Least Squares Inference on Integrated Volatility and the Relationship Between Efficient Prices and Noise

The expected value of sums of squared intraday returns (realized variance) gives rise to a least squares regression which adapts itself to the assumptions of the noise process and allows for joint inference on integrated variance (<inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="ubes_a_637876_o_ilm0001.gif"/>), noise moments, and price-noise relations. In the iid noise case, we derive the asymptotic variance of the <inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="ubes_a_637876_o_ilm0002.gif"/> and noise variance estimators and show that they are consistent. The joint estimation approach is particularly attractive as it reveals important characteristics of the noise process which can be related to liquidity and market efficiency. The analysis of dependence between the price and noise processes provides an often missing link to market microstructure theory. We find substantial differences in the noise characteristics of trade and quote data arising from the effect of distinct market microstructure frictions. This article has supplementary material online.