在时间序列预测领域,精准的预测模型对于诸多实际应用场景具有重要意义。本文聚焦于基于函数型数据分析的时间序列模型预测方法,首先以构造小波基来拟合函数为例介绍了函数型数据分析在处理离散时序数据时进行降噪的方法,并阐述了主成分分析在面对线性和非线性的高维数据的降维方法,并以LSTM为模型对比了在多类数据集当中数据降维的效果。在此理论基础上,本文将所研究的方法应用于中国大兴安岭地区部分气象站的森林火险指数(Fire Weather Index, FWI)时序数据预测实践。通过对数据进行小波变换降噪、降维处理后,运用所构建的LSTM模型进行预测,并进一步对火灾风险进行科学评估。实验结果表明,所提出的基于函数型数据分析的时间序列预测方法在实际应用中展现出了较高的预测精度和良好的可靠性,为相关领域的时序预测与风险评估工作提供了新的有效途径和方法参考。In the field of time series forecasting, accurate predictive models hold significant importance for numerous practical application scenarios. This paper focuses on the forecasting methods of time series models based on functional data analysis. Firstly, it introduces the method of using wavelet basis construction to fit functions as an example, illustrating how functional data analysis can be applied to denoise discrete time series data. It also elaborates on the dimensionality reduction methods of principal component analysis (PCA) when dealing with high-dimensional linear and nonlinear data. Furthermore, the paper compares the dimensionality reduction effects of these methods on various datasets using LSTM models as a benchmark. Building on this theoretical foundation, the methods studied in this paper are applied to the practice of predicting the Forest Fire Weather Index (FWI) time series data from some meteorological stations in the Greater Khingan Region of China. After denoising and dimensio
