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研究生:陳定鴻
研究生(外文):CHEN, TING-HUNG
論文名稱:根基於線性檢定以比較統計及機器學習預測模型之研究
論文名稱(外文):A Comparison Study of Statistical and Machine Learning Prediction Models Based on Linearity Test
指導教授:邵曰仁邵曰仁引用關係
指導教授(外文):SHAO, YUEH-JEN
口試委員:盧宏益王信忠
口試委員(外文):LU, HUNG-YIWANG, HSIN-CHUNG
口試日期:2020-07-01
學位類別:碩士
校院名稱:輔仁大學
系所名稱:統計資訊學系應用統計碩士在職專班
學門:數學及統計學門
學類:統計學類
論文種類:學術論文
論文出版年:2020
畢業學年度:108
語文別:中文
論文頁數:81
中文關鍵詞:預測線性關係非線性關係線性檢定自我迴歸移動平均整合模型類神經網路多元適應性雲型迴歸
外文關鍵詞:predictionlinearitynonlinearitylinearity testautoregressive integrated moving average model (ARIMA)artificial neural network (ANN)multivariate adaptive regression spiline (MARS)
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一般而言,數據分為線性關係及非線性關係,若觀測值之間存在線性關係,表示數據之間是直線屬性且較容易解釋,若觀測值屬於非線性關係,則表示數據之間可能較複雜且不易解釋。故在建立預測模型前,可以透過歷史訊息觀察資料的特性及趨勢,選擇適合的預測模型,進而降低預測成本及建模時間。本研究欲瞭解當數據存在線性關係或是非線性關係時,則統計及機器學習預測模型之預測能力是否有顯著差異?本研究以電腦模擬的方式產生兩組數據,且採用線性檢定判斷其數據屬於線性關係或是非線性關係,為了提高客觀性,本研究進而探討兩組實務數據以進行驗證,並比較數據在線性統計方法及非線性機器學習方法預測模型之預測能力,而在本文中,線性統計方法是以ARIMA為主要考量;非線性機器學習方法則是以ANN及MARS為主。根據本研究結果顯示,當數據屬於線性關係時,則ARIMA之預測能力優於ANN及MARS預測模型,當數據為非線性關係時,則ANN及MARS之預測能力優於ARIMA預測模型。
In general, the data can be divided into linear and nonlinear relationships. If there is a linear relationship between the feature values, it means that the data is a straight line attribute and is easy to explain. If the feature values are in a nonlinear relationship, it means that the data may be more complicated. It is not easy to explain. In order to reduce the prediction cost and modeling time, the feature variables and data trends can be researched through historical information as the strong sign for appropriate prediction model selection.
The purpose of this study is to observe whether there is a significant difference between the prediction capabilities of statistical and machine learning models in different relationships. In this study, two sets of data are generated by computer simulations, and the linear test is used to determine whether the data is linear or nonlinear. In order to improve the objectivity, this study also considers two practical datasets for verification. This study compares the prediction performance between the linear statistical and nonlinear machine learning methods. In this study, ARIMA is used for linear statistical modeling, and the ANN and MARS are utilizd for nonlinear modeling.
Based upon the results, when data is in a linear relationship, the prediction ability of ARIMA is superior to ANN and MARS. Moreover, when there is a nonlinear relationship of data, the prediction ability of ANN and MARS is superior to ARIMA.

第壹章 緒論 1
第一節 研究背景 1
第二節 研究動機與目的 1
第三節 研究流程與架構 2
第貳章 文獻探討 5
第一節 AQI及美國汽油價格相關文獻 5
第二節 線性檢定相關文獻 6
第三節 差分整合移動平均自我迴歸相關文獻 7
第四節 類神經網路相關文獻 8
第五節 多元適應性雲型迴歸相關文獻 9
第參章 研究方法 10
第一節 線性檢定 10
第二節 差分整合移動平均自我迴歸 12
第三節 類神經網路 14
第四節 多元適應性雲型迴歸 16
第肆章 實證研究分析 18
第一節 模擬資料及實務資料說明 18
第二節 線性檢定 22
第三節 模擬資料預測能力分析 24
第四節 實務資料預測能力分析 51
第五節 實證結果討論 74
第伍章 結論與建議 76
第一節 研究發現 76
第二節 研究限制與未來研究建議 76
參考文獻 78

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