未來展望

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表 24 展示所有策略的績效表現，分別以最大策略虧損報酬以及樣本外獲利 作為主要衡量策略品質的因子。在作圖方式的部分，GASF 似乎效果較好，表示 時間序列的前後關係有重要資訊。雖然在較短的時間刻度上(10 分 k、15 分 k)策 略績效並不理想，但原因不是 CNN 模型在短時間的分類能力較長時間不佳，而 是在考慮交易手續費後拖累整個策略績效。

第二節 未來展望

本研究嘗試將深度學習引進金融交易領域，對於未來的研究，建議可以往以 下幾個方向發展：

1. 本篇所用的時間序列資訊僅只有台指期貨指數之價格，在辨識下跌的召 回率(recall)普遍偏低，若能取得交易過程中上下五檔掛單的資料，應能 降低 CNN 模型在辨識漲跌的難度，因為上下五檔的掛單資料傳遞的資 訊直接是此商品的供給與需求。

2. 大部分深度學習技術之目標函數設計是以精確度(Accuracy)做參數優化，

然而金融交易性質與一般圖片的分類問題有蠻大的差異。在交易中勝率 可以不高但賺賠比達一定水準也同樣是有獲利能力的。若能以本篇的最 大策略虧損報酬或是夏普值作為優化目標也許會有更好的結果。

3. 本研究所使用的 CNN 架構為 CNN 家族裡最基礎的 LeNet 架構，隨著技 術不斷進步，更複雜的卷積神經網路架構還有 AlexNet、VGG、GoogleNet 以及 ResNet，也許使用較先進的架構來訓練會得到更好的效果。

4. 除了價格資訊外，金融市場還有許多因素會影響價格走勢，若模型能容 納更多方面的資訊，如公司財報資料、總經數據、市場新聞等等，進而 建構一個多樣化投資組合，應能獲得更穩定的超額報酬。

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附錄

以下以兩層類神經網路，四個神經元舉例。如圖五所示，說明反向傳播演算法，激勵函數以 sigmoid 函數為例。

圖 56 兩層類神經網路、四個神經元 (1) 前向傳播

x, y 和 b(bias)=1 傳入第一層神經元𝑛₁₁和𝑛₁₂：

𝑛₁₁^(𝑖𝑛) = 𝑤_11,𝑥𝑥 + 𝑤_11,𝑦𝑦 + 𝑤_11,𝑏 (23)

𝑛₁₁^(𝑖𝑛) = 𝑤_12,𝑥𝑥 + 𝑤_12,𝑦𝑦 + 𝑤_12,𝑏 (24)

𝑛₁₁^{(𝑜𝑢𝑡)} = 1

1 + 𝑒^{−𝑛11(𝑖𝑛)} (25) 𝑛₁₂^{(𝑜𝑢𝑡)} = 1

1 + 𝑒^{−𝑛12(𝑖𝑛)} (26)

其中，𝑛₁₁^(𝑖𝑛)代表傳入神經元𝑛₁₁的值，而𝑛₁₁^{(𝑜𝑢𝑡)}表示傳出神經元𝑛₁₁的值，𝑤_11,𝑥表示值從𝑥傳入神經元 𝑛₁₁時所乘上的權重，𝑤_11,𝑦同理。

4 http://cpmarkchang.logdown.com/posts/277349-neural-network-backward-propagation

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接著使用鏈法則(chain rule)

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𝜕𝐽

𝜕𝑤_11,𝑦 = 𝛿₁₁^(𝑖𝑛)𝑦 (56)

𝜕𝐽

𝜕𝑤_11,𝑏 = 𝛿₂₁^(𝑖𝑛) (57)

𝛿₂₁^(𝑖𝑛)可用後層傳回來的𝛿₁₁^(𝑖𝑛)和𝛿₂₂^(𝑖𝑛)表示，如下：

𝛿₁₁^{(𝑜𝑢𝑡)} = 𝑤_21,11𝛿₂₁^(𝑖𝑛)+ 𝑤_22,11𝛿₂₂^(𝑖𝑛) (58)

𝛿₁₁^(𝑖𝑛) = 𝛿₁₁^{(𝑜𝑢𝑡)}𝑛₁₁^{(𝑜𝑢𝑡)}(1 − 𝑛₁₁^{(𝑜𝑢𝑡)}) = 𝛿₁₁^{(𝑜𝑢𝑡)}𝜕𝑛₁₁^{(𝑜𝑢𝑡)}

𝜕𝑛₁₁^(𝑖𝑛)

(59) 這些δ的物理意義一樣可由下圖表示：

圖 58 反向傳播

從圖 58 中可以看到𝛿₁₁^{(𝑜𝑢𝑡)}是由𝛿₂₁^(𝑖𝑛)和𝛿₂₂^(𝑖𝑛)往反方向傳遞，再乘上其權重𝑤_21,11和𝑤_22,11所得出的。接著

可將𝛿₁₁^{(𝑜𝑢𝑡)}替換到梯度下降法公式中(44)、(45)、(46)，結果如下：

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𝑤_11,𝑥 ← 𝑤_11,𝑥− 𝛼𝛿₁₁^(𝑖𝑛)𝑥 (60)

𝑤_11,𝑦← 𝑤_11,𝑦− 𝛼𝛿₁₁^(𝑖𝑛)𝑦 (61)

𝑤_11,𝑏 ← 𝑤_11,𝑏− 𝛼𝛿₁₁^(𝑖𝑛) (62) 同理，𝑤_12,𝑥、𝑤_12,𝑦和𝑤_12,𝑏的梯度下降公式也可以用相同的方法推導出來：

𝑤_12,𝑥 ← 𝑤_12,𝑥− 𝛼𝛿₁₂^(𝑖𝑛)𝑥 (63)

𝑤_12,𝑦← 𝑤_12,𝑦− 𝛼𝛿₁₂^(𝑖𝑛)𝑦 (64)

𝑤_12,𝑏 ← 𝑤_12,𝑏− 𝛼𝛿₁₂^(𝑖𝑛) (65)

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