707.3. To adjust the infrequent trading bias introduced that is introduced into reported returns, we can "unsmooth" or "de-smooth" the reported returns. Ang suggests this is a filtering problem: "Filtering algorithms are normally used to separate signals from noise … standard filtering problems are designed to remove noise. The key difference is that unsmoothing adds noise back to the reported returns to uncover the true returns."²

The essence of unsmoothing of returns is illustrated by Ang's formulas 13.1, 13.2 and 13.4 below:

$$r_t^* = c + \phi r_{t-1}^* + \varepsilon_t \quad \text{(Ang 13.1)}$$ $$r_t = \frac{1}{1 - \phi} r_t^* - \frac{\phi}{1 - \phi} r_{t-1}^* \quad \text{(Ang 13.2)}$$ $$r_t^* = (1 - \phi) r_t + \phi r_{t-1}^* \quad \text{(Ang 13.4)}$$

In these formulas $r^*(t)$ is the reported (aka, observed) return and $r(t)$ is the true but unobserved return. Importantly, as is almost always the case in finance, the model used in this particular unsmoothing process makes key assumptions. However, if the assumptions are correct, then each of the following statements about the unsmoothing process is true EXCEPT which is false?