虛擬貨幣市場的價格波動劇烈，且單一貨幣價格的跳動不只影響自身市場還會帶動其他貨幣的價格跳躍，傳統金融模型難以充分捕捉此種特性。本研究以比特幣（BTC）與以太幣（ETH）的對數報酬率作為研究樣本，2023 年全年作為訓練期，2024 年至 2026 年 5 月作為預測期。模型以跨資產雙向互激 Hawkes 過程來做分析，並且最後得出每個時機點的大漲、大跌與震盪的機率，以供後續預測與策略設計使用。本研究將預測期切分為 109 段互不重疊的時間區間，並比較三種分布假設下的預測表現，此三種模型分別為：模型一之各變數皆採經驗分布，模型二與模型三則分別採用傳統參數分布，以此檢驗經驗分布取代傳統分布假設是否能提升預測準確性。
實證結果顯示，BTC 與 ETH 的跳躍傳染（jump contagion）效果在大漲、大跌（正、負跳躍）之間呈現明顯不對稱：大漲（正跳躍）彼此激發的效果較強，但造成後續的影響相對大跌來的少；大跌（負跳躍）激發力程度相對弱，造成的影響時間相對久。跨資產傳染方面，又以 BTC 大漲對 ETH 大漲的連動效果最為明顯，反映 BTC 為有一定程度主導 ETH 的角色。在比較三種模型的預測表現後發現，採用經驗分布的模型一，其分類指標整體優於採用傳統分布假設的模型二與模型三，顯示不預設分布形狀的做法較能反映虛擬貨幣市場報酬率的特性。
本研究之貢獻在於：提出以經驗分布取代傳統分布假設的建模方式，並採取平衡參數穩定性與市場即時性的統計量設計；同時建立起一套從 Hawkes 強度動態更新，到大漲、大跌與震盪的機率（後續將簡稱為三狀態機率）轉換，再到後續交易策略設計的完整分析流程。

Cryptocurrency markets are characterized by highly volatile price movements, in which jumps in one coin’s price not only affect its own market but also trigger jumps in other coins’ prices — a feature that traditional financial models struggle to fully capture. This study uses the hourly log returns of Bitcoin (BTC) and Ethereum (ETH) as the research sample, with the full year of 2023 serving as the training period and January 2024 through May 2026 serving as the forecasting period. A bidirectional cross-asset mutually-exciting Hawkes process is employed to model the data, ultimately yielding, for each time point, the probabilities of a surge, a crash, and oscillation, which serve as inputs for subsequent forecasting and trading strategy design. The forecasting period is divided into 109 non-overlapping segments, and the forecasting performance under three distributional assumptions is compared: in Model 1, all variables follow empirical distributions, while Models 2 and 3 each adopt conventional parametric distributions. This comparison is used to examine whether replacing conventional distributions with empirical distributions improves forecasting accuracy.
The empirical results show that the jump contagion effects between BTC and ETH exhibit clear asymmetry across surges and crashes (positive and negative jumps): surges (positive jumps) exhibit stronger mutual excitation, but their subsequent influence dissipates more quickly than that of crashes; crashes (negative jumps) exhibit relatively weaker excitation, but their influence persists for a comparatively longer duration. In terms of cross-asset contagion, the linkage between BTC surges and subsequent ETH surges is the most pronounced, suggesting that BTC plays a leading role in driving ETH to a certain extent. A comparison of the three models’ forecasting performance further shows that Model 1, which adopts empirical distributions, outperforms Models 2 and 3, which adopt conventional distributional assumptions, across classification metrics overall — indicating that not pre-specifying a distributional form better captures the characteristics of cryptocurrency market returns.
The contributions of this study are as follows: it proposes a modeling approach that replaces conventional distributional assumptions with empirical distributions, and adopts a statistic design that balances parameter stability with market responsiveness; it also establishes a complete analytical pipeline that proceeds from the dynamic updating of Hawkes intensities, to the conversion into surge, crash, and oscillation probabilities (hereafter referred to as the three-state probabilities), and finally to subsequent trading strategy design.

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