Univariate approach to the monthly total ozone time series over Kolkata,India: autoregressive integrated moving average (ARIMA) and autoregressive neural network (AR-NN) models

This study reports univariate modelling methodologies applied to the monthly total ozone concentration (TOC) over Kolkata (22°32′, 88°20′), India, derived from the measurements made by the Earth Probe Total Ozone Mapping Spectrometer (EP/TOMS). The univariate models have been generated in two forms, namely autoregressive integrated moving average (ARIMA) and autoregressive neural network (AR-NN). Three ARIMA models in the forms of ARIMA(1,1,1), ARIMA(0,1,1) and ARIMA(0,2,2) and 11 autoregressive neural network models, AR-NN(n), have been generated for a time series. Goodness of fit of the models to the time series of monthly TOC has been assessed using prediction error, Pearson correlation coefficient and Willmott's indices. After rigorous skill assessment, the ARIMA (0,2,2) has been identified as the best predictive model for the time series under study.     

Prediction of mean monthly total ozone time series – application of radial basis function network

The primary objective of the present paper is to apply Artificial Neural Network in the form of Radial Basis Function network to predict the mean monthly total ozone concentration over Arosa, Switzerland (46.8° N/9.68° E). The satellite observations of the total ozone content are based on the total ozone observations performed by the ground‐based instrumentation. While analysing the dataset it was found that January, February and March are the months of maximum variability in the mean monthly total ozone over the stated region. Then, these three months were considered as the target months to frame the predictive model. After appropriate training and testing, it was found that Radial Basis Function network is a suitable neural net type for predicting the aforesaid time series. Moreover, this kind of neural net was found most adroit in predicting the mean monthly total ozone in the month of January.     

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.     

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.     

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.     

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.     

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.     

基于小波非线性自回归网络的水文预测模型

不同时间尺度上的水文序列预测在水资源调配和防洪减灾决策中起着重要的作用。提出了一种基于小波分解和非线性自回归神经网络相结合的水文时间序列预测模型(WNARN)。运用Daubechies 5(db5)离散小波将水文序列数据分解为低频和高频子序列,作为非线性自回归神经网络模型(NARN)的输入变量,贝叶斯正则化优化算法用来泛化网络,训练模型对各子序列进行模拟预测,预测值经db5小波重构后得到原序列预测值。利用渭河流域三个水文站40多年的月径流量序列对所提出的WNARN模型进行验证和向前48步的预测能力测试,并与单一NARN模型的验证和预测结果进行对比。结果显示在相同的网络结构下所提出的方法能够显著提高水文序列的预测精度、预测周期及对重大水文事件的预测性,具有较高的泛化能力。     

Ozone dynamics over Greece as derived from satellite and! in situ measurements

A comprehensive analysis of the records of surface ozone available for Athens, Greece ( 38° N, 24° E) for the periods 1901–1940 and 1987–1990 is presented. Both records are analysed to explore the intraseasonal fluctuations and the harmonic components of surface ozone and also compared to other historical surface ozone records. The variation in surface ozone concentration during rainfall is also investigated, using the hourly measurements of the surface ozone concentration obtained by a network of four stations within the Greater Athens area. The results indicate that, during rainfall events which are associated with the passing of a cold front, an important decrease of the surface ozone concentration is observed. Daily measurements of surface ozone and NO_x, from five stations in the Greater Athens Basin overthe period 1986–1990 are also used in order to examine the main features of basin-wide 0₃-HC-NO_x relations. A simple regression model between the surface ozone concentration and the temperature at the 850 hPa level, which was first tested in Los Angeles, gave satisfactory results in reproducing the mean monthly ozone variation in Athens, when coefficients extracted from local data were used in the regression equation. A series of vertical ozone soundings over Athens has been also performed in order to explore the tropospheric ozone variations and to examine further the transport that occurs at the 700hPa level with advection from the north-western sector. The relevant results are discussed. The existing uncertainties concerning the stratosphere-troposphere exchange of ozone which mainly occurs during midlatitude tropopause folding as well as during cut-off low events are also discussed. The examination of the role of the atmospheric circulation in the lower stratosphere in relation to the laminated structure of ozone is also attempted. The data collected during the balloon ascents have been compared with those during the balloon descents. Both profiles are compared with the total ozone measurements derived from the TOMS on the Nimbus-7 satellite and the Dobson spectrophotometer. The data collected for the vertical distribution of ozone and temperature have been compared with the satellite-derived reference models which provide the monthly latitudinal variations of vertical structure of both ozone and temperature. We have also used total ozone measurements obtained with a Dobson spectrophotometer ( No. 118) which has been instituted in Athens from 1989 in order to examine the consistency of data from TOMS with the corresponding Dobson data on a daily basis. Furthermore monthly mean total ozone data were first estimated for the entire period and were then Fourier analysed to obtain the amplitude, phase and percentage contribution to the total variance of the first, second and third harmonics.     

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.     

模糊神经网络与SARIMA结合的时间序列预测模型

模糊神经网络和SARIMA模型分别对非线性和线性时间序列有很好的预测能力,但在实际应用中大多数序列并非稳定、单纯线性或非线性的。为了提高预测精度,提出了一种基于T-S模糊神经网络与SARIMA结合的时间序列预测模型。针对悉尼航班乘客收入数据给出了三种混合模型,并与模糊神经网络、支持向量机、SARIMA和BP神经网络四种单独模型进行比较。实验结果表明,从预测精度和参数选择方面来看,所给模型是有效的。     

Time Series Prediction With Genetic-Algorithm Designed Neural Networks: An Empirical Comparison With Modern Statistical Models

Neural networks whose architecture is determined by genetic algorithms outperform autoregressive integrated moving average forecasting models in six different time series examples. Refinements to the autoregressive integrated moving average model improve forecasting performance over standard ordinary least squares estimation by 8% to 13%. In contrast, neural networks achieve dramatic improvements of 10% to 40%. Additionally, neural networks give evidence of detecting patterns in data which remain hidden to the autoregression and moving average models. The consequent forecasting potential of neural networks makes them a very promising addition to the variety of techniques and methodologies used to anticipate future movements in time series.
     

Forecasting peak air pollution levels using NARX models

Air pollution has a negative impact on human health. For this reason, it is important to correctly forecast over-threshold events to give timely warnings to the population. Nonlinear models of the nonlinear autoregressive with exogenous variable (NARX) class have been extensively used to forecast air pollution time series, mainly using artificial neural networks (NNs) to model the nonlinearities. This work discusses the possible advantages of using polynomial NARX instead, in combination with suitable model structure selection methods. Furthermore, a suitably weighted mean square error (MSE) (one-step-ahead prediction) cost function is used in the identification/learning process to enhance the model performance in peak estimation, which is the final purpose of this application. The proposed approach is applied to ground-level ozone concentration time series. An extended simulation analysis is provided to compare the two classes of models on a selected case study (Milan metropolitan area) and to investigate the effect of different weighting functions in the identification performance index. Results show that polynomial NARX are able to correctly reconstruct ozone concentrations, with performances similar to NN-based NARX models, but providing additional information, as, e.g., the best set of regressors to describe the studied phenomena. The simulation analysis also demonstrates the potential benefits of using the weighted cost function, especially in increasing the reliability in peak estimation.     

Level estimation, classification and probability distribution architectures for trading the EUR/USD exchange rate

Dunis and Williams (Derivatives: use, trading and regulation 8(3):211–239, 2002; Applied quantitative methods for trading and investment. Wiley, Chichester, 2003) have shown the superiority of a Multi-layer perceptron network (MLP), outperforming its benchmark models such as a moving average convergence divergence technical model (MACD), an autoregressive moving average model (ARMA) and a logistic regression model (LOGIT) on a Euro/Dollar (EUR/USD) time series. The motivation for this paper is to investigate the use of different neural network architectures. This is done by benchmarking three different neural network designs representing a level estimator, a classification model and a probability distribution predictor. More specifically, we present the Mulit-layer perceptron network, the Softmax cross entropy model and the Gaussian mixture model and benchmark their respective performance on the Euro/Dollar (EUR/USD) time series as reported by Dunis and Williams. As it turns out, the Multi-layer perceptron does best when used without confirmation filters and leverage, while the Softmax cross entropy model and the Gaussian mixture model outperforms the Multi-layer perceptron when using more sophisticated trading strategies and leverage. This might be due to the ability of both models using probability distributions to identify successfully trades with a high Sharpe ratio.

A probe into the chaotic nature of total ozone time series by correlation dimension method

The endeavor of the present paper is to investigate the existence of chaotic behavior in the underlying dynamics of the total ozone concentration over Arosa, Switzerland (9.68°E, 46.78°N). For this purpose, the correlation dimension method is employed to the mean monthly total ozone concentration data collected over a period of 40 years (1932–1971) at the above location. Based on the observation of a low correlation dimension value of 1 for this data set, the study reports the existence of low-dimensional chaotic behavior in the ozone concentration dynamics.     

Forecasting daily total ozone concentration—a comparison between neurocomputing and statistical approaches

The present paper develops three predictive models for daily total ozone concentration over Arosa, Switzerland. The models are artificial neural network, multiple linear regression, and persistence forecast. Each model was judged for their predictive ability using analysis of variance, Pearson correlation study, and scatterplot analysis. Prediction errors were computed for each model. After painstaking analysis it was established that artificial neural network produces better forecasts than the statistical approaches like multiple linear regression and persistence forecast models.     

Improving the prediction of average total ozone in column over the Iberian Peninsula using neural networks banks

In this letter we propose a class of neural network banks to improve the performance of average total ozone in column (TOC) prediction, using real satellite data over the Iberian Peninsula. The proposed neural network banks exploit the possibility of separating the average TOC series into its known components, applying different neural networks as input to different structures which form the final bank. These neural network banks have proven to be very effective in the experiments carried out, obtaining important improvements over standard networks in the prediction of average TOC data series over the Iberian Peninsula. Also, we show that this good performance of the neural network banks is maintained when different procedures of deseasonalization are applied to the ozone measure and also to the prediction variables.     

Automatic spectral analysis with missing data

The current computational power and some recently developed algorithms allow a new automatic spectral analysis method for randomly missing data. Accurate spectra and autocorrelation functions are computed from the estimated parameters of time series models, without user interaction. If only a few data are missing, the accuracy is almost the same as when all observations were available. For larger missing fractions, low-order time series models can still be estimated with a good accuracy if the total observation time is long enough. Autoregressive models are best estimated with the maximum likelihood method if data are missing. Maximum likelihood estimates of moving average and of autoregressive moving average models are not very useful with missing data. Those models are found most accurately if they are derived from the estimated parameters of an intermediate autoregressive model. With statistical criteria for the selection of model order and model type, a completely automatic and numerically reliable algorithm is developed that estimates the spectrum and the autocorrelation function in randomly missing data problems. The accuracy was better than what can be obtained with other methods, including the famous expectation–maximization (EM) algorithm.     

Autoregressive causal relation: Digital filtering approach to causality measures in frequency domain

A novel measure of the Autoregressive Causal Relation based on a multivariate autoregressive model is proposed. It reveals the strength of the connections among a simultaneous time series and also the direction of the information flow. It is defined in the frequency domain, similar to the formerly published methods such as: Directed Transfer Function, Direct Directed Transfer Function, Partial Directed Coherence, and Generalized Partial Directed Coherence. Compared to the Granger causality concept, frequency decomposition extends the possibility to reveal the frequency rhythms participating on the information flow in causal relations.The Autoregressive Causal Relation decomposes diagonal elements of a spectral matrix and enables a user to distinguish between direct and indirect causal relations. The main advantage lies in its definition using power spectral densities, thus allowing for a clear interpretation of strength of causal relation in meaningful physical terms.The causal measures can be used in neuroscience applications like the analysis of underlying structures of brain connectivity in neural multichannel time series during different tasks measured via electroencephalography or functional magnetic resonance imaging, or other areas using the multivariate autoregressive models for causality modeling like econometrics or atmospheric physics but this paper is focused on theoretical aspects and model data examples in order to illustrate a behavior of methods in known situations.     

基于小波变换的网络流量组合预测模型

为了提高网络流量的预测精度,利用小波变换、差分自回归移动平均模型和最小二乘支持向量机等优点,提出一种基于小波变换的网络流量预测模型(WA-ARIMA-LSSVM)。针对网络流量多尺度特性,首先对网络流量时间序列进行小波分解,然后分别采用差分自回归移动平均模型和最小二乘支持向量机对网络流量的高频和低频进行建模与预测,最后小波重构高频和低频的预测结果,并采用仿真实验对模型性能进行分析。结果表明,WA-ARIMA-LSSVM提高了网络流量的预测精度,可以更加准确地描述网络流量的非平稳变化趋势。