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- + O(K−1 n ), with a diagonalized version ˜ Ik of Ik. Along the same lines as in the proof of Corollary 4.3 in Bibinger et al. (2014), we derive that COV vec Σ̂or s = (2 + O(1)) bsh−1 n c+Kn X k=bsh−1 n c−Kn (2Kn + 1)−2 × Σkhn ⊗ Σkhn H 1/2 + Σkhn H 1/2 ⊗ Σkhn
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- The two-factor model introduced by Chernov et al. (2003) allows for more pronounced movements in the instantaneous volatility by a feedback mechanism. The corresponding parameterization is Ã̃t = s–exp(β0 + β1v1,t + β2v2,t), (41) dv1,t = α1v1,tdt+dW1,t, dv2,t = α2v2,tdt + (1 + βvv2,t) dW2,t, s–exp(u) = ( exp(u) if u ≤ u0 exp(u0) p 1 − u0 + u2/u0 else, where W1,t and W2,t are standard Brownian motions with Corr(dW1,t, dBt) = ÃÂ1 and Corr(dW2,t, dBt) = ÃÂ2. We consider the configuration β0 = −1.2, β1 = 0.04, β2 = 1.5, α1 = −0.137e−2, α2 = −1.386, βv = 0.25, ÃÂ1 = ÃÂ2 = −0.3 and u0 = ln (1.5). C Tables and Figures
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ZU, Y. AND P. H. BOSWIJK (2014): “Estimating Spot Volatility with High-Frequency Financial Data,†Journal of Econometrics, forthcoming. A Proofs A.1 Preliminaries Consider the process X̃t = Z t Ãbsh−1 n chn dBs , (25) without drift and with block-wise constant volatility as a simplified approximation of X. In the following, we distinguish between the estimator of the spot covariance matrix (12) based on oracle optimal weights (13), Σ̂or s , and the adaptive estimator Σ̂s. Furthermore, we write Σ̂s(X̃ + ) for the estimator built from observations in the simplified model in which X̃ is observed in noise and denote the associated spectral statistics by: S̃jk = Àjh−1 n np X i=1 X̃ (p) t (p) i + (p) i − X̃ (p) t (p) i−1 − (p) i−1 !