Multiscale Inference for High-Frequency Data

This paper proposes a novel multiscale estimator for the integrated volatility of an It\^o process with harmonizable increments, in the presence of market microstructure noise. The multiscale structure is modelled frequency-by frequency and the concept of the multiscale ratio is introduced to quantify the bias in the quadratic variation due to the microstructure noise process. The multiscale ratio is estimated from a single sample path, and a frequency-by-frequency bias correction procedure is proposed. The new method is implemented to estimate the integrated volatility for the Heston model, and the improved performance of our method is illustrated by simulation studies.