利用小波轉換分析美國總體指標與道瓊工業指數之關係

THE RELATIONSHIP BETWEEN MACROECONOMIC INDICATORS AND DJIA INDEX: A WAVELET TRANSFORM ANALYSIS

本文利用小波轉換（wavelet transform）的分析方法，將股價與總體指標拆解成「趨勢走向」與「波動情形」兩項；再輔以多重解析度（multi-resolution）的概念，計算資料在各次頻帶（sub-band）的相關係數，以探討股價與各項總體指標在趨勢項與波動項的相關性。研究結果顯示，在所有觀察尺度下，股價趨勢項與六個總體指標的趨勢項有顯著且持續的相關性，即：出口年增率（EXYR）、消費者物價指數（CPI）、耐久財訂單（DUOR）、M1年增率（M1YR）、非農就業人數（NFE）和個人儲蓄率（PSR）；而股價波動項則與消費者信心指數（CCI）和個人消費支出（PCE）這兩項總體指標的波動項顯著相關。最後，根據實證結果選取相關的總體指標與股價進行驗證，藉此做為實證結果可信度的再驗證，進而提供投資者更正確的選擇。

The goal of this paper is to investigate the relationship between the macro-economic indices and the stock index by using wavelet transform. According to wavelet analysis, the Dow Jones Industrial Index and the macroeconomics indicators are first decomposed into “trend components” (scaling coefficients) and “volatility components” (wavelet compo-nent). Then, with the concept of multi-resolution representation, we evaluate the correla-tion coefficients between each sub-band of the stock price and the macro-economic indices. Consequently, the connection between the “trend-components/volatility-components” of stock price and macro-economic indices could be discussed and thus revealed. Based on our results, the “trend component” of the Dow Jones Index has significant relations to those of the following six indices: EXYR (Export Annual Growth Rate), CPI (Consumer Price Index), DUOR (Durable Goods Orders), M1YR (M1 Annual Growth Rate), NFE (Non-Farm Employment) and PSR (Personal Savings Rate). Meanwhile, the “volatility component” of the Dow Jones Index is connected to those of the CCI (Consumer Confidence Index) and PCE (Personal Consumption Expenditure). Finally, we use recent Dow Jones Industrial Index and macroeconomics indicators data to carry out the ex-ante analysis and get the same results. This confirms the efficacy of our analysis.