Autoregressive forecast of monthly total ozone concentration: A neurocomputing approach

The present study endeavors to generate autoregressive neural network (AR-NN) models to forecast the monthly total ozone concentration over Kolkata (22°34′, 88°22′), India. The issues associated with the applicability of neural network to geophysical processes are discussed. The autocorrelation structure of the monthly total ozone time series is investigated, and stationarity of the time series is established through the periodogram. From various autoregressive moving average (ARMA) and autoregressive models fit to the time series, the autoregressive model of order 10 is identified as the best. Subsequently, 10 autoregressive neural network (AR-NN) models are generated; the 10th order autoregressive neural network model with extensive input variable selection performs the best among all the competitive models in forecasting the monthly total ozone concentration over the study zone.     

Hybridization of autoregressive integrated moving average (ARIMA) with probabilistic neural networks (PNNs)

Autoregressive integrated moving average (ARIMA) models are one of the most important time series models applied in financial market forecasting over the past three decades. Improving forecasting especially time series forecasting accuracy is an important yet often difficult task facing forecasters. Both theoretical and empirical findings have indicated that integration of different models can be an effective way of improving upon their predictive performance, especially when the models in the ensemble are quite different. In the literature, several hybrid techniques have been proposed by combining different time series models together, in order to yield results that are more accurate. In this paper, a new hybrid model of the autoregressive integrated moving average (ARIMA) and probabilistic neural network (PNN), is proposed in order to yield more accurate results than traditional ARIMA models. In proposed model, the estimated values of the ARIMA model are modified based on the distinguished trend of the ARIMA residuals and optimum step length, which are respectively obtained from a probabilistic neural network and a mathematical programming model. Empirical results with three well-known real data sets indicate that the proposed model can be an effective way in order to construct a more accurate hybrid model than ARIMA model. Therefore, it can be used as an appropriate alternative model for forecasting tasks, especially when higher forecasting accuracy is needed.     

Forecasting time series using a methodology based on autoregressive integrated moving average and genetic programming

The autoregressive integrated moving average (ARIMA), which is a conventional statistical method, is employed in many fields to construct models for forecasting time series. Although ARIMA can be adopted to obtain a highly accurate linear forecasting model, it cannot accurately forecast nonlinear time series. Artificial neural network (ANN) can be utilized to construct more accurate forecasting model than ARIMA for nonlinear time series, but explaining the meaning of the hidden layers of ANN is difficult and, moreover, it does not yield a mathematical equation. This study proposes a hybrid forecasting model for nonlinear time series by combining ARIMA with genetic programming (GP) to improve upon both the ANN and the ARIMA forecasting models. Finally, some real data sets are adopted to demonstrate the effectiveness of the proposed forecasting model.     

Stationary and integrated autoregressive neural network processes

We consider autoregressive neural network (AR-NN) processes driven by additive noise and demonstrate that the characteristic roots of the shortcuts-the standard conditions from linear time-series analysis-determine the stochastic behavior of the overall AR-NN process. If all the characteristic roots are outside the unit circle, then the process is ergodic and stationary. If at least one characteristic root lies inside the unit circle, then the process is transient. AR-NN processes with characteristic roots lying on the unit circle exhibit either ergodic, random walk, or transient behavior. We also analyze the class of integrated AR-NN (ARI-NN) processes and show that a standardized ARI-NN process "converges" to a Wiener process. Finally, least-squares estimation (training) of the stationary models and testing for nonstationarity is discussed. The estimators are shown to be consistent, and expressions on the limiting distributions are given.     

Time-delay neural networks for time series prediction: an application to the monthly wholesale price of oilseeds in India

Agricultural price forecasting is one of the challenging areas of time series forecasting. The feed-forward time-delay neural network (TDNN) is one of the promising and potential methods for time series prediction. However, empirical evaluations of TDNN with autoregressive integrated moving average (ARIMA) model often yield mixed results in terms of the superiority in forecasting performance. In this paper, the price forecasting capabilities of TDNN model, which can model nonlinear relationship, are compared with ARIMA model using monthly wholesale price series of oilseed crops traded in different markets in India. Most earlier studies of forecast accuracy for TDNN versus ARIMA do not consider pretesting for nonlinearity. This study shows that the nonlinearity test of price series provides reliable guide to post-sample forecast accuracy for neural network model. The TDNN model in general provides better forecast accuracy in terms of conventional root mean square error values as compared to ARIMA model for nonlinear patterns. The study also reveals that the neural network models have clear advantage over linear models for predicting the direction of monthly price change for different series. Such direction of change forecasts is particularly important in economics for capturing the business cycle movements relating to the turning points.     

A flexible coefficient smooth transition time series model

We consider a flexible smooth transition autoregressive (STAR) model with multiple regimes and multiple transition variables. This formulation can be interpreted as a time varying linear model where the coefficients are the outputs of a single hidden layer feedforward neural network. This proposal has the major advantage of nesting several nonlinear models, such as, the self-exciting threshold autoregressive (SETAR), the autoregressive neural network (AR-NN), and the logistic STAR models. Furthermore, if the neural network is interpreted as a nonparametric universal approximation to any Borel measurable function, our formulation is directly comparable to the functional coefficient autoregressive (FAR) and the single-index coefficient regression models. A model building procedure is developed based on statistical inference arguments. A Monte Carlo experiment showed that the procedure works in small samples, and its performance improves, as it should, in medium size samples. Several real examples are also addressed.     

A comparative study of neural network and Box-Jenkins ARIMA modeling in time series prediction

This paper aims to investigate suitable time series models for repairable system failure analysis. A comparative study of the Box-Jenkins autoregressive integrated moving average (ARIMA) models and the artificial neural network models in predicting failures are carried out. The neural network architectures evaluated are the multi-layer feed-forward network and the recurrent network. Simulation results on a set of compressor failures showed that in modeling the stochastic nature of reliability data, both the ARIMA and the recurrent neural network (RNN) models outperform the feed-forward model; in terms of lower predictive errors and higher percentage of correct reversal detection. However, both models perform better with short term forecasting. The effect of varying the damped feedback weights in the recurrent net is also investigated and it was found that RNN at the optimal weighting factor gives satisfactory performances compared to the ARIMA model.     

区间时间序列的混合预测模型

提出一种基于自回归求和移动平均(ARIMA) 与人工神经网络(ANN) 的区间时间序列混合模型, 并用混合模型分别对区间中值序列和区间半径序列建模. 采用Monte Carlo 方法生成模拟区间序列, 分别用ARIMA、ANN和混合模型3 种方法进行建模和预测实验, 并用统计学方法检验模型误差. 最后分别采用3 种方法对H市轨道交通某号线牵引能耗区间序列进行了建模和预测, 实验结果表明混合模型的建模精度和预测性能均优于单一模型.

     

A moving-average filter based hybrid ARIMA–ANN model for forecasting time series data

A suitable combination of linear and nonlinear models provides a more accurate prediction model than an individual linear or nonlinear model for forecasting time series data originating from various applications. The linear autoregressive integrated moving average (ARIMA) and nonlinear artificial neural network (ANN) models are explored in this paper to devise a new hybrid ARIMA–ANN model for the prediction of time series data. Many of the hybrid ARIMA–ANN models which exist in the literature apply an ARIMA model to given time series data, consider the error between the original and the ARIMA-predicted data as a nonlinear component, and model it using an ANN in different ways. Though these models give predictions with higher accuracy than the individual models, there is scope for further improvement in the accuracy if the nature of the given time series is taken into account before applying the models. In the work described in this paper, the nature of volatility was explored using a moving-average filter, and then an ARIMA and an ANN model were suitably applied. Using a simulated data set and experimental data sets such as sunspot data, electricity price data, and stock market data, the proposed hybrid ARIMA–ANN model was applied along with individual ARIMA and ANN models and some existing hybrid ARIMA–ANN models. The results obtained from all of these data sets show that for both one-step-ahead and multistep-ahead forecasts, the proposed hybrid model has higher prediction accuracy.     

Multiple forecasts with autoregressive time series models: case studies

It is indisputable that accurate forecasts of economic activities are vital to successful business and government policies. In many circumstances, instead of a single forecast, simultaneous prediction intervals for multiple forecasts are more useful to decision-makers. For example, based on previous monthly sales records, a production manager would be interested in the next 12 interval forecasts of the monthly sales using for the annual inventory and manpower planning. For Gaussian autoregressive time series processes, several procedures for constructing simultaneous prediction intervals have been proposed in the literature. These methods assume a normal error distribution and can be adversely affected by departures from normality which are commonly encountered in business and economic time series. In this article, we explore the bootstrap methods for the construction of simultaneous multiple interval forecasts. To understand the mechanisms and characteristics of the proposed bootstrap procedures, several macro-economic time series are selected for illustrative purposes. The selected series are fitted reasonably well with autoregressive models which form an important class in time series. As a matter of fact, the major ideas discussed in this paper with autoregressive processes can be extended to other more complicated time series models.     

Combining seasonal time series ARIMA method and neural networks with genetic algorithms for predicting the production value of the mechanical industry in Taiwan

Supplying industrial firms with an accurate method of forecasting the production value of the mechanical industry to facilitate decision makers in precise planning is highly desirable. Numerous methods, including the autoregressive integrated-moving average (ARIMA) model and artificial neural networks can make accurate forecasts based on historical data. The seasonal ARIMA (SARIMA) model and artificial neural networks can also handle data involving trends and seasonality. Although neural networks can make predictions, deciding the most appropriate input data, network structure and learning parameters are difficult. Therefore, this article presents a hybrid forecasting method that combines the SARIMA model and neural networks with genetic algorithms. Analytical results generated by the SARIMA model are inputted as the input data of a neural network. Subsequently, the number of neurons in the hidden layer and the number of learning parameters of the neural network architecture are globally optimized using genetic algorithms. This model is subsequently adopted to forecast seasonal time series data of the production value of the mechanical industry in Taiwan. The results presented here provide a valuable reference for decision makers in industry.     

Univariate modeling and forecasting of monthly energy demand time series using abductive and neural networks

Neural networks have been widely used for short-term, and to a lesser degree medium and long-term, demand forecasting. In the majority of cases for the latter two applications, multivariate modeling was adopted, where the demand time series is related to other weather, socio-economic and demographic time series. Disadvantages of this approach include the fact that influential exogenous factors are difficult to determine, and accurate data for them may not be readily available. This paper uses univariate modeling of the monthly demand time series based only on data for 6 years to forecast the demand for the seventh year. Both neural and abductive networks were used for modeling, and their performance was compared. A simple technique is described for removing the upward growth trend prior to modeling the demand time series to avoid problems associated with extrapolating beyond the data range used for training. Two modeling approaches were investigated and compared: iteratively using a single next-month forecaster, and employing 12 dedicated models to forecast the 12 individual months directly. Results indicate better performance by the first approach, with mean percentage error (MAPE) of the order of 3% for abductive networks. Performance is superior to naı¨ve forecasts based on persistence and seasonality, and is better than results quoted in the literature for several similar applications using multivariate abductive modeling, multiple regression, and univariate ARIMA analysis. Automatic selection of only the most relevant model inputs by the abductive learning algorithm provides better insight into the modeled process and allows constructing simpler neural network models with reduced data dimensionality and improved forecasting performance.     

Modelling and forecasting tourism from East Asia to Thailand under temporal and spatial aggregation

Tourism is one of the key service industries in Thailand, with a 5.27% share of Gross Domestic Product in 2003. Since 2000, international tourist arrivals, particularly those from East Asia, to Thailand have been on a continuous upward trend. Tourism forecasts can be made based on previous observations, so that historical analysis of tourist arrivals can provide a useful understanding of inbound trips and the behaviour of trends in foreign tourist arrivals to Thailand. As tourism is seasonal, a good forecast is required for stakeholders in the industry to manage risk. Previous research on tourism forecasts has typically been based on annual and monthly data analysis, while few past empirical tourism studies using the Box–Jenkins approach have taken account of pre-testing for seasonal unit roots based on Franses [P.H. Franses, Seasonality, nonstationarity and the forecasting of monthly time series, International Journal of Forecasting 7 (1991) 199–208] and Beaulieu and Miron [J.J. Beaulieu, J.A. Miron, Seasonal unit roots in aggregate U.S. data, Journal of Econometrics 55 (1993) 305–328] framework. An analysis of the time series of tourism demand, specifically monthly tourist arrivals from six major countries in East Asia to Thailand, from January 1971 to December 2005 is examined. This paper analyses stationary and non-stationary tourist arrivals series by formally testing for the presence of unit roots and seasonal unit roots prior to estimation, model selection and forecasting. Various Box–Jenkins autoregressive integrated moving average (ARIMA) models and seasonal ARIMA models are estimated, with the tourist arrivals series showing seasonal patterns. The fitted ARIMA and seasonal ARIMA models forecast tourist arrivals from East Asia very well for the period 2006(1)–2008(1). Total monthly and annual forecasts can be obtained through temporal and spatial aggregation.     

Wavelet based time-varying vector autoregressive modelling

Vector autoregressive (VAR) modelling is one of the most popular approaches in multivariate time series analysis. The parameters interpretation is simple, and provide an intuitive identification of relationships and Granger causality among time series. However, the VAR modelling requires stationarity conditions which could not be valid in many practical applications. Locally stationary or time dependent modelling seem attractive generalizations, and several univariate approaches have already been proposed. In this paper we propose an estimation procedure for time-varying vector autoregressive processes, based on wavelet expansions of autoregressive coefficients. The asymptotic properties of the estimator are derived and illustrated by computer intensive simulations. We also present an application to brain connectivity identification using functional magnetic resonance imaging (fMRI) data sets.     

Wavelet based time-varying vector autoregressive modelling

Vector autoregressive (VAR) modelling is one of the most popular approaches in multivariate time series analysis. The parameters interpretation is simple, and provide an intuitive identification of relationships and Granger causality among time series. However, the VAR modelling requires stationarity conditions which could not be valid in many practical applications. Locally stationary or time dependent modelling seem attractive generalizations, and several univariate approaches have already been proposed. In this paper we propose an estimation procedure for time-varying vector autoregressive processes, based on wavelet expansions of autoregressive coefficients. The asymptotic properties of the estimator are derived and illustrated by computer intensive simulations. We also present an application to brain connectivity identification using functional magnetic resonance imaging (fMRI) data sets.     

A self-organising mixture autoregressive network for FX time series modelling and prediction

Nowadays a great deal of effort has been made in order to gain advantages in foreign exchange (FX) rates predictions. However, most existing techniques seldom excel the simple random walk model in practical applications. This paper describes a self-organising network formed on the basis of a mixture of adaptive autoregressive models. The proposed network, termed self-organising mixture autoregressive (SOMAR) model, can be used to describe and model nonstationary, nonlinear time series by means of a number of underlying local regressive models. An autocorrelation coefficient-based measure is proposed as the similarity measure for assigning input samples to the underlying local models. Experiments on both benchmark time series and several FX rates have been conducted. The results show that the proposed method consistently outperforms other local time series modelling techniques on a range of performance measures including the mean-square-error, correct trend predication percentage, accumulated profit and model variance.     

应用DRNN和ARIMA组合模型的时空集成预测方法

在评析目前时空预测研究现状的基础上,提出基于动态回归神经网络(DRNN)和自回归集成移动平均(ARIMA)组合模型的时空集成预测方法.该方法先用ARIMA模型对时空数据的时序进行预测,再用DRNN捕获时空数据间隐藏的空间关系,最后用线性回归将二者整合起来,得到集成预测结果.案例实验结果表明:该方法比不考虑空间影响的预测方法或单一的预测方法有更高的精度;该方法具有良好的动态处理和计算能力,对跨空间的动态过程的预测有效可行.     

Forecasting of monthly river flow with autoregressive modeling and data-driven techniques

This study was conducted by using autoregressive (AR) modeling and data-driven techniques which include gene expression programming (GEP), radial basis function network and feed-forward neural networks, and adaptive neural-based fuzzy inference system (ANFIS) techniques to forecast monthly mean flow for K?z?l?rmak River in Turkey. The lagged monthly river flow measurements from 1955 to 1995 were taken into consideration for development of the models. The correlation coefficient and root-mean-square error performance criteria were used for evaluating the accuracy of the developed models. When the results of developed models were compared with flow measurements using these criteria, it was shown that the AR(2) model gave the best performance among all developed models and the GEP and ANFIS models had good performance in data-driven techniques.     

A hybrid neural network and ARIMA model for water quality time series prediction

Accurate predictions of time series data have motivated the researchers to develop innovative models for water resources management. Time series data often contain both linear and nonlinear patterns. Therefore, neither ARIMA nor neural networks can be adequate in modeling and predicting time series data. The ARIMA model cannot deal with nonlinear relationships while the neural network model alone is not able to handle both linear and nonlinear patterns equally well. In the present study, a hybrid ARIMA and neural network model is proposed that is capable of exploiting the strengths of traditional time series approaches and artificial neural networks. The proposed approach consists of an ARIMA methodology and feed-forward, backpropagation network structure with an optimized conjugated training algorithm. The hybrid approach for time series prediction is tested using 108-month observations of water quality data, including water temperature, boron and dissolved oxygen, during 1996–2004 at Büyük Menderes river, Turkey. Specifically, the results from the hybrid model provide a robust modeling framework capable of capturing the nonlinear nature of the complex time series and thus producing more accurate predictions. The correlation coefficients between the hybrid model predicted values and observed data for boron, dissolved oxygen and water temperature are 0.902, 0.893, and 0.909, respectively, which are satisfactory in common model applications. Predicted water quality data from the hybrid model are compared with those from the ARIMA methodology and neural network architecture using the accuracy measures. Owing to its ability in recognizing time series patterns and nonlinear characteristics, the hybrid model provides much better accuracy over the ARIMA and neural network models for water quality predictions.     

Seasonal and trend time series forecasting based on a quasi-linear autoregressive model

Modeling and forecasting seasonal and trend time series is an important research topic in many areas of industrial and economic activity. In this study, we forecast the seasonal and trend time series using a quasi-linear autoregressive model. This quasi-linear autoregressive model belongs to a class of varying coefficient models in which its autoregressive coefficients are constructed by radial basis function networks. A combined genetic optimization and gradient-based optimization algorithm is applied for automatic selection of proper input variables and model-dependent variables, and optimizing the model parameters simultaneously. The model is tested by five monthly time series. We compare the results with those of other various methods, which show the effectiveness of the proposed approach for the seasonal time series.