Variance ratio from autocorrelations

The first four sample autocorrelations of daily Nifty log returns (2007–2026, $T = 4{,}693$) are $0.037, -0.005, -0.025, -0.024$. (a) Use (2.7) to approximate $\widehat{VR}(5)$ and compare with the exact estimator value 1.021 reported in 2.3. (b) Compute the homoskedastic $z(5)$ from your approximation. (c) Explain why $z^*(5) = 0.32$ is smaller than $z(5)$, using Proposition 2.8(b) and the stylized facts.