本研究探討不同模型在比特幣市場價格預測中的適用性與誤差表現，選用跳躍擴散模型（Jump Diffusion Model, JDM）與長短期記憶網路模型（Long Short-Term Memory, LSTM）進行比較分析。研究資料採用2020年3月至2024年11月之比特幣每小時價格，並劃分為全時段市場與盤整市場兩種樣本條件，以觀察模型在不同波動性環境下的行為差異。JDM為結構模型，模擬價格分布並產出預測區間；LSTM則為資料驅動模型，進行逐點預測並藉由教師引導抑制遞迴誤差擴散。本研究依據模型特性設計對應誤差衡量指標，分別以涵蓋率、區間寬度與點估誤差作為評估基準。實證結果指出：JDM能合理捕捉價格分布的極端變異，特別適用於區間預測需求；而LSTM在資訊維度充足與穩定條件下具備較佳點估準確度。兩者各具強項，並應依預測目標與市場狀態進行選擇與應用。本研究亦針對市場高峰度、偏態與跳躍特徵提供統計驗證，並強調JDM預測結果應從整體分布觀點解釋，而非單次模擬。整體而言，本研究建立一套可兼顧理論可解釋性與資料彈性的比較分析架構，提供後續模型應用與實務操作之參考。

This study compares the forecasting performance of the Jump Diffusion Model (JDM) and Long Short-Term Memory (LSTM) in predicting Bitcoin prices using hourly data from March 2020 to November 2024. The analysis distinguishes between full-market and sideways-market periods. JDM simulates price distributions to generate prediction intervals, while LSTM conducts point forecasts with teacher forcing to reduce recursive error. Results show JDM is effective for interval-based risk assessment, whereas LSTM performs better in stable conditions. The study emphasizes interpreting JDM outcomes from a distributional view rather than individual paths, and provides a framework for model selection across varying market conditions.

第一章	緒論	1
第一節	研究背景與動機	1
第二節	研究方法	3
第三節	研究流程	5
第二章	文獻回顧	7
第一節	機器學習方法與加密資產預測應用	7
2.1.1門控循環單元(GRU)	8
2.1.2變壓器模型(Transformer)	9
2.1.3長短期記憶網路模型(LSTM)	10
第二節	傳統金融模型於加密貨幣市場的適用性	13
2.2.1 GARCH (Generalized Autoregressive Conditional Heteroskedasticity)	13
2.2.2 向量誤差修正模型(VECM)	14
2.2.3幾何布朗運動(Geometric Brownian Motion, GBM)	15
2.2.4 跳躍擴散模型(Jump Diffusion Model, JDM)	16
2.2.5 小結	17
第三章	研究方法	19
第一節	幾何布朗運動模型(GBM)	19
第二節	跳躍擴散模型(JDM)	20
第三節	機器學習模型設計與應用說明	21
3.3.1特徵選擇與設計邏輯	22
3.3.2 長短期記憶網路模型(LSTM)架構	22
第四節	誤差評估方法	24
3.4.1 預測區間涵蓋率	24
3.4.2 預測區間寬度	24
3.4.3 點估預測誤差指標	25
第五節	資料敘述統計	26
第四章	實證結果	27
第一節	JDM 模型之參數估計與預測結果分析	28
4.1.1 模型參數估計結果與市場異質性分析	29
4.1.2 模擬預測結果與涵蓋表現分析	30
4.1.3 涵蓋率統計結果分析	33
4.1.4平均預測區間寬度分析	35
4.1.5預測涵蓋與效率表現總結	36
第二節	LSTM模型之預測誤差分析	37
4.2.1 LSTM模型建構與參數設定	37
4.2.2 LSTM預測誤差比較分析	38
4.2.3 JDM與LSTM模型預測表現	44
第五章	結論與建議	45
第一節	結論	45
第二節	研究貢獻	46
第三節	研究限制與反思	47
參考文獻	49
中文文獻	49
英文文獻	49


 
圖目錄
圖 1: 2020~2024比特幣價格時間段	4
圖 2:全時段市場的蒙地卡羅方法7日預測	31
圖 3:盤整市場的蒙地卡羅方法7日預測	31
圖 4:全時段市場的蒙地卡羅方法31日預測	32
圖 5:盤整市場的蒙地卡羅方法31日預測	32
圖 6:全時段市場使用2特徵的7日預測	39
圖 7:全時段市場時段使用6特徵的7日預測	39
圖 8:全時段市場使用2特徵的31日預測	40
圖 9:盤整市場使用6特徵的31日預測	40
圖 10:盤整市場使用2特徵的7日預測	41
圖 11:盤整市場使用6特徵的7日預測	41
圖 12:盤整市場使用2特徵的31日預測	42
圖 13:盤整市場使用6特徵的31日預測	42
 
表目錄
表 1:比特幣價格資料之敘述統計	26
表2:±2Σ與±1.5Σ之差異	29
表3: JDM不同時段下的歷史平均參數	30
表 4:不同市場條件與預測期間下的區間涵蓋率統計	34
表 5:不同市場條件與預測期間下的平均預測區間寬度	35
表 6:不同市場條件與預測期間下的預測效率	35
表 7:不同特徵之誤差比較(全時段7日)	39
表 8:不同特徵之誤差比較(全時段31日)	40
表 9:不同特徵之誤差比較(盤整市場7日)	41
表 10:不同特徵之誤差比較(盤整市場31日)	42
表 11:不同特徵之誤差比較(全時期)	43

中文文獻
蔡佩珊 (2023)。以長短期記憶網路預測加密貨幣投資風險。碩士論文，國立中興大學企業管理學系。

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