A New Multiplicative Seasonal Neural Network Model Based on Particle Swarm Optimization

In recent years, artificial neural networks (ANNs) have been commonly used for time series forecasting by researchers from various fields. There are some types of ANNs and feed forward neural networks model is one of them. This type has been used to forecast various types of time series in many implementations. In this study, a novel multiplicative seasonal ANN model is proposed to improve forecasting accuracy when time series with both trend and seasonal patterns is forecasted. This neural networks model suggested in this study is the first model proposed in the literature to model time series which contain both trend and seasonal variations. In the proposed approach, the defined neural network model is trained by particle swarm optimization. In the training process, local minimum traps are avoided by using this population based heuristic optimization method. The performance of the proposed approach is examined by using two real seasonal time series. The forecasts obtained from the proposed method are compared to those obtained from other forecasting techniques available in the literature. It is seen that the proposed forecasting model provides high forecasting accuracy.     

Application of seasonal SVR with chaotic immune algorithm in traffic flow forecasting

Accurate forecasting of inter-urban traffic flow has been one of the most important issues globally in the research on road traffic congestion. Because the information of inter-urban traffic presents a challenging situation, the traffic flow forecasting involves a rather complex nonlinear data pattern, particularly during daily peak periods, traffic flow data reveals cyclic (seasonal) trend. In the recent years, the support vector regression model (SVR) has been widely used to solve nonlinear regression and time series problems. However, the applications of SVR models to deal with cyclic (seasonal) trend time series had not been widely explored. This investigation presents a traffic flow forecasting model that combines the seasonal support vector regression model with chaotic immune algorithm (SSVRCIA), to forecast inter-urban traffic flow. Additionally, a numerical example of traffic flow values from northern Taiwan is used to elucidate the forecasting performance of the proposed SSVRCIA model. The forecasting results indicate that the proposed model yields more accurate forecasting results than the seasonal autoregressive integrated moving average, back-propagation neural network, and seasonal Holt–Winters models. Therefore, the SSVRCIA model is a promising alternative for forecasting traffic flow.     

Combining seasonal ARIMA models with computational intelligence techniques for time series forecasting

Seasonal autoregressive integrated moving average (SARIMA) models form one of the most popular and widely used seasonal time series models over the past three decades. However, in several researches it has been argued that they have two basic limitations that detract from their popularity for seasonal time series forecasting tasks. SARIMA models assume that future values of a time series have a linear relationship with current and past values as well as with white noise; therefore, approximations by SARIMA models may not be adequate for complex nonlinear problems. In addition, SARIMA models require a large amount of historical data to produce desired results. However, in real situations, due to uncertainty resulting from the integral environment and rapid development of new technology, future situations must be forecasted using small data sets over a short span of time. Using hybrid models or combining several models has become a common practice to overcome the limitations of single models and improve forecasting accuracy. In this paper, a new hybrid model, which combines the seasonal autoregressive integrated moving average (SARIMA) and computational intelligence techniques such as artificial neural networks and fuzzy models for seasonal time series forecasting is proposed. In the proposed model, these two techniques are applied to simultaneously overcome the linear and data limitations of SARIMA models and yield more accurate results. Empirical results of forecasting two well-known seasonal time series data sets indicate that the proposed model exhibits effectively improved forecasting accuracy, so that it can be used as an appropriate seasonal time series model.     

Characterising economic trends by Bayesian stochastic model specification search

A recently proposed Bayesian model selection technique, stochastic model specification search, is carried out to discriminate between two trend generation hypotheses. The first is the trend-stationary hypothesis, for which the trend is a deterministic function of time and the short run dynamics are represented by a stationary autoregressive process. The second is the difference-stationary hypothesis, according to which the trend results from the cumulation of the effects of random disturbances. A difference-stationary process may originate in two ways: from an unobserved components process adding up an integrated trend and an orthogonal transitory component, or implicitly from an autoregressive process with roots on the unit circle. The different trend generation hypotheses are nested within an encompassing linear state space model. After a reparameterisation in non-centred form, the empirical evidence supporting a particular hypothesis is obtained by performing variable selection on the model components, using a suitably designed Gibbs sampling scheme. The methodology is illustrated with reference to a set of US macroeconomic time series which includes the traditional Nelson and Plosser dataset. The conclusion is that most series are better represented by autoregressive models with time-invariant intercept and slope and coefficients that are close to boundary of the stationarity region. The posterior distribution of the autoregressive parameters provides useful insight on quasi-integrated nature of the specifications selected.     

Traffic flow forecasting by seasonal SVR with chaotic simulated annealing algorithm

Accurate forecasting of inter-urban traffic flow has been one of the most important issues globally in the research on road traffic congestion. However, the information of inter-urban traffic presents a challenging situation; the traffic flow forecasting involves a rather complex nonlinear data pattern, particularly during daily peak periods, traffic flow data reveals cyclic (seasonal) trend. In the recent years, the support vector regression model (SVR) has been widely used to solve nonlinear regression and time series problems. However, the applications of SVR models to deal with cyclic (seasonal) trend time series have not been widely explored. This investigation presents a traffic flow forecasting model that combines the seasonal support vector regression model with chaotic simulated annealing algorithm (SSVRCSA), to forecast inter-urban traffic flow. Additionally, a numerical example of traffic flow values from northern Taiwan is employed to elucidate the forecasting performance of the proposed SSVRCSA model. The forecasting results indicate that the proposed model yields more accurate forecasting results than the seasonal autoregressive integrated moving average (SARIMA), back-propagation neural network (BPNN) and seasonal Holt-Winters (SHW) models. Therefore, the SSVRCSA model is a promising alternative for forecasting traffic flow.     

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。     

基于时间序列自回归模型的绿色建筑供暖能耗短期预测

为实时了解绿色建筑供暖能耗的变化趋势,提升能耗预测效果,设计基于时间序列自回归模型的绿色建筑供暖能耗短期预测方法。利用增强迪基-福勒检验法,检验绿色建筑历史供暖能耗时间序列平稳性;对非平稳的历史能耗时间序列进行差分平稳化处理,获取平稳的历史能耗时间序列;在时间序列自回归模型内添加移动平均模型,并考虑能耗的气温影响因素,建立时间序列自回归移动平均模型;利用赤池信息准则确定模型阶数,通过粒子群算法确定模型参数;在模型阶数与参数确定后的模型内,输入平稳的历史能耗时间序列,输出供暖能耗短期预测值。实验证明：该方法可精准预测不同类型绿色建筑的短期供暖能耗;在不同绿色建筑渗透量时,该方法短期供暖能耗预测误差较小;在不同室外温度时,该方法短期供暖能耗预测的可决系数较高,即预测精度较高。     

Exact maximum likelihood estimation for non-stationary periodic time series models

Time series models with parameter values that depend on the seasonal index are commonly referred to as periodic models. Periodic formulations for two classes of time series models are considered: seasonal autoregressive integrated moving average and unobserved components models. Convenient state space representations of the periodic models are proposed to facilitate model identification, specification and exact maximum likelihood estimation of the periodic parameters. These formulations do not require a priori (seasonal) differencing of the time series. The time-varying state space representation is an attractive alternative to the time-invariant vector representation of periodic models which typically leads to a high dimensional state vector in monthly periodic time series models. A key development is our method for computing the variance-covariance matrix of the initial set of observations which is required for exact maximum likelihood estimation. The two classes of periodic models are illustrated for a monthly postwar US unemployment time series.     

A new hybrid approach based on SARIMA and partial high order bivariate fuzzy time series forecasting model

In the literature, there have been many studies using fuzzy time series for the purpose of forecasting. The most studied model is the first order fuzzy time series model. In this model, an observation of fuzzy time series is obtained by using the previous observation. In other words, only the first lagged variable is used when constructing the first order fuzzy time series model. Therefore, this model can not be sufficient for some time series such as seasonal time series which is an important class in time series models. Besides, the time series encountered in real life have not only autoregressive (AR) structure but also moving average (MA) structure. The fuzzy time series models available in the literature are AR structured and are not appropriate for MA structured time series. In this paper, a hybrid approach is proposed in order to analyze seasonal fuzzy time series. The proposed hybrid approach is based on partial high order bivariate fuzzy time series forecasting model which is first introduced in this paper. The order of this model is determined by utilizing Box-Jenkins method. In order to show the efficiency of the proposed hybrid method, real time series are analyzed with this method. The results obtained from the proposed method are compared with the other methods. As a result, it is observed that more accurate results are obtained from the proposed hybrid method.     

A hybrid machine learning and computing model for forecasting displacement of multifactor-induced landslides

A novel hybrid model composed of least squares support vector machines (LSSVM) and double exponential smoothing (DES) was proposed and applied to calculate one-step ahead displacement of multifactor-induced landslides. The wavelet de-noising and Hodrick-Prescott filter methods were used to decompose the original displacement time series into three components: periodic term, trend term and random noise, which respectively represent periodic dynamic behaviour of landslides controlled by the seasonal triggers, the geological conditions and the random measuring noise. LSSVM and DES models were constructed and trained to forecast the periodic component and the trend component, respectively. Models’ inputs include the seasonal triggers (e.g. reservoir level and rainfall data) and displacement values which are measurable variables in a specific prior time. The performance of the hybrid model was evaluated quantitatively. Calculated displacement from the hybrid model is excellently consistent with actual monitored value. Results of this work indicate that the hybrid model is a powerful tool for predicting one-step ahead displacement of landslide triggered by multiple factors.

     

Burned area forecasting using past burned area records and Southern Oscillation Index for tropical Africa (1981-1999)

An 18-year time series of monthly NOAA-AVHRR Pathfinder Land burned area was analyzed for the region of tropical Africa, from July 1981 to June 1999. The transition period between NOAA-11 and NOAA-14 platforms from July 1993 to June 1995 was not included due to missing and outlier data. Stability of the time series was addressed for the input variables in the burned area algorithm, reflectance and temperature channels.A Seasonal AutoRegressive Integrated Moving-Average (SARIMA) model was developed for forecasting potential burned area. The SARIMA model identified an autoregressive regular term with 1-month lag and an autoregressive 12-month seasonal term with one season (12 months) component. A cross-correlation between Southern Oscillation Index (SOI) and burned area was statistically significant predictor variable in a time series with 20-month lag. Results show that the SARIMA model with this predictor improved both, fitting and forecasting, residual variance, by 4.1% and 5.6%, respectively, thereby, demonstrating potential relationship between SOI and burned area for the study region. Forecasting was estimated by considering only the first 16 years of the monthly burned area in the time series, from July 1981 to June 1997. The prediction for the following 24 months (from July 1997 to June 1999) was within the 95% confidence level indicating that the forecast was a valid characterization of the modeled process.     

ARMA(p,q) type high order fuzzy time series forecast method based on fuzzy logic relations

Within classic time series approaches, a time series model can be studied under 3 groups, namely AR (autoregressive model), MA (moving averages model) and ARMA (autoregressive moving averages model). On the other hand, solutions are based mostly on fuzzy AR time series models in the fuzzy time series literature. However, just a few fuzzy ARMA time series models have proposed until now. Fuzzy AR time series models have been divided into two groups named first order and high order models in the literature, highlighting the impact of model degree on forecast performance. However, model structure has been disregarded in these fuzzy AR models. Therefore, it is necessary to eliminate the model specification error arising from not utilizing of MA variables in the fuzzy time series approaches. For this reason, a new high order fuzzy ARMA(p,q) time series solution algorithm based on fuzzy logic group relations including fuzzy MA variables along with fuzzy AR variables has been proposed in this study. The main purpose of this article is to show that the forecast performance can be significantly improved when the deficiency of not utilizing MA variables. The other aim is also to show that the proposed method is better than the other fuzzy ARMA time series models in the literature from the point of forecast performance. Therefore, the new proposed method has been compared regarding forecast performance against some methods commonly used in literature by applying them on gold prices in Turkey, Istanbul Stock Exchange (IMKB) and the Taiwan Stock Exchange Capitalization Weighted Stock Index (TAIEX).     

GM(1,1)残差修正的季节性神经网络预测模型及其应用

季节性时间序列具有增长性和波动性的二重趋势。灰色模型GM(1,1)能反映时间序列的总体变化趋势,但不能很好反映其季节性波动变化的具体特征,在模拟与预测季节性时间序列中有明显的局限性。文中介绍了季节性神经网络建立的残差修正模型。通过季节性神经网络模型对GM(1,1)的残差序列进行分析,提取其中的非线性成分作为预测时的补偿项,以进行残差修正,从而形成GMSANN叠合预测模型。实例表明,所建模型具有较好的适应性和预测精度。     

Discrete variable stochastic approximation procedures and recursive autoregressive model identification

Two stochastic approximation procedures are proposed for finding a point attaining the maximum of a regression function defined and observable only at points on a set of discrete variables. The asymptotic convergence property of the procedures is discussed using the theorem of almost supermartingales. The procedures are applied to the recursive identification of autoregressive time series models. The identification procedure consists of a recursive order estimation stage and a recursive autoregressive parameter updating stage, and gives the true autoregressive model or the best autoregressive approximation model.     

Boosting nonlinear additive autoregressive time series

Several methods for the analysis of nonlinear time series models have been proposed. As in linear autoregressive models the main problems are model identification, estimation and prediction. A boosting method is proposed that performs model identification and estimation simultaneously within the framework of nonlinear autoregressive time series. The method allows one to select influential terms from a large number of potential lags and exogenous variables. The influence of the selected terms is modeled by an expansion in basis function allowing for a flexible additive form of the predictor. The approach is very competitive in particular in high dimensional settings where alternative fitting methods fail. This is demonstrated by means of simulations and two applications to real world data.     

基于动态隶属度的模糊时间序列模型的水质预测研究

科学有效的水质预测对于水资源的管理与水污染预警尤为重要。由于水质指标序列存在非线性、非平稳性、模糊性和季节性等特点,传统预测模型的精度受到一定的限制。结合差分整合自回归移动平均ARIMA模型和经典模糊时间序列模型的特性,提出了一种基于动态隶属度的模糊时间序列水质预测新模型。首先,利用模糊C均值聚类从原始数据中构建隶属度序列;其次,利用经典的时间序列模型对不同的子隶属度序列进行预测,得到动态隶属度;最后,去模糊化得到水质指标的预测值。应用提出的新模型对岷江某断面的水质指标进行了短期预测,并与经典模糊时间序列模型和ARIMA乘积季节模型进行对比。实验结果表明,新模型在RMSE、MAPE和MAE上均优于经典模糊时间序列模型和ARIMA乘积季节模型,极大地提高了预测精度,可为水污染防治提供有价值的参考。     

A hybrid SARIMA and support vector machines in forecasting the production values of the machinery industry in Taiwan

This paper proposes a hybrid methodology that exploits the unique strength of the seasonal autoregressive integrated moving average (SARIMA) model and the support vector machines (SVM) model in forecasting seasonal time series. The seasonal time series data of Taiwan’s machinery industry production values were used to examine the forecasting accuracy of the proposed hybrid model. The forecasting performance was compared among three models, i.e., the hybrid model, SARIMA models and the SVM models, respectively. Among these methods, the normalized mean square error (NMSE) and the mean absolute percentage error (MAPE) of the hybrid model were the lowest. The hybrid model was also able to forecast certain significant turning points of the test time series.     

Real time-adaptive control of systems containing inaccessible state variables†

This paper describes an adaptive scheme for controlling a non-linear process which is attractive from the point of view of implementation in a real time mode. Effective process control can be maintained, even when certain of the state variables are inaccessible, without the need for excessive computation. The process is repeatedly identified as a series of quasi-linear systems. The nature of the control is defined by a model, static or dynamic, set a priori. A ‘sub-optimal’ controller is modified by each successive identification.     

System shape optimization and stabilization of controlled quasi-linear stochastic systems that operate on an infinite time interval

The necessary conditions in the stabilization and optimization problem for a stationary quasi-linear stochastic system in continuous time, with its matrices depending on a vector parameter to be chosen, i.e., the optimization problem for the system shape, are obtained. An equivalent deterministic problem is stated and a numerical method to solve it using the analytical formula obtained for the criterion gradient, which is the function of a finite number of variables, is proposed. The optimization problem for an output-controlled system is a particular case, sufficient optimality conditions are obtained for it in the case that the complete information of the state is available. Optimality conditions are found for the proportional–integral–derivative controller in the quasi-linear stochastic system. These optimality conditions are applied to the optimal control problem for a small unmanned aerial vehicle moving in a disturbed atmosphere.