Research On Probabilistic Forecasting And Analysis Of Time Series

Time series contain many important information.Research on time series mainly focuses on anomaly detection and time series forecasting.Based on the prediction results time series forecasting can be divided into two types:point forecasting and probabilistic forecasting.Compared with point forecasting,probabilistic forecasting can provide more comprehensive analysis information by giving the interval and probability distribution of future changes,so it has a broader application prospect.At present,there are several issues with multivariate probabilistic forecasting for long time series,including high model complexity and poor forecasting performance.Thus,this thesis introduces transformer structure,utilizing variational autoencoder and self-attention mechanism to achieve low complexity long time series multivariate probabilistic forecasting with seq2seq structure.Furthermore,Fourier transform and autocorrelation mechanism are used to analyze the periodic characteristics of time series,and achieve decomposition-based multivariate probabilistic forecasting for long time series.The research work described in this thesis includes four parts.(1)A probabilistic forecasting model V-trans based on variational autoencoder and self-attention mechanisms is proposed.The V-trans model adopts an encoder-decoder architecture and obtains the evidence lower bound through variational inference.By maximizing the evidence lower bound,the model encoder can approximate the posterior distribution of the latent variables.the decoder can then reconstruct the predicted data from the latent variables.The model combines self-attention mechanisms in both the encoder and decoder to avoid problems such as vanishing and exploding gradient,and can better capture long-term dependencies in time series.Through validation on an electricity load dataset,the V-trans model achieved better performance for long time series forecasting problems compared to baseline models.(2)To tackle the quadratic complexity issue of the self-attention mechanism,a Max Self-Attention mechanism is proposed,which takes the sparsity of the self-attention mechanism and measures information entropy to select attention dot products.This method reduces the time complexity of long time series forecasting models to O(N log(N)).It has been validated that using the Max Self-Attention model is more efficient for the same size of problems.(3)A probabilistic forecasting model VD-trans based on series decomposition is presented,aiming at taking the periodic property that widely exists in time series to improve forecasting accuracy.Fourier transform an autocorrelation are used to extract the periodic properties of time series,and moving average to extract trend properties for probabilistic forecasting.The evaluation experiments show that compared with V-trans,VD-trans has better prediction results,which reflects the necessity and superiority of the series decomposition.(4)An electricity load forecasting software was developed and validated in an actual project.The software integrates the proposed V-trans and VD-trans models,as well as some other time series forecasting models.It provides important functions such as importing time series,adjusting model parameters,saving training models,loading forecasting models,and presenting forecasting results,etc.The above work demonstrates that the time series probabilistic forecasting model V-trans and time series probabilistic decomposition forecasting model VD-trans proposed in this article effectively solves the problem of low accuracy in the field of multivariate long time series probabilistic forecasting.V-trans and VD-trans can provide more accurate and comprehensive forecasting results in the form of probability distributions,which will better support user decision analysis.Therefore,it has broad application prospects.