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 a joint inference on integrated volatility (IV), noise moments and price-noise relations. In the iid noise case we derive the asymptotic variance of the regression parameter estimating the IV, show that it is consistent and compare its asymptotic efficiency against alternative consistent IV measures. In case of noise which is correlated with the efficient return process, we postulate a new “asymptotically increasing” type of dependence and analyze its ability to cope with the empirically observed price-noise dependence in quote data. In the empirical section of the paper we apply the LS methodology to estimate the integrated volatility as well as the noise properties of 25 liquid stocks both with midquote and transaction price data. We find that while iid noise is an oversimplification, its non-iid characteristics have a decidedly negligible effect on volatility estimation within our framework, for which we provide a sound theoretical reason. In terms of noise-price endogeneity, we are not able o find empirical support for simple ad hoc theoretical models and we provide an alternative explanation for the observed patterns in midquote data, based on market microstructure theory.