Hello  this is more of a conceptual question. I'm whether a linear relationship exists between two time series: shortterm interest rate differential of U.S. and U.K. and the GBP/USD exchange rate where observations are taken on a daily frequency since 2015.
I ran DickeyFuller test on both and find both series to be nonstationary, which indicates that as a framework a linear regression model may not be useful (here shortterm rates are the independent variable and GBP/USD is the dependent variable) . However, if the two series are nonstationary and cointegrated then the residuals from a linear regression model will be stationary and hence the linear regression model could be useful. However, when I test for cointegration using Johansen's test I find no cointegration equation between the two series (the output results are below using XLSTAT), which undermines the case for a linear regression I presume.
I'm not sure what to make of this result as it's hard to believe that differentials in shortterm interest rates between U.S. and U.K. and the respective exchange rate aren't cointegrated. What am I missing here?
Results from Johansen's test at 5% significance level (the variable 'Actual' is the GBP/USD exchange rate and SHORT_RATES is the variable capturing the differential in shortterm interest rates):
I ran DickeyFuller test on both and find both series to be nonstationary, which indicates that as a framework a linear regression model may not be useful (here shortterm rates are the independent variable and GBP/USD is the dependent variable) . However, if the two series are nonstationary and cointegrated then the residuals from a linear regression model will be stationary and hence the linear regression model could be useful. However, when I test for cointegration using Johansen's test I find no cointegration equation between the two series (the output results are below using XLSTAT), which undermines the case for a linear regression I presume.
I'm not sure what to make of this result as it's hard to believe that differentials in shortterm interest rates between U.S. and U.K. and the respective exchange rate aren't cointegrated. What am I missing here?
Results from Johansen's test at 5% significance level (the variable 'Actual' is the GBP/USD exchange rate and SHORT_RATES is the variable capturing the differential in shortterm interest rates):
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