202026 May
How to Interpret Cointegration Test Results | Aptech
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In particular, we will examine if there is a cointegrated, long-run relationship between the S&P 500 price index and monetary policy indicators of the M2 money stock and the bond yields. Our ADF test statistics again suggest that even when accounting for the structural break, we cannot reject the null hypothesis of a unit root for any of our time series data. We will choose our normalization to reflect our theoretical question of whether the S&P 500 index is cointegrated with the money stock and the bond yield. When we specify which model to use we impact two things: There are three options to choose from: For our example, we will include a constant and trend in our first-stage cointegration regression by setting: In the second-stage ADF residual unit root test, the error terms should be serially independent. For example, lets consider the last case, where the constant, coefficients, and trend are all impacted by the structural break: The procedure provides more extensive results than the test.

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