Problem
Generate a time series from an IID Gaussian random process. This is a memoryless, stationary series:
(a) Compute the ADF statistic on this series. What is the p-value?
(b) Compute the cumulative sum of the observations. This is a non-stationary series without memory.
(i) What is the order of integration of this cumulative series?
(ii) Compute the ADF statistic on this series. What is the p-value?
(c) Differentiate the series twice. What is the p-value of this over-differentiated series?