Problem
Generate a time series that follows a sinusoidal function. This is a stationary series with memory.
(a) Compute the ADF statistic on this series. What is the p-value?
(b) Shift every observation by the same positive value. Compute the cumulative sum of the observations. This is a non-stationary series with memory.
(i) Compute the ADF statistic on this series. What is the p-value?
(ii) Apply an expanding window fracdiff, with τ = 1E - 2. For what minimum d value do you get a p-value below 5%?
(iii) Apply FFD, with τ = 1E - 5. For what minimum d value do you get a p-value below 5%?