以往有關於價量關係的文獻，大多數都只針對價格和交易量這兩個變數進行探 討，鮮少在探討價量關係時控制其他影響。此外，資產定價的研究一直以來都是學 術上的重點議題，各個學者致力於尋找出與資產價格有關的變數。因此，本文嘗試 收集這些已被證實與股票報酬有關的變數，接著結合機器學習的方式，來對這些變 數進行降維。 本文收集總共 46 個變數，其樣本期間為 2002 年 1 月到 2022年 12 月， 將該樣本期間區分為樣本內及樣本外，其中樣本內期間為2002 年 1 月至 2006 年 12月，而樣本外期間則為 2007 年 1 月至 2022 年 12 月。首先，我們藉由 不同的降維技術 (PCA、PLS和PQR) 來對變數進行降維，接著對報酬進行樣本外 預測，並且比較這三個模型的預測力。 最後，本文參考 Stock and Watson (2002) 的建議，將46 個變數進行分類接著 進行預測，結果顯示 PLS 在預測報酬時，其績效皆最優，PQR(0.5) 則次之，故最 後利用 PLS 和 PQR(0.5) 來對具有預測力的類別萃取因子。接著，將上述因子納 入到分量迴歸模型裡來觀察樣本外期間的價量關係，將迴歸結果與未控制因子的迴 歸結果進行比較，結果發現這些因子確實會影響價量關係。此外，我們也利用這些 因子來過濾報酬率，接著藉由 Granger 因果檢定來觀察過濾後的報酬率和交易量 之間的因果關係。

In the past, most of the literature on the price-volume relationship has focused on two variables, namely price and volume, and seldom controlled for other effects when investigating the price-volume relationship. In addition, the study of asset pricing has always been an important academic topic, and various scholars have tried to find out the variables related to asset prices. Therefore, this paper tries to collect these variables that have been proven to be related to stock returns, and then combine them with machine learning to reduct the dimension of these variables. We collect a total of 46 variables with a sample period from January 2002 to December 2022 and divide the sample period into in-sample and out-of-sample periods, where the in-sample period is from January 2002 to December 2006 and the out-of sample period is from January 2007 to December 2022. First, we reduct the dimension of these variables by supervised/unsupervised dimensionality reduction methods (PCA, PLS, and PQR), and then make out-of-sample predictions of stock returns and compare the predictability of the three models. Finally, this paper refers to the suggestion of Stock and Watson's (2002) to categorize the 46 variables and then make predictions for stock returns. The result shows that PLS has the best predictability in stock returns, while PQR(0.5) has the second best predictability. Therefore, we finally used PLS and PQR(0.5) to extract the factors for all categories. Next, the above factors are incorporated into the quantile regression model to observe the price-volume relationship during the out-of-sample period, and the regression results are compared to those without controlling for any factors, the result shows that these factors affect the price-volume relationship. In addition, we also use these factors to filter stock returns, and then observe the causality between the filtered returns and the trading volume via Granger causality test.

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