A novel procedure for multimodel development using the grey silhouette coefficient for small-data-set forecasting

Small-data-set forecasting problems are a critical issue in various fields, with the early stage of a manufacturing system being a good example. Manufacturers require sufficient knowledge to minimize overall production costs, but this is difficult to achieve due to limited number of samples available at such times. This research was thus conducted to develop a modelling procedure to assist managers or decision makers in acquiring stable prediction results from small data sets. The proposed method is a two-stage procedure. First, we assessed some single models to determine whether the tendency of a real sequence can be reflected using grey incidence analysis, and we then evaluated their forecasting stability based on the relative ratio of error range. Second, a grey silhouette coefficient was developed to create an applicable hybrid forecasting model for small samples. Two real cases were analysed to confirm the effectiveness and practical value of the proposed method. The empirical results showed that the multimodel procedure can minimize forecasting errors and improve forecasting results with limited data. Consequently, the proposed procedure is considered a feasible tool for small-data-set forecasting problems.     

A mega-trend-diffusion grey forecasting model for short-term manufacturing demand

Accurate short-term demand forecasting is critical for developing effective production plans; however, a short forecasting period indicates that the product demands are unstable, rendering tracking of product development trends difficult. Determining the actual developing data patterns by using forecasting models generated using historical observations is difficult, and the forecasting performance of such models is unfavourable, whereas using the latest limited data for forecasting can improve management efficiency and maintain the competitive advantages of an enterprise. To solve forecasting problems related to a small data set, this study applied an adaptive grey model for forecasting short-term manufacturing demand. Experiments involving the monthly demand data for thin film transistor liquid crystal display panels and wafer-level chip-scale packaging process data showed that the proposed grey model produced favourable forecasting results, indicating its appropriateness as a short-term forecasting tool for small data sets.     

Hybrid evolutionary algorithms in a SVR traffic flow forecasting model

Accurate urban traffic flow forecasting is critical to intelligent transportation system developments and implementations, thus, it has been one of the most important issues in the research on road traffic congestion. Due to complex nonlinear data pattern of the urban traffic flow, there are many kinds of traffic flow forecasting techniques in literature, thus, it is difficult to make a general conclusion which forecasting technique is superior to others. Recently, the support vector regression model (SVR) has been widely used to solve nonlinear regression and time series problems. This investigation presents a SVR traffic flow forecasting model which employs the hybrid genetic algorithm-simulated annealing algorithm (GA-SA) to determine its suitable parameter combination. Additionally, a numerical example of traffic flow data from northern Taiwan is used to elucidate the forecasting performance of the proposed SVRGA-SA 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), Holt-Winters (HW) and seasonal Holt-Winters (SHW) models. Therefore, the SVRGA-SA model is a promising alternative for forecasting traffic flow.     

Bayesian forecasting with the Holt–Winters model

Exponential smoothing methods are widely used as forecasting techniques in inventory systems and business planning, where reliable prediction intervals are also required for a large number of series. This paper describes a Bayesian forecasting approach based on the Holt–Winters model, which allows obtaining accurate prediction intervals. We show how to build them incorporating the uncertainty due to the smoothing unknowns using a linear heteroscedastic model. That linear formulation simplifies obtaining the posterior distribution on the unknowns; a random sample from such posterior, which is not analytical, is provided using an acceptance sampling procedure and a Monte Carlo approach gives the predictive distributions. On the basis of this scheme, point-wise forecasts and prediction intervals are obtained. The accuracy of the proposed Bayesian forecasting approach for building prediction intervals is tested using the 3003 time series from the M3-competition.     

An extended grey forecasting model for omnidirectional forecasting considering data gap difference

To achieve effective and efficient decision making in a highly competitive business environment, an enterprise must have an appropriate forecasting technique that can meet the requirements of both timeliness and accuracy. Accordingly, in the early stages, building a forecasting model with incomplete information and limited samples is very important to a business. Grey system theory is one of the prediction methods that can be built with a small sample and yet has a strong ability to make short-term predictions. The purpose of this study is to come up with an improved forecasting model based on the concept of this theory to enlarge the applicability of the grey forecasting model in various situations. By extending the data transforming approach, this method generalizes a building procedure for the grey model to grasp the data outline and information trend. Specifically, a novel inverse accumulating generation operator is developed to enable omnidirectional forecasting. The research utilizes observations of the titanium alloy fatigue limit along with temperature changes as raw data to verify the performance of the proposed method. The experimental results show that not only can this method expand the application scope of the grey forecasting model, but also improve its forecasting accuracy.     

模糊时间数列的分析与预测:以台湾地区加权股价指数为例

随着我国经济快速成长，衍生性金融商品的投资分析，已成为国内财务数学研究热门课题。以股票市场而言，人们总希望比别人早一步掌握行情的脉动，以获取最高的报酬率，然而，影响股市加权股价指数波动的因素众多，要如何进行趋势分析与预测，是很多学者相当感兴趣与研究的主题。本文考虑以模糊统计方法，作模糊时间数列的趋势分析与预测。其望应用模糊统计分析方法比传统的时间数列分析方法能得到更合理的解释，且预测结果可以提供决策者更多的信息，做出正确的决策。最后以台湾地区加权股票指数为例，做一实证上的详细探讨。     

A novel grey forecasting model and its optimization

Although the grey forecasting model has been successfully employed in many fields and demonstrated promising results, its prediction results may be inaccurate sometimes. For the purposes of enhancing the predictive performance of grey forecasting model and enlarging its suitable ranges, this paper puts forward a novel grey forecasting model termed NGM model and its optimized model, develops a calculative formula for solving the parameters of the novel NGM model through the least squares method, and obtains the time response sequence of NGM model by using differential equation as a procedure for reasoning. It performs a numerical demonstration on the prediction accuracy of NGM model and its optimized models. As shown in the results, the proposed model and it optimized model can enhance the prediction accuracy. Numerical results illustrate that the proposed NGM model and its optimized model are effective. They are suitable for predicting the data sequence with the characteristics of non-homogeneous exponential law. This work makes important contribution to the enrichment of grey prediction theory.     

A grey modeling procedure based on the data smoothing index for short-term manufacturing demand forecast

Product life cycles have become increasingly shorter because of global competition. Under fierce competition, the use of small samples to establish demand forecasting models is crucial for enterprises. However, limited samples typically cannot provide sufficient information; therefore, this presents a major challenge to managers who must determine demand development trends. To overcome this problem, this paper proposes a modified grey forecasting model, called DSI–GM(1,1). Specifically, we developed a data smoothing index to analyze the data behavior and rewrite the calculation equation of the background value in the applied grey modeling, constructing a suitable model for superior forecasting performance according to data characteristics. Employing a test on monthly demand data of thin film transistor liquid crystal display panels and the monthly average price of aluminum for cash buyers, the proposed modeling procedure resulted in high prediction outcomes; therefore, it is an appropriate tool for forecasting short-term demand with small samples.     

Info-gap forecasting and the advantage of sub-optimal models

We consider forecasting in systems whose underlying laws are uncertain, while contextual information suggests that future system properties will differ from the past. We consider linear discrete-time systems, and use a non-probabilistic info-gap model to represent uncertainty in the future transition matrix. The forecaster desires the average forecast of a specific state variable to be within a specified interval around the correct value. Traditionally, forecasting uses a model with optimal fidelity to historical data. However, since structural changes are anticipated, this is a poor strategy. Our first theorem asserts the existence, and indicates the construction, of forecasting models with sub-optimal-fidelity to historical data which are more robust to model error than the historically optimal model. Our second theorem identifies conditions in which the probability of forecast success increases with increasing robustness to model error. The proposed methodology identifies reliable forecasting models for systems whose trajectories evolve with Knightian uncertainty for structural change over time. We consider various examples, including forecasting European Central Bank interest rates following 9/11.     

基于小波变换和改进萤火虫算法优化极限学习机的短期负荷预测

提出了一种基于小波变换和改进萤火虫优化极限学习机的短期负荷预测方法.通过小波分解和重构,对原始负荷序列进行降噪;在模型训练阶段利用改进的萤火虫算法优化极限学习机参数,获得各序列的最优模型;针对各子序列分别预测叠加得到最终预测值.通过在两种时间尺度的数据序列上进行数值计算,与传统的ARMA、BP神经网络、支持向量机及LSSVM等多种经典预测模型相比,模型预测效果更优.     

A novel hybrid multivariate nonlinear grey model for forecasting the traffic-related emissions

In this paper, we proposed a novel forecasting method using grey system theory for the traffic-related emissions at a national level. In our tests, grey relational analysis was used to identify time lags between input and output variables. We introduced a multivariate nonlinear grey model based on the kernel method to improve the accuracy of traffic-related emissions prediction. By solving a convex optimization problem instead of using an ordinary least squares estimation, the proposed model overcame the limitations of the classic grey forecasting models. A model confidence set test on the realistic results of forecasting traffic-related emissions in European Union member countries showed that the proposed model demonstrated a marked superiority over robust linear regression and support vector regression. Based on the non-methane volatile organic compounds from road transport and the relevant factors of the emission from 2004 to 2016, a more stringent European Union emission reduction commitment to the road transport for each year from 2020 to 2029 was suggested. We also investigated the advantages of the proposed model via the analysis on convergence, robustness, and sensitivity.     

Improving demand forecasting accuracy using nonlinear programming software

We address the problem of forecasting real time series with a proportion of zero values and a great variability among the nonzero values. In order to calculate forecasts for a time series, the model coefficients must be estimated. The appropriate choice of values for the smoothing parameters in exponential smoothing methods relies on the minimization of the fitting errors of historical data. We adapt the generalized Holt–Winters formulation so that it can consider the starting values of the local components of level, trend and seasonality as decision variables of the nonlinear programming problem associated with this forecasting procedure. A spreadsheet model is used to solve the problems of optimization efficiently. We show that our approach produces accurate forecasts with little data per product.     

Parallel Lagrangean approximation procedure

We investigate the potential of the parallelised Lagrangean approximation procedure (PLAP) for certain combinatorial optimisation problems in manufacturing systems. The framework of a PLAP is proposed for some combinatorial manufacturing problems which are decomposable into well-structured subproblems. The synchronous PLAP for the multistage dynamic lot-sizing problem is implemented on a parallel computer (Alliant FX/4) and its computational experience is reported as a promising application of vector-concurrent computing.     

基于Theil不等系数的加权几何平均组合预测模型的性质

加权几何平均组合预测为一种非线性的组合预测方法。本文提出了基于Theil不等系数的加权几何平均的组合预测模型,针对该模型定义了优性组合预测、预测方法优超和组合预测冗余度等新的概念;探讨了非劣性组合预测和优性组合预测存在的充分条件;给出了一个冗余预测方法出现的判定定理。     

基于向量夹角余弦的加权调和平均组合预测模型的有效性

加权调和平均组合预测为一种非线性的组合预测方法.提出了基于向量夹角余弦的加权调和平均组合预测模型,针对该模型定义了优性组合预测、预测方法优超和组合预测冗余度等新的概念;探讨了非劣性组合预测和优性组合预测存在的充分条件;给出了一个冗余预测方法出现的判定定理.     

基于ARIMA和LSSVM的非线性集成预测模型

针对复杂时间序列预测困难的问题,在综合考虑线性与非线性复合特征的基础上,提出一种基于ARIMA和最小二乘支持向量机(LSSVM)的非线性集成预测方法.首先采用ARIMA模型进行时间序列线性趋势建模,并为LSSVM建模确定输入阶数;接着根据确定的输入阶数进行时间序列样本重构,采用LSSVM模型进行时间序列非线性特征建模;最后采用基于LSSVM的非线性集成技术形成一个综合的预测结果.将该方法用于中国GDP预测取得的结果,与单独预测方法及流行的其他集成预测方法相比,预测精度有了较大的提高,从而验证了方法的有效性和可行性.     

Fitting a Gompertz Curve

In this paper, a simple Gompertz curve-fitting procedure is proposed. Its advantages include the facts that the stability of the saturation level over the sample period can be checked, and that no knowledge of its value is necessary for forecasting. An application to forecasting the stock of cars in the Netherlands illustrates its merits.     

Forecasting urban traffic flow by SVR with continuous ACO

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. In the recent years, the support vector regression model (SVR) has been widely used to solve nonlinear regression and time series problems. This investigation presents a short-term traffic forecasting model which combines the support vector regression model with continuous ant colony optimization algorithms (SVRCACO) 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 SVRCACO model. The forecasting results indicate that the proposed model yields more accurate forecasting results than the seasonal autoregressive integrated moving average (SARIMA) time series model. Therefore, the SVRCACO model is a promising alternative for forecasting traffic flow.     

Rainfall forecasting by technological machine learning models

Accurate forecasting of rainfall has been one of the most important issues in hydrological research. Due to rainfall forecasting involves a rather complex nonlinear data pattern; there are lots of novel forecasting approaches to improve the forecasting accuracy. Recurrent artificial neural networks (RNNS) have played a crucial role in forecasting rainfall data. Meanwhile, support vector machines (SVMs) have been successfully employed to solve nonlinear regression and time series problems. This investigation elucidates the feasibility of hybrid model of RNNs and SVMs, namely RSVR, to forecast rainfall depth values. Moreover, chaotic particle swarm optimization algorithm (CPSO) is employed to choose the parameters of a SVR model. Subsequently, example of rainfall values during typhoon periods from Northern Taiwan is used to illustrate the proposed RSVRCPSO model. The empirical results reveal that the proposed model yields well forecasting performance, RSVRCPSO model provides a promising alternative for forecasting rainfall values.     

Model Identification in Exponential Smoothing

Model identification has traditionally been ignored in forecasting via exponential smoothing. The usual practice is to apply the same model to every time-series in a collection. This paper develops a procedure for model identification in large forecasting applications based on an examination of variances of differences of the time-series. The order of differencing yielding minimum variance suggests an appropriate model for the series. Empirical results show that this procedure selects models that give reasonable ex ante forecast accuracy.