台灣外匯市場投機性泡沫研究－卡爾曼濾波器之應用

金融市場中投機性泡沫的存在長久以來一直是爭論的話題，許多經濟學者相信人們在理性預期和理性行為的假設下，資產應該依據市場基要來定價。所以當某一資產價格偏離了市場基要時，常會被解釋為不合理且非理性。依據過去傳統文獻對於泡沫(bubbles)的定義為資產價格偏離市場基要(market fundamentals)的部份，如Meese(1986)，Woo(1987)，West(1987)，Wu(1995)等。但事實上，這部分的偏離是我們所無法觀察到的變數。因此，本文想藉以狀態空間模型(state space model)為基礎，運用卡門濾波器(Kalman Filter)的遞迴運算來估計不可觀察(unobservable)的變數（泡沫），以觀察外匯市場是否因為泡沫現象造成資產價格偏離市場基要價值。所使用的方法不但能夠檢定泡沫現象存在與否，且能夠針對每一時期的泡沫來估計其參數，不同於以往的共整合檢定，提供了直接量化的數據，藉以了解實質匯率與市場資產基本面之間的差距。本研究區分樣本期間為日圓自1970年1月至2004年3月；英鎊自1982年7至2004年4月；德國則自1970年1月至1998年12月。檢定日圓／美元、英鎊／美元和馬克／美元三組匯率間是否存在泡沫現象。經由實證結果得知：無論日圓對美元、英鎊對美元或馬克對美元匯率間，在這段期間的確存在泡沫現象且造成資產價格偏離市場基要。

關鍵字

狀態空間模型；卡爾曼濾波器；泡沫；匯率

並列摘要

The existence of speculative bubbles in financial markets has been a longstanding issue under debate. Many economists believe that given the assumption of rational expectations and rational behavior of economic agents, an asset should be priced according to its 'market fundamentals'. So deviations of an asset's price from the value dictated by its market fundamentals are often interpreted as evidence of irrationality. Bubbles, means the deviations of an asset’s price from the value of its market fundamentals according to the past in traditional literature. Serious testing of this issue began with the work of Meese (1986), Woo(1987), West(1987), Wu(1995), etc. But these part of deviations were variables we can not observe. Thus, In these paper, We use state-space analysis employing the Kalman filter to estimate models that specify rational speculative bubbles as an unobserved component to test for the presence of bubbles in at least some exchange markets. The method different from integration test could not only test for the presence of bubble, but also estimate the parameter for each date of bubble. We differentiate the samples for three periods in my paper, Japanese Yen from January 1970 to March 2004, British Pound from July 1982 to April 2004 and Deutsche mark from January 1970 to December 1998. By testing for stochastic bubbles for exchange rate between the Japanese Yen and U.S Dollar, the British Pound and U.S Dollar, Deutsche mark and U.S Dollar, we find a significant evidence showing that there exist bubbles in Taiwan foreign exchange market.