Exercise 4 :   Cointegration Test

et+1 = st+1 - 0.0658 - 0.9766 ft
wt+1 = st+1 - ft

DF-t(st) DF-t(Dst) DF-t(ft) DF-t(Dft) DF-t(et) DF-t(wt)   Q(12)  
-1.6425 -12.7511* -1.6163 -12.4778* -12.1583* -12.3265* 8.92
             

*(**) Meaningful at the 1% (5%) level.
Monthly data for the period January 1979 to January 1994.
Currency: French Franc

where et+1 is the residual of the cointegration equation, wt+1 is the forecasting error, and DF-t(...) is the Dickey-Fuller-t statistic

The table presents the results of the unit-root and cointegration tests. The first four columns present the results of the unit-root tests, specifically the DF-t statistics applied on the exchange rates. The fourth column presents the cointegration test, specifically the DF-t statistic applied on the residual of the cointegrating equation. The last two columns present an indirect test of efficiency (which suppose that the forward exchange rate is an unbiased predictor of the future exchange rate), DF-t and Q(12) Ljung-Box statistics applied on the forecasting errors, wt.

  1. Forward exchange rate is stationary
    yes          no
  2. We reject the null hypothesis of two unit roots for the spot exchange rate
    yes          no
  3. Cointegration hypothesis is not rejected
    yes          no
  4. DF-t(wt) indicates that forecasting errors are stationary
    yes          no
  5. Alternative test indicates that the market is efficient
    yes          no

 
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