Forecasting model selection through out-of-sample rolling horizon weighted errors

Demand forecasting is an essential process for any firm whether it is a supplier, manufacturer or retailer. A large number of research works about time series forecast techniques exists in the literature, and there are many time series forecasting tools. In many cases, however, selecting the best time series forecasting model for each time series to be dealt with is still a complex problem. In this paper, a new automatic selection procedure of time series forecasting models is proposed. The selection criterion has been tested using the set of monthly time series of the M3 Competition and two basic forecasting models obtaining interesting results. This selection criterion has been implemented in a forecasting expert system and applied to a real case, a firm that produces steel products for construction, which automatically performs monthly forecasts on tens of thousands of time series. As result, the firm has increased the level of success in its demand forecasts.     

A review and comparison of strategies for multi-step ahead time series forecasting based on the NN5 forecasting competition

Multi-step ahead forecasting is still an open challenge in time series forecasting. Several approaches that deal with this complex problem have been proposed in the literature but an extensive comparison on a large number of tasks is still missing. This paper aims to fill this gap by reviewing existing strategies for multi-step ahead forecasting and comparing them in theoretical and practical terms. To attain such an objective, we performed a large scale comparison of these different strategies using a large experimental benchmark (namely the 111 series from the NN5 forecasting competition). In addition, we considered the effects of deseasonalization, input variable selection, and forecast combination on these strategies and on multi-step ahead forecasting at large. The following three findings appear to be consistently supported by the experimental results: Multiple-Output strategies are the best performing approaches, deseasonalization leads to uniformly improved forecast accuracy, and input selection is more effective when performed in conjunction with deseasonalization.     

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.     

基于启发式遗传算法的SVM模型自动选择

支撑矢量机(SVM)模型的自动选择是其实际应用的关键.常用的基于穷举搜索的留一法(LOO)很繁杂且效率很低.到目前为止,大多数的算法并不能有效地实现模型自动选择.本文利用实值编码的启发式遗传算法实现基于高斯核函数的SVM模型自动选择.在重点分析了SVM超参数对其性能的影响和两种SVM性能估计的基础上,确定了合适的遗传算法适应度函数.人造数据及实际数据的仿真结果表明了所提方法的可行性和高效性.     

基于相关向量回归的非线性时间序列预测方法

针对非线性时间序列预测建模的复杂性和不确定性,提出一种基于相关向量回归的非线性时间序列预测方法。该方法在传统的核函数基础上,融入Bayesian推理框架,得到具有概率特性的预报结果,无须对误差/边界参数进行预估计,具有学习算法简单、易实现的特点。仿真计算表明,该方法能反映非线性时间序列的内在特性,预测结果较好。     

A class of hybrid morphological perceptrons with application in time series forecasting

In this work a class of hybrid morphological perceptrons, called dilation–erosion perceptron (DEP), is presented to overcome the random walk dilemma in the time series forecasting problem. It consists of a convex combination of fundamental operators from mathematical morphology (MM) on complete lattices theory (CLT). A gradient steepest descent method is presented to design the proposed DEP (learning process), using the back propagation (BP) algorithm and a systematic approach to overcome the problem of nondifferentiability of morphological operators. The learning process includes an automatic phase fix procedure that is geared at eliminating time phase distortions observed in some time series. Finally, an experimental analysis is conducted with the proposed DEP using five real world time series, where five well-known performance metrics and an evaluation function are used to assess the forecasting performance of the proposed model. The obtained results are compared with those generated by classical forecasting models presented in the literature.     

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.     

Feature selection with kernel class separability

Classification can often benefit from efficient feature selection. However, the presence of linearly nonseparable data, quick response requirement, small sample problem and noisy features makes the feature selection quite challenging. In this work, a class separability criterion is developed in a high-dimensional kernel space, and feature selection is performed by the maximization of this criterion. To make this feature selection approach work, the issues of automatic kernel parameter tuning, the numerical stability, and the regularization for multi-parameter optimization are addressed. Theoretical analysis uncovers the relationship of this criterion to the radius-margin bound of the SVMs, the KFDA, and the kernel alignment criterion, providing more insight on using this criterion for feature selection. This criterion is applied to a variety of selection modes with different search strategies. Extensive experimental study demonstrates its efficiency in delivering fast and robust feature selection.     

Time series forecasting with a neuro-fuzzy modeling scheme

Time series forecasting concerns the prediction of future values based on the observations previously taken at equally spaced time points. Statistical methods have been extensively applied in the forecasting community for the past decades. Recently, machine learning techniques have drawn attention and useful forecasting systems based on these techniques have been developed. In this paper, we propose an approach based on neuro-fuzzy modeling for time series prediction. Given a predicting sequence, the local context of the sequence is located in the series of the observed data. Proper lags of relevant variables are selected and training patterns are extracted. Based on the extracted training patterns, a set of TSK fuzzy rules are constructed and the parameters involved in the rules are refined by a hybrid learning algorithm. The refined fuzzy rules are then used for prediction. Our approach has several advantages. It can produce adaptive forecasting models. It works for univariate and multivariate prediction. It also works for one-step as well as multi-step prediction. Several experiments are conducted to demonstrate the effectiveness of the proposed approach.     

Short-term sales forecasting with change-point evaluation and pattern matching algorithms

The hotel and car manufacturing industries share many common points in their sales forecasting. For example, both are greatly affected by the fluctuation of economy, and closely related to the inertia. According to the principle characters of forecasting problem concerning these two kinds of industries, a short-term quantitative sales forecasting model is proposed based on the economic fluctuation analysis and the na?¨ve forecasting technology. The sales time series and its curve are used to construct this model. The relative concepts of the model are presented and corresponding algorithms are brought forward. Firstly, economic fluctuation of products sales is analyzed and the historical patterns of economic fluctuation change are divided. According to the geometric characteristics of a sales curve, the best historical matching for the current status is then found out, which corresponds to the process of activating the historical experiences of a manager. Finally the changing trend of the sales curve in the next period is determined, from which the short-term sales forecasting results can be obtained. The number of scattered guests of a hotel and the short-term sales for cars manufactured by a factory are forecasted by means of the model, which shows satisfactory forecasting accuracy. In fact, the forecasting approach proposed herein is the mathematical representation of the naïve forecasting method that is a kind of regular deduction based on the similarity between historical pattern and current status. Thus, this approach is good at forecasting the time series with the similarity between historical pattern and current status no matter whether the time series is seasonal or not, and gives better forecasting accuracy than ARMA and ANN models.     

A spatio-temporal decomposition based deep neural network for time series forecasting

Spatio-temporal problems arise in a broad range of applications, such as climate science and transportation systems. These problems are challenging because of unique spatial, short-term and long-term patterns, as well as the curse of dimensionality. In this paper, we propose a deep learning framework for spatio-temporal forecasting problems. We explicitly design the neural network architecture for capturing various types of spatial and temporal patterns, and the model is robust to missing data. In a preprocessing step, a time series decomposition method is applied to separately feed short-term, long-term and spatial patterns into different components of the neural network. A fuzzy clustering method finds clusters of neighboring time series residuals, as these contain short-term spatial patterns. The first component of the neural network consists of multi-kernel convolutional layers which are designed to extract short-term features from clusters of time series data. Each convolutional kernel receives a single cluster of input time series. The output of convolutional layers is concatenated by trends and followed by convolutional-LSTM layers to capture long-term spatial patterns. To have a robust forecasting model when faced with missing data, a pretrained denoising autoencoder reconstructs the model’s output in a fine-tuning step. In experimental results, we evaluate the performance of the proposed model for the traffic flow prediction. The results show that the proposed model outperforms baseline and state-of-the-art neural network models.     

TAGUCHI'S DESIGN OF EXPERIMENT IN COMBINATION SELECTION FOR A CHAOTIC TIME SERIES FORECASTING METHOD USING ENSEMBLE ARTIFICIAL NEURAL NETWORKS

Taguchi's design of experiment, an effective approach to identify factor-level combinations, was utilized to improve the result of a proposed chaotic time series forecasting method. In the proposed method, a residual analysis using a combination of embedding theorem and ensemble neural networks was employed to forecast chaotic time series. The time series was reconstructed into proper phase space points and fed into the first neural network. The network was trained to predict the future value of phase space points and chaotic time series. The analysis of residuals of the predicted time series showed that in many events they demonstrate chaotic behaviour. The residuals were treated as a new chaotic time series and reconstructed. A new network was trained to predict the future of the residual time series. The residual analysis was repeated several times. Finally, the last network was trained using a forecast value of the original time series and residuals as input and the original time series as output. The final network was used to capture the relationship between the forecast values of the original time series and residuals and the original time series. A systematic approach is introduced using Taguchi's method to improve the combination selection of networks and their parameters. The method was applied to some real-life chaotic time series. The experimental results confirmed that the proposed method performed more effectively and accurately compared to the same method using randomized factor-level combinations and other existing forecasting methods in the literature.     

Gaussian小波SVM及其混沌时间序列预测

为了提高混沌时间序列的预测精度,针对小波有利于信号细微特征提取的优点,结合小波技术和SVM的核函数方法,提出基于Gaussian小波SVM的混沌时间序列预测模型.证明了偶数阶Ganssian小波函数满足SVM平移不变核条件,并构建相应的Gaussian小波SVM.时混沌时间序列进行相空间重构,将重构相空间中的向量作为SVM的输入参量.用Ganssian小波SVM与常用的径向基SVM及Morlet小渡SVM进行对比实验,通过对Chen's混沌时间序列和负荷混沌时间序列的预测,结果表明,Ganssian小波SVM的效果比其他两种SVM更好.     

A SAX-GA approach to evolve investment strategies on financial markets based on pattern discovery techniques

This paper presents a new computational finance approach, combining a Symbolic Aggregate approXimation (SAX) technique together with an optimization kernel based on genetic algorithms (GA). The SAX representation is used to describe the financial time series, so that, relevant patterns can be efficiently identified. The evolutionary optimization kernel is here used to identify the most relevant patterns and generate investment rules. The proposed approach was tested using real data from S&P500. The achieved results show that the proposed approach outperforms both B&H and other state-of-the-art solutions.     

Pattern similarity-based methods for short-term load forecasting – Part 1: Principles

Load forecasting is an integral problem in the power system operation, planning and maintenance. The article presents the principles of the pattern similarity-based methods for short-term load forecasting. A common feature of these methods is learning from the data and using similarities between patterns of the seasonal cycles of the load time series. These series are non-stationary in mean and variance, contain long run trend, many cycles of seasonal fluctuations and random noise. The new approach based on the pattern similarity and local nonparametric regression simplifies the forecasting problem and enables us to develop effective forecasting models. Several functions mapping daily cycles of the load time series into input and output patterns are defined. The assumption underlying the pattern similarity-based methods of forecasting and the way of its verification are presented. Some indicators of the strength and stability of the relationship between patterns are described. In the experimental part of the work pattern definitions and the validity of the assumption were verified using Polish power system data. The data analysis was performed specific for load time series. The results show that pattern similarity-based methods can be very useful for forecasting time series with multiple seasonal cycles.     

基于EMD和SVR的混合智能预测模型及实证研究

针对非平稳、非线性时间序列变化复杂、难以用单一智能方法进行有效预测的问题,提出一种新的基于经验模式分解和支持向量回归的混合智能预测模型。经验模式分解能将非平稳时间序列按其内在的时间特征尺度自适应地分解为多个基本模式分量,根据这些分量各自趋势变化的剧烈程度选择不同的核函数进行支持向量回归预测,对各预测分量进行加权组合,得到原始序列的准确预测值。实证研究表明对于非平稳、非线性时间序列的预测,不论是单步预测还是多步预测,该模型均能取得很好的预测效果。     

A linear hybrid methodology for improving accuracy of time series forecasting

Modeling and forecasting of time series data are integral parts of many scientific and engineering applications. Increasing precision of the performed forecasts is highly desirable but a difficult task, facing a number of mathematical as well as decision-making challenges. This paper presents a novel approach for linearly combining multiple models in order to improve time series forecasting accuracy. Our approach is based on the assumption that each future observation of a time series is a linear combination of the arithmetic mean and median of the forecasts from all participated models together with a random noise. The proposed ensemble is constructed with five different forecasting models and is tested on six real-world time series. Obtained results demonstrate that the forecasting accuracies are significantly improved through our combination mechanism. A nonparametric statistical analysis is also carried out to show the superior forecasting performances of the proposed ensemble scheme over the individual models as well as a number of other forecast combination techniques.     

Using multiplicative neuron model to establish fuzzy logic relationships

Determination of fuzzy logic relationships between observations is quite effective on the forecasting performance of fuzzy time series approaches. In various studies available in the literature, it has been seen that utilizing artificial neural networks for establishing fuzzy relations increase the forecasting accuracy. In this study, a novel high order fuzzy time series forecasting approach in which multiplicative neuron model is used to define fuzzy relations is proposed in order to reach high forecasting level. Also, particle swarm optimization method is utilized to train multiplicative neuron model. In order to show forecasting performance of the proposed method, it is applied to a well-known data Taiwan future exchange and the results produced by the proposed approach is compared to those obtained from other fuzzy time series forecasting models. As a result of the implementation, it is observed that the proposed approach gives the best forecasts for Taiwan future exchange time series.     

基于混合核支持向量机的金融时间序列分析

核函数是支持向量机（SVM）的重要部分,它直接影响到SVM的各项性能。当前SVM在金融时间序列分析中,基本上采用高斯径向核函数（RBF）,其次才是多项式核函数。然而,每种核函数都有它的优势和不足,整合两个或多个核函数对于学习能力和泛化能力的提高是一个有效的途径。采用高斯径向核函数与多项式核函数的混合核函数运用于金融时间序列预测中,且与其单个核函数的支持向量机的实验结果进行了比较。结果表明,混合核函数具有更好的性能。     

Hybrid neural network models for hydrologic time series forecasting

The need for increased accuracies in time series forecasting has motivated the researchers to develop innovative models. In this paper, a new hybrid time series neural network model is proposed that is capable of exploiting the strengths of traditional time series approaches and artificial neural networks (ANNs). The proposed approach consists of an overall modelling framework, which is a combination of the conventional and ANN techniques. The steps involved in the time series analysis, e.g. de-trending and de-seasonalisation, can be carried out before gradually presenting the modified time series data to the ANN. The proposed hybrid approach for time series forecasting is tested using the monthly streamflow data at Colorado River at Lees Ferry, USA. Specifically, results from four time series models of auto-regressive (AR) type and four ANN models are presented. The results obtained in this study suggest that the approach of combining the strengths of the conventional and ANN techniques provides a robust modelling framework capable of capturing the non-linear nature of the complex time series and thus producing more accurate forecasts. Although the proposed hybrid neural network models are applied in hydrology in this study, they have tremendous scope for application in a wide range of areas for achieving increased accuracies in time series forecasting.