應用貝氏統計方法於建立顧客消費行為預測之時間序列模型

Abstract

隨著顧客關係管理觀念的發展，如何從第一手的顧客資料庫之中萃取有用的資訊加以研究，並以此為基礎發展各項行銷策略，將是行銷人員如何化被動為主動的重要關鍵。由於資料庫技術的成熟，消費者每次的消費行為可被詳實地記錄並加以分析，因此本研究之目的即為試圖以時間序列研究方法分析消費者過去的消費紀錄，並在沒有外生變數介入的情形下，建立預測模型以求有效預測消費者未來可能的消費行為。 本研究分析的對象為國內某大行動電話電信業者之資料庫，隨機挑選一千名顧客樣本、為期三十四週之通話記錄，對消費者撥打各家電信業者金額佔總通話金額之比例進行分析與預測，研究模型除了採用自我迴歸整合移動平均(ARIMA)模型、向量自我迴歸(VAR)模型以外，並應用貝氏統計方法中不同的先驗分配：Minnesota先驗分配與Non-informative standard Jeffrey’s先驗分配，建立兩種不同的貝氏向量自我迴歸(BVAR)模型，對消費者未來的通話行為加以預測，最後並利用誤差均方根(RMSE)、平均誤差絕對值(MAE)、及平均誤差百分比值(MAPE)等指標比較各模型在樣本內以及樣本外之預測能力。 本研究發現，若綜合考量預測能力以及在實務應用上之可行性，採用Minnesota先驗分配的貝氏向量自我迴歸模型表現優於其他各模型，然因國內對於貝氏向量自我迴歸模型之相關研究仍少，故未來研究若能對模型內各適當參數進行微調設定，相信將可更進一步改善模型之預測能力。

With the development of the concept of customer relationship management, it is the key point on how marketers to regain the initiative and make research on the useful information derived from the first-hand customer database, and to serve it as a basis for the development of various marketing strategies. As the database techniques mature, every consumer’s consuming behavior may be recorded and analyzed elaborately. Therefore, the purpose of this study is to analyze the consumers’ previous consumption records, and try to establish time-series models to forecast the potential consuming behavior in the absence of exogenous variables involved. This research targets at the database of one of the leading domestic mobile telephone operators, randomly selects 1,000 customers’ sample and the phone records called for a period of 34 weeks, and analyzes and predicts the percentage of the total amount of calls the consumer phoned via different telecommunication operators. This research adopts the Autoregressive Moving Average Model (ARIMA) model and Vector Autoregressive Model (VAR) model. Besides, it also applies two kinds of prior distribution methods in Bayesian Analysis, which are Minnesota priori distribution and Non-informative standard Jeffrey's priori distribution, to establish different Bayesian Vector Autoregressive (BVAR) model. And finally, by using the Root Mean Square Error (RMSE), the Mean Absolute Error (MAE), and the Mean Absolute Percentage Error (MAPE), we compare the performance of different models inside or outside the samples. The study finds out that if integratively consider the predictive ability and the substantive feasibility, the Bayesian Vector Autoregressive Model using the Minnesota prior performs better than the other models. However, the domestic research on Bayesian Vector Autoregressive Models is comparatively lacking. Thus, if future studies can make the appropriate settings within the parameters of the model, we believe the predictive ability will be further improved.