A Hybrid Neural Network and Box-Jenkins Models for Time Series Forecasting

Time series forecasting plays a significant role in numerous applications,including but not limited to,industrial planning,water consumption,medical domains,exchange rates and consumer price index.The main problem is insufficient forecasting accuracy.The present study proposes a hybrid forecastingmethods to address this need.The proposed method includes three models.The first model is based on the autoregressive integrated moving average(ARIMA)statistical model;the second model is a back propagation neural network(BPNN)with adaptive slope and momentum parameters;and the thirdmodel is a hybridization between ARIMA and BPNN(ARIMA/BPNN)and artificial neural networks and ARIMA(ARIMA/ANN)to gain the benefits of linear and nonlinearmodeling.The forecasting models proposed in this study are used to predict the indices of the consumer price index(CPI),and predict the expected number of cancer patients in the Ibb Province in Yemen.Statistical standard measures used to evaluate the proposed method include(i)mean square error,(ii)mean absolute error,(iii)root mean square error,and(iv)mean absolute percentage error.Based on the computational results,the improvement rate of forecasting the CPI dataset was 5%,71%,and 4%for ARIMA/BPNN model,ARIMA/ANN model,and BPNN model respectively;while the result for cancer patients’dataset was 7%,200%,and 19%for ARIMA/BPNNmodel,ARIMA/ANN model,and BPNNmodel respectively.Therefore,it is obvious that the proposed method reduced the randomness degree,and the alterations affected the time series with data non-linearity.The ARIMA/ANN model outperformed each of its components when it was applied separately in terms of increasing the accuracy of forecasting and decreasing the overall errors of forecasting.

Auto-Regressive Models of Non-Stationary Time Series with Finite Length

To analyze and simulate non-stationary time series with finite length, the statistical characteris- tics and auto-regressive (AR) models of non-stationary time series with finite length are discussed and stud- ied. A new AR model called the time varying parameter AR model is proposed for solution of non-stationary time series with finite length. The auto-covariances of time series simulated by means of several AR models are analyzed. The result shows that the new AR model can be used to simulate and generate a new time series with the auto-covariance same as the original time series. The size curves of cocoon filaments re- garded as non-stationary time series with finite length are experimentally simulated. The simulation results are significantly better than those obtained so far, and illustrate the availability of the time varying parameter AR model. The results are useful for analyzing and simulating non-stationary time series with finite length.

Smoothing Non-Stationary Time Series Using the Discrete Cosine Transform

This paper considers the problem of smoothing a non-stationary time series(having either deterministic and/or stochastic trends) using the discrete cosine transform(DCT).The DCT is a powerful tool which has found fruitful applications in filtering and smoothing as it can closely approximate the optimal Karhunen-Loeve transform(KLT).In fact,it is known that it almost corresponds to the KLT for first-order autoregressive processes with a root close to unity:This is the case with most economic and financial time series.A number of new results are derived in the paper:(a) The explicit form of the linear smoother based on the DCT,which is found to have time-varying weights and that uses all observations;(b) the extrapolation of the DCT-smoothed series;(c) the form of the average frequency response function,which is shown to approximate the frequency response of the ideal low pass filter;(d) the asymptotic distribution of the DCT coefficients under the assumptions of deterministic or stochastic trends;(e) two news method for selecting an appropriate degree of smoothing,in general and under the assumptions in(d).These findings are applied and illustrated using several real world economic and financial time series.The results indicate that the DCT-based smoother that is proposed can find many useful applications in economic and financial time series.

The Research of Fractal Characteristics of the Electrocardiogram in a Real Time Mode

The article presents the results of recent investigations into Holter monitoring of ECG, using non-linear analysis methods. This paper discusses one of the modern methods of time series analysis--a method of deterministic chaos theory. It involves the transition from study of the characteristics of the signal to the investigation of metric （and probabilistic） properties of the reconstructed attractor of the signal. It is shown that one of the most precise characteristics of the functional state of biological systems is the dynamical trend of correlation dimension and entropy of the reconstructed attractor. On the basis of this it is suggested that a complex programming apparatus be created for calculating these characteristics on line. A similar programming product is being created now with the support of RFBR. The first results of the working program, its adjustment, and further development, are also considered in the article.

Analytical Fitting Functions of Finite Sample Discrete Entropies of White Gaussian Noise

In order to find the convergence rate of finite sample discrete entropies of a white Gaussian noise(WGN), Brown entropy algorithm is numerically tested.With the increase of sample size, the curves of these finite sample discrete entropies are asymptotically close to their theoretical values.The confidence intervals of the sample Brown entropy are narrower than those of the sample discrete entropy calculated from its differential entropy, which is valid only in the case of a small sample size of WGN. The differences between sample Brown entropies and their theoretical values are fitted by two rational functions exactly, and the revised Brown entropies are more efficient. The application to the prediction of wind speed indicates that the variances of resampled time series increase almost exponentially with the increase of resampling period.

An Econometric Model for SINOPEC Stock Price Tendency on Domestic Securities Market

A time series analysis method was used to establish an econometric model for SINOPEC＇S stock price tendency on the domestic securities market under the background of sharp oil price rises in recent years. The model was proven to be a non-stationary time series and unit root process, as tested with the Dickey-Fuller method, and the result of a practical case showed that this model could well reflect SINOPEC stock price tendency on the securities market of China. It would be a guide for research and prediction of stock price tendency.

Statistical Forecasting Models of Atmospheric Carbon Dioxide and Temperature in the Middle East

Time series models are very powerful methods that help to drive hidden visions of a phenomenon and make informed future decisions. The purpose of this study is to develop statistical time series forecasting models to predict atmospheric carbon dioxide concentration in the Middle East and temperature in Saudi Arabia using multiplicative seasonal autoregressive integrated moving average models. We proceed to verify the quality and usefulness of our proposed probabilistic models by utilizing essential statistical properties to evaluate them according to their performance in forecasting the carbon dioxide in the atmosphere and the corresponding temperatures and it was shown that both statistical forecasting models produced good estimates.

Problems Existed in Applications of Cointegration Theory in China

Although the Cointegration Theory was founded by the C.W.J Granger and other economists in the 1980s, it was not widely used in China until C.W.J Granger was awarded with Nobel Prize in 2003. Since then, a lot of economic papers introducing or applying Cointegration Theory have emerged, but the phenomenon of misuse of this theory possibly arose at the same time. Based on some of these papers obtained from web site （www.cnki.net）, this paper explores the applications of Cointegration Theory in China and draws some initial conclusions. Most of these applications are reasonable, but some of them are a bit blindfold or even contradictory in conclusions, which indicates that the overall application quality has a large room to get improved and should be paid more attention by academe.

A Novel Operational Partition between Neural Network Classifiers on Vulnerability to Data Mining Bias

It is difficult if not impossible to appropriately and effectively select from among the vast pool of existing neural network machine learning predictive models for industrial incorporation or academic research exploration and enhancement. When all models outperform all the others under disparate circumstances, none of the models do. Selecting the ideal model becomes a matter of ill-supported opinion ungrounded on the extant real world environment. This paper proposes a novel grouping of the model pool grounded along a non-stationary real world data line into two groups: Permanent Data Learning and Reversible Data Learning. This paper further proposes a novel approach towards qualitatively and quantitatively demonstrating their significant differences based on how they alternatively approach dynamic and raw real world data vs static and prescient data mining biased laboratory data. The results across 2040 separate simulation runs using 15,600 data points in realistically operationally controlled data environments show that the two-group division is effective and significant with clear qualitative, quantitative and theoretical support. Results across the empirical and theoretical spectrum are internally and externally consistent yet demonstrative of why and how this result is non-obvious.

Identification of non-linear autoregressive models with exogenous inputs for room air temperature modelling

This paper proposes non-linear autoregressive models with exogenous inputs to model the air temperature ineach room of a Danish school building connected to the local district heating network. To obtain satisfactorymodels, the authors find it necessary to estimate the solar radiation effect as a function of the time of the dayusing a B-spline basis expansion. Furthermore, this paper proposes a method for estimating the valve positionof the radiator thermostats in each room using modified Hermite polynomials to ensure monotonicity of theestimated curve. The non-linearities require a modification in the estimation procedure: Some parametersare estimated in an outer optimisation, while the usual regression parameters are estimated in an inneroptimisation. The models are able to simulate the temperature 24 h ahead with a root-mean-square-errorof the predictions between 0.25℃ and 0.6℃. The models seem to capture the solar radiation gain in away aligned with expectations. The estimated thermostatic valve functions also seem to capture the importantvariations of the individual room heat inputs.

Nonlinear Dynamic Characteristics of Turbulent Non-Premixed Acoustically Perturbed Swirling Flames

The main objective of this article was to experimentally investigate the dynamic response of diffusion flame under acoustic excitation in a laboratory-scale burner.Two parametric variations of the burner,the burner inlet length and variation of the airflow rate,were studied.Experimental results were analyzed through nonlinear time series analysis and several resonance characteristics were obtained.Results indicate that the flame-acoustic resonance only appears under certain frequencies together with the fuel tube vibration.Resonance characteristics of the combustion chamber and air inlet in the non-premixed burner indicate quasi-periodic or limit cycle oscillations,respectively.Flame-acoustic resonance would trigger the frequency and amplitude mode-transition in burners.Moreover,the intermittency of flame heat release was observed under variation of inlet length and airflow rate in the burner;the 445 mm case shows more frequency peaks and fluctuations than the 245 mm one.Four typical flame forms were examined during the flame-acoustic resonance conditions,evolves from wrinkled flames to diverged flames,then evolves to reattached flames and finally to blow-off flames.This study proposed the practical application of nonlinear time-series analysis method as a detection tool for flame-acoustic resonance in laboratory non-premixed burners,which could contribute to the detection and prevention of potential thermoacoustic instabilities or resonance structure failures of industrial boilers.Finally,this study demonstrates an alternative to conventional linear tool for the characterization of nonlinear acoustic resonance in industrial boilers.