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Autoregressive time series prediction by means of fuzzy inference systems using nonparametric residual variance estimation

机译：基于非参数残差估计的模糊推理系统的自回归时间序列预测

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摘要

We propose an automatic methodology framework for short- and long-term prediction of time series by means of fuzzy inference systems. In this methodology, fuzzy techniques and statistical techniques for nonparametric residual variance estimation are combined in order to build autoregressive predictive models implemented as fuzzy inference systems. Nonparametric residual variance estimation plays a key role in driving the identification and learning procedures. Concrete criteria and procedures within the proposed methodology framework are applied to a number of time series prediction problems. The learn from examples method introduced by Wang and Mendel (W&M) is used for identification. The Levenberg-Marquardt (L-M) optimization method is then applied for tuning. The W&M method produces compact and potentially accurate inference systems when applied after a proper variable selection stage. The L-M method yields the best compromise between accuracy and interpretability of results, among a set of alternatives. Delta test based residual variance estimations are used in order to select the best subset of inputs to the fuzzy inference systems as well as the number of linguistic labels for the inputs. Experiments on a diverse set of time series prediction benchmarks are compared against least-squares support vector machines (LS-SVM), optimally pruned extreme learning machine (OP-ELM), and k-NN based autoregressors. The advantages of the proposed methodology are shown in terms of linguistic interpretability, generalization capability and computational cost. Furthermore, fuzzy models are shown to be consistently more accurate for prediction in the case of time series coming from real-world applications.
机译：我们提出了一种通过模糊推理系统对时间序列进行短期和长期预测的自动方法框架。在这种方法中，将用于非参数残差估计的模糊技术和统计技术相结合，以构建实现为模糊推理系统的自回归预测模型。非参数残差方差估计在驱动识别和学习过程中起关键作用。所提出的方法框架内的具体标准和程序适用于许多时间序列预测问题。 Wang和Mendel（W＆M）引入的“从示例中学习”方法用于识别。然后将Levenberg-Marquardt（L-M）优化方法应用于调整。在适当的变量选择阶段之后应用W＆M方法可生成紧凑且可能准确的推理系统。在一组备选方案中，L-M方法可在结果的准确性和可解释性之间取得最佳折衷。为了选择模糊推理系统的最佳输入子集以及用于输入的语言标签数量，使用了基于增量测试的残差方差估计。将针对各种时间序列预测基准的实验与最小二乘支持向量机（LS-SVM），最佳修剪的极限学习机（OP-ELM）和基于k-NN的自回归进行比较。从语言的可解释性，泛化能力和计算成本方面显示了所提出方法的优势。此外，在来自实际应用的时间序列的情况下，模糊模型显示出一致的预测准确度。

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