Let \(P_{t}\) be the observed market price of an asset, which is related to the fundamental value of the asset \(P_{t}^{*}\) via Eq. (5.9). Assume that \(\Delta P_{t}^{*}=P_{t}^{*}-P_{t-1}^{*}\) forms a Gaussian white noise series with mean zero and variance 1.0. Suppose that the bid-ask spread is two ticks. What is the lag-1 autocorrelation of the price change series \(\Delta P_{t}=P_{t}-P_{t-1}\) when the tick size is \(\$ 1 / 8\) ? What is the lag-1 autocorrelation of the price change when the tick size is \(\$ 1 / 16\) ?