0.1 Proofs of Theorems 4.1, 4.2 & 5.2 Proof of Theorem 4.1: Let bn = pn+ln, where pn = b √ nc. Define a block of observations as Bn(i) = i + bn(0, 1], i ∈ Z. We first divide Rn into non-overlapped blocks of observations. Let Kn = {k ∈ Z : Bn(bnk) ⊂ Rn} represents the index set of all complete blocks Bn(bnk) = bn(k + (0, 1]) lying inside Rn. For each k ∈ Kn, we further divide each block into lar...