Brooks 2002 Introductory Econometrics for Finance 计量经济学.pptVIP

‘Introductory Econometrics for Finance’ ? Chris Brooks 2002 * Cointegration Tests using Johansen: Three Examples Example 1: Hamilton(1994, pp.647 ) Does the PPP relationship hold for the US / Italian exchange rate - price system? ? A VAR was estimated with 12 lags on 189 observations. The Johansen test statistics were ? r ?max critical value 0 22.12 20.8 1 10.19 14.0 ? Conclusion: there is one cointegrating relationship. ‘Introductory Econometrics for Finance’ ? Chris Brooks 2002 * Example 2: Purchasing Power Parity (PPP) PPP states that the equilibrium exchange rate between 2 countries is equal to the ratio of relative prices A necessary and sufficient condition for PPP is that the log of the exchange rate between countries A and B, and the logs of the price levels in countries A and B be cointegrated with cointegrating vector [ 1 –1 1] . Chen (1995) uses monthly data for April 1973-December 1990 to test the PPP hypothesis using the Johansen approach. ‘Introductory Econometrics for Finance’ ? Chris Brooks 2002 * Cointegration Tests of PPP with European Data ‘Introductory Econometrics for Finance’ ? Chris Brooks 2002 * Example 3: Are International Bond Markets Cointegrated? Mills Mills (1991) ? If financial markets are cointegrated, this implies that they have a “common stochastic trend”. ? Data: Daily closing observations on redemption yields on government bonds for 4 bond markets: US, UK, West Germany, Japan. ? For cointegration, a necessary but not sufficient condition is that the yields are nonstationary. All 4 yields series are I(1).  ‘Introductory Econometrics for Finance’ ? Chris Brooks 2002 * Testing for Cointegration Between the Yields The Johansen procedure is used. There can be at most 3 linearly independent cointegrating vectors. ? Mills Mills use the trace test statistic: ? where ?i are the ordered eigenvalues. ? ? ? ? ? ? ? ? ? ?  ‘Introductory Econometrics for Finance’ ? Chris Brooks 2002 * Testing for Cointegr