Construct an ARMA Model with Exogenous Variables and Use Kalman Filter to Adjust the Prediction of the Model

• Main Author: 許項涵
• Other Authors: 吳柏林
• Format: Others
• Language: zh-TW
• Published: 2019
• Online Access: http://ndltd.ncl.edu.tw/handle/e82wsf

碩士 === 國立政治大學 === 應用數學系 === 108 === Motivation: Kalman Filter is an algorithm which can update the estimate with adding current information. Due to computing conveniently, the filter has been broadly applied in various type of time series data. Kalman Filter can also applied in data identified by ARMA model, directly. In addition, the filter is flexible for extending exogenous variable. Objective: In some time series data with exogenous factors, the applications of Kalman filter are still limited. Therefore, the research focus on how to construct ARMA model with exogenous variables and how to applied by Kalman Filter. Innovation: For construction of ARMA model with exogenous variable, we propose orderly steps about method of separating the exogenous influence, im- proved the recognizing ability of model, and integrating both ARMA model and exogenous influence. In addition, we analyze the application of Kalman filter in the model. Method: The research use Kalman Filter, ARIMA model and State-space Representation for design new model and applied by Kalman Filter. Conclusion: Some time series data which failed to be identified by ARIMA model can be identified by ARMA model after process of decomposing exogenous influence method. Moreover, comparing with Kalman filter applied in ARIMA model, the predction of Kalman filter applied in new model get smaller error.