A Time Series Forecasting Algorithm Based On State Space Model

Time series analysis has important applications in many fields.For example,in the field of economics,the analysis of stock market prices or various financial indices that we are exposed to every day can help investors make decisions and affect the flow of money.Social scientists will pay attention to time series data of population series,such as birth rate or school enrollment rate,etc.,so as to predict the trend of population health in the future,and then provide the government with appropriate population policy recommendations.Existing time series analysis methods include two perspectives: time domain and frequency domain.Time-domain methods focus on lag relationships between sequences,in other words how what happened in the past few days will affect what happens tomorrow,while frequency-domain methods focus on periodic research,For example,the economic cycle,its expansions and recessions show a regular pattern.The above two methods are independent,but they are not necessarily mutually exclusive,and there are also some works that start from the time domain and the frequency domain at the same time.Time series forecasting is an application after analysis,and the forecasting algorithm can be adjusted after facing different types of time series analysis.However,the existing prediction algorithms for target time series,whether starting from the frequency domain or the time domain,are mainly based on the prior knowledge of the sequence itself,but ignore the background information behind the target sequence.This neglected information is often necessary to build a robust time series model in complex real-world scenarios.Background information is usually not obvious in the prediction task of the target sequence.For example,the content of various pollutants in the air of the target object is predicted,and it is intuitive to feel that some effective information is missing from the prediction based on the information of the pollutant itself.However,if the background information such as temperature,humidity and pressure that affect the pollutant content are introduced into the modeling,it will provide more effective information to improve the prediction effect.These shared information requires us to conduct additional mining and discovery based on prior information and experiments.In our task,how to extract the shared background information behind multiple sequences and how to incorporate the extracted information into the prediction model are two main challenges.To address the above two challenges,we propose a shared state space model(SSSM)by introducing a shared background information component into the state space model.In SSSM,we consider all sequences as a whole and model each target series by utilizing a state space model with shared same parameters and background information.The specific method is as follows: First,we employ two recurrent neural networks to extract the temporal characteristic of the target sequence as well as the background information.Second,the above extracted information is integrated into a state space model in the form of a linear Gaussian component,whose inference procedure is accomplished by Kalman Filter.Finally,the model is optimized following a log-likelihood of the model with the above two components.We compare with multiple mainstream baseline methods in three real datasets,and find that SSM outperforms all baseline methods in prediction accuracy,proving the rationality of our ideas.At the same time,through the experimental analysis of correlation,it is found that the model can extract the correlation between the shared information behind the data and the target sequence,and there is a positive feedback effect on the prediction of the target sequence.