【统计学】时间序列建模与预测初探

时间序列建模与预测在实际应用中具有重要的意义。因此，近几年来在这一课题上进行了大量的研究工作。为了提高时间序列建模和预测的精度和效率，已经提出了许多重要的模型。本书的目的是提出一个在实践中使用的一些流行的时间序列预测模型的简要描述，尤其是相关的突出特点。在这本书中，我们描述了三类重要的时间序列模型，即基于随机、神经网络和支持向量机的模型，以及它们固有的预测优势和缺点。我们还讨论了与时间序列建模相关的基本问题，如平稳性、简约性、过度拟合等。我们对不同时间序列模型的讨论得到了对6个实时时间序列数据集的实验预测结果的支持。在将模型拟合到数据集时，要特别注意选择最简洁的模型。为了评估预测精度，并比较拟合时间序列的不同模型，我们使用了五个性能指标，即MSE、MAD、RMSE、MAPE和Theil的U-statistics。对于这六个数据集，我们都给出了所得到的预测图，该图以图形化方式描述了原始观测值和预测观测值之间的密切关系。为了在我们关于时间序列建模和预测的讨论中保持真实性和清晰性，我们从著名期刊和一些标准中获取了各种已发表的研究成果。

Time series modeling and forecasting hasfundamental importance to various practical domains. Thus a lot of activeresearch works is going on in this subject during several years. Many importantmodels have been proposed in literature for improving the accuracy andeffeciency of time series modeling and forecasting. The aim of this book is topresent a concise description of some popular time series forecasting modelsused in practice, with their salient features. In this book, we have describedthree important classes of time series models, viz. the stochastic, neuralnetworks and SVM based models, together with their inherent forecastingstrengths and weaknesses. We have also discussed about the basic issues relatedto time series modeling, such as stationarity, parsimony, overfitting, etc. Ourdiscussion about different time series models is supported by giving theexperimental forecast results, performed on six real time series datasets.While fitting a model to a dataset, special care is taken to select the mostparsimonious one. To evaluate forecast accuracy as well as to compare amongdifferent models fitted to a time series, we have used the five performancemeasures, viz. MSE, MAD, RMSE, MAPE and Theil’s U-statistics. For each of thesix datasets, we have shown the obtained forecast diagram which graphicallydepicts the closeness between the original and forecasted observations. To haveauthenticity as well as clarity in our discussion about time series modelingand forecasting, we have taken the help of various published research worksfrom reputed journals and some standard books.

1 引言
2 时间序列建模的基本概念
3 基于随机模型的时间序列预测
4 基于人工神经网络的时间序列预测
5 基于支持向量机的时间序列预测
6 预测性能衡量
7 实验结果
8 结论

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