people itself at least should know the basic knowledge of the current gold price. Besides, they should have the best model as a benchmark tool in order to make the decision whether they are supposed to buy or sell the gold. Therefore, to forecast the gold price in Malaysia for the first quarter of year 2017, the time series data of gold price in Malaysia since 4th January until 30th December 2016 were used for this study. The purpose of this study is to determine the possible chaotic behavior of gold in term of price changes using forecasting methods which are Nonlinear prediction (NLP) method and Box-Jenkins method. NLP method consists of the reconstruction of phase space and local linear approximation approach. Meanwhile for Box-Jenkins method, three different ARIMA models with first order differencing have been chosen based on the plots of Autocorrelation Function (ACF) and Partial Autocorrelation Function (PACF). The Bayesian Information Criterion (BIC), Mean Square Error (MSE), and Mean Absolute Percentage Error (MAPE) for each model were compared for identifying the best model that suit the time series data of gold price in Malaysia. Out of the three Box-Jenkins model that have been applied to the data series, it was found that the ARIMA (1,1,0) was the best model and it suit the time series model of the gold price trend in Malaysia. A comparison of prediction performance between NLP and Box-Jenkins models based on MAPE was employed and as a result, NLP shows the better prediction performance. Thus, this paper provides a summary of how price of gold can benefit to the investors and also provide a better view of the current gold prices movement and gold investment in Malaysia specifically.

Abstract: This paper analyses and characterizes the nonindustrial demand of Iran power system in the last decade and proposes a seasonal autoregressive integrated moving average model (SARIMA) for its mid-term load forecasting (MTLF). Detrending an observed growth and a seasonal additive, the orders of the SARIMA's components are determined by autocorrelation and partial autocorrelation functions. The model residuals are explored for normality by statistical moments including mean, variance, skewness and kurtosis indices. Moreover, the predictive performance of the model is validated with distinct real data. The results proved the applicability of the model for MTLF in power systems.

Abstract: The invention discloses a BP neural network resident community daily water consumption predicting method based on correlation analysis. The method comprises firstly analyzing water consumption influence factors by using a correlation analysis theory and sorting the water consumption influence factors according to influence severities; then analyzing a daily water consumption sequence by using a partial autocorrelation theory; finding out the correlation in a daily water consumption time series; determining the optimal delay time; determining an input variable, and establishing a BP neural network community water consumption prediction model based on correlation analysis. When the model is trained, a data sequence formed by disorganizing the daily water consumptions arranged in chronological order is used as a training set, thereby breaking the limitation of the time series, eliminating the influence of a time factor, and improving the generalization ability of the prediction method.

Abstract: We consider the problem of estimating the high-dimensional autocovariance matrix of a stationary random process, with the purpose of out of sample prediction and feature extraction. This problem has received several solutions. In the nonparametric framework, the literature has concentrated on banding and tapering the sample autocovariance matrix. This paper proposes and evaluates an alternative approach, based on regularizing the sample partial autocorrelation function, via a modified Durbin-Levinson algorithm that receives as input the banded and tapered partial autocorrelations and returns a sample autocovariance sequence which is positive definite. We show that the regularized estimator of the autocovariance matrix is consistent and its convergence rates is established. We then focus on constructing the optimal linear predictor and we assess its properties. The computational complexity of the estimator is of the order of the square of the banding parameter, which renders our method scalable for high-dimensional time series. The performance of the autocovariance estimator and the corresponding linear predictor is evaluated by simulation and empirical applications.

Abstract: The invention relates to the field of early warning models and method, and discloses a population ultralimit early warning method based on ARMA (Auto-Regressive and Moving Average). The method comprises the following steps that: obtaining population data; classifying the obtained population data according to time characteristics; when categories have a tendency difference, carrying out data sampling on each category of population data, and carrying out fitting to establish a fit model; according to the autocorrelation coefficient and the partial autocorrelation coefficient of the established fit model, determining the order of the ARMA model; and utilizing the ARMA model with the determined order to obtain threshold value estimation. Through the above technical scheme, an integral population ultralimit early warning model, including offline data collection, data processing and data modeling, online data threshold value estimation, tendency analysis and the like, is put forward. The data of the collected time sequence data is aimed, the ARMA model is adopted to predict data, potential influence factors are calculated, potential factors which influence the tendency change utilize theautocorrelation coefficient and the partial autocorrelation coefficient for calculation, and therefore, prediction accuracy is greatly optimized.

Abstract: The invention discloses an MIMO radar signal modulation type identification method based on the partial autocorrelation spectrum and aims to solve problems of relatively large computational complexityand over-long identification time existing in a method utilizing the instantaneous autocorrelation spectrum to carry out MIMO radar signal modulation type identification in the prior art The methodis characterized by comprising steps that sample radar signals are extracted according to radar signals received by a radar reconnaissance receiver, and a zero-time delay instantaneous autocorrelationfunction of the sample radar signals is acquired; the function is simplified and normalized to acquire the spectral peak height of the partial zero-delay instantaneous autocorrelation spectrum of theMIMO radar signals; the threshold is set, and modulation type identification of the centralized MIMO radar signals is carried out according to the ratio of the second highest peak to the highest peak The method is advantaged in that the quantity of required MIMO radar signal sample points is relatively small, computational complexity is low, the code radar signals can be identified without othercharacteristic parameters, the identification time is shortened, the timeliness requirement is realized, and the method can be applied to an electronic counter reconnaissance system

Abstract: The invention provides a water level prediction method based on a hybrid model of a neural network and local Kalman filtering. An original time sequence array of water level data is collected, and a root-mean-square test method is adopted to determine stability of the original time sequence array; if a stability condition is not met, difference processing is carried out on the original data untila stability test thereof is successful; autocorrelation coefficients and partial autocorrelation coefficients are adopted to determine a water level time sequence lag period after a stable data set is acquired; the original time sequence array is split into a set of training samples of which length is the water level time sequence lag period; the artificial neural network is established and trained, and an artificial neural network model is generated to acquire a water level prediction result of a next day; and the water level prediction result of the next day is corrected by Kalman filtering. According to the method, water level data restoration and short-term prediction can be effectively realized, and prediction precision can be improved.

Abstract: The invention discloses a short-term wind speed prediction method of Gaussian process regression and particle filtering, thereby realizing on-line dynamic detection and correction of abnormal values and improving wind speed prediction accuracy. According to the method, an input variable set having the highest correlation with a wind speed value at a to-be-predicted time is determined by using a partial autocorrelation function, a state vector is determined, and a proper training sample set is constructed; a Gaussian-process-regression-based short-term wind speed prediction model is establishedin the training sample set and a fitting residue during the training process is given; on the basis of combination of the state vector and the Gaussian process regression model, a particle filteringstate space equation is established and state estimation is carried out on a current measurement value by using a particle filtering algorithm; and the estimation value and the measurement value residual of particle filtering are analyzed, determination is carried out based on a 3 sigma principle, and an abnormal value is corrected. According to the method provided by the invention, the abnormal value can be detected and corrected effectively; the short-term wind speed prediction precision is improved; and a wind speed prediction problem of the power system is solved.

Abstract: The invention discloses a cash flow prediction method based on ARIMA, which includes the following steps: acquiring cash flow time sequence data, establishing a scatter diagram, an autocorrelation function and a partial autocorrelation function, and testing the sequence stability through a run test method; stabilizing the time sequence data, and establishing a corresponding ARIMA model according to identification rules; estimating parameters, and testing whether the parameters have statistical significance; carrying out hypothesis test, and diagnosing whether the residual sequence is white noise; and predicting and analyzing the cash flow by using the model passing test. The cash flow prediction problem is solved based on a differential autoregressive moving average algorithm, and both cash inflow and cash outflow can be predicted.

Abstract: The popular diagnostic checking methods in linear time series models are portmanteau tests based on either residual autocorrelation functions (acf) or partial autocorrelation functions (pacf). In this paper, we device some new weighted mixed portmanteau tests by appropriately combining individual tests based on both acf and pacf. We derive the asymptotic distribution of such weighted mixed portmanteau statistics and study their size and power. It is found that the weighted mixed tests outperform when higher order ARMA models are fitted and diagnostic checks are performed via testing lack of residual autocorrelations. Simulation results suggest to use the proposed tests as complementary to those classical tests found in literature. An illustrative application is given to demonstrate the usefulness of the mixed test.

Abstract: The incidence of dengue cases and dengue death has grown-up dramatically around the world in recent decades. Recently, the number of reported cases, especially in Malaysia continued to increase. Over the year, many researchers try to estimate the number of deaths that cause by dengue. One of the methods in Biostatistics is ARIMA method which is involving time series analysis. Time series analysis commonly referred to any analysis which involved in a time series data. If the continuous observation is dependable, then the values that will come are able to be forecasted from the previous observation. The objective of this research paper is to forecast the number of dengue deaths, to describe the behavior of the time series data and afterwards made use of skilled statistical techniques for estimation, forecasting but also the controlling. In this paper the recognition of concerning the SARIMA (p,d,q) (P,D,Q) 15 was given attention through the approach to the Autocorrelation Function ACF and Partial Autocorrelation Function (PACF) theory plot. SARIMA (2,1,0) (0,1,1) 15 is being selected as the best model to represent the dengue death data. The gained model will be used as a tool for the prediction of the dengue death. Keywords: Autoregressive Process model AR (p), Moving Average Process MA (q), SARIMA (p,d,q), time series, forecasting and dengue.

Abstract: The invention relates to a method and system for constructing a photovoltaic power generation scene. The method comprises the following steps of: determining the mean square deviation of the autocorrelation coefficients of each photovoltaic field station in the photovoltaic power generation scene according to the autocorrelation coefficients of the historical power series and the hysteresis historical power series of each photovoltaic field station in the photovoltaic power generation scene, and the autocorrelation coefficients of the generated success rate series corresponding to the historical power series and the hysteresis generation success rate series of each photovoltaic field station; The mean square deviation of partial autocorrelation coefficients of each photovoltaic field station in the photovoltaic power generation scene is determined according to the partial autocorrelation coefficients of the historical power series and the hysteresis historical power series of each photovoltaic field station in the photovoltaic power generation scene, and the partial autocorrelation coefficients of the corresponding generation success rate series and the hysteresis generation success rate series of the historical power series. The photovoltaic power generation scenario is constructed by using the mean square deviation of autocorrelation coefficient and the mean square deviationof partial autocorrelation coefficient. The invention restricts the temporal correlation in the photovoltaic power generation scene construction, and improves the modeling accuracy of the photovoltaicpower generation scene construction.

Abstract: The central idea of this text is to guide researchers through the application of regression modeling when the data under analysis are observed over time. In general, there are no doubts regarding the application of this modeling in cross sections. However, when there is dependence on the data over time, some care needs to be taken for the results to be reliable and have the same interpretation of the coefficients obtained using the least squares method. The text begins with a presentation of the concept of autocorrelation and partial autocorrelation to identify and apply autoregressive modeling. Following this approach, the Augmented Dickey-Fuller test for detecting stationarity is presented, an essential condition for the estimators of ordinary least squares to be consistent. The Granger causality test is also presented and an example of regression applied to the series of the Cost of Living Index and the National Price Index for General Consumers. All the examples are presented with the help of Microsoft Excel to universalize the technique.

Abstract: The present invention relates to an impact assessment model and a verification method for economic development in the standard, which is designed in order to solve the technical problems of the lack of an impact assessment model and a verification method for the economic development in the existing standard, the difficulty of application, the impact of different industrial standards for differentareas on the economy, and the reference provided by the different industrial standards for the follow-up standard construction and application. The main points are that the model is subject to stationarity tests, co-integration tests, and causality tests to determine the time series data is stable, there is a long-term stable equilibrium relationship among variables, and the standard stocks impacts the change of regional GDP; and regression analysis is carried out, and a current regression model, that is, the logarithmic regression model, that quantifies the relationship among variables is established. The independence test of the residual sequence of the model is introduced into the residual independence test of the model, the white noise test uses the correlation graph and the Q statistic amount to perform the test, the test is to calculate the autocorrelation and partial autocorrelation function of the normal sequence, the table is made, and the curve graph is drawn.

Abstract: The invention provides a re-drying machine, and a water control fluctuation period acquisition method and system. The water control fluctuation period acquisition method can effectively acquire an autocorrelation coefficient and a partial autocorrelation coefficient of a time series X of a near-infrared water value, can calculate a large fluctuation period T1 of water control according to the autocorrelation coefficient, can calculate a small fluctuation period set {T2} of water control according to the partial autocorrelation coefficient, can intelligent perform corresponding adjustment on acontrol parameter of water control according to the large fluctuation period T1 and the small fluctuation period set {T2}, can stably control water in a re-drying machine, and is good in re-drying uniformity.