1) Think of at least three examples from economics where theory suggests that the variables involved are cointegrated. For one of these cases, explain how you would test for cointegration between the variables involved and how you could use this information to improve forecasting.
My three examples are, GDP vs CPI, JPY(Japanese Yen) vs TOPIX((Tokyo Stock Price Index) and JPY vs PPP. When I use JPY vs PPP, I will convert two variables to logarithm. After tnat I will check a stationarity and test the Dickey-Fuller test. Is it better to use the first difference of two variables?