Reduced-rank Decomposition on Spatial Temporal Data with Applications to PM2.5 Daily Forecasts

• Main Authors: Chung, Teng-Yi, 鍾騰逸
• Other Authors: Hsu, Nan-Jung
• Format: Others
• Language: zh-TW
• Published: 2018
• Online Access: http://ndltd.ncl.edu.tw/handle/k4gh9c

碩士 === 國立清華大學 === 統計學研究所 === 106 === In recent years, air pollution becomes a serious problem in Taiwan, in particular PM2.5 plays an important role to affect the public health. This thesis studies the topic of PM2.5 forecast. The data used in this study is from AirBox Project which collects high-frequency data from more than one thousand small measurement devices using IoT technologies. The data are available instantaneously but very irregular in time, having excessive observation errors and many missing data. This study suggests a reduced-rank decomposition model to analyze AirBox data. The model consists two parts. The mean structure of daily pattern is specified via a linear combination of products of spatial eigen-functions and temporal (hourly) eigen-functions obtained via singular value decomposition. The dependence structure is specified via the fixed rank spatial-temporal random effect model. For parameter estimation, the method of moments is used. Given the model with estimated parameters, the kalman filter is used to generate the map of the best linear spatial prediction and their prediction errors for the one-step-ahead and multi-step-ahead PM2.5 values. The methodology is demonstrated using the data at south Taiwan.