Comment

The authors are to be congratulated for an excellent contribution, from both a theoretical and an applied standpoint, to the problem of measuring integrated variance in the presence of microstructure noise, an inescapable reality. The negative effects of microstructure noise on measuring volatility have been well known for years. For instance, French, Schwert, and Stambaugh (1987) incorporated the cross-product of consecutive days to take into account the first-order autocorrelation of daily returns caused by nonsynchronous trading of securities. Note that the estimator proposed by French et al. (1987) coincides with the one proposed by Zhou (1996) and analyzed by Hansen and Lunde (HL). Of course, we know from the current literature (e.g., Zhang, Mykland, and Aït-Sahalia 2004; Bandi and Russell 2005a; Hansen and Lunde 2005a,b, 2006) that microstructure noise plays a crucial role in measuring daily integrated variance, but less so in measuring monthly integrated variance. This gives a theoretical foundation to the work of French et al. (1987), who found that the correction is not that important quantitatively. Microstructure noise was also a well-known problem at the inception of the current literature. Fifteen years ago, Daniel Nelson (1958–1995) was among the pioneers who established the theoretical foundations for measuring instantaneous variance from high-frequency data. Bollerslev and Rossi (1995) reviewed his numerous contributions, particularly that on measuring, filtering, and forecasting variance. Daniel Nelson’s research agenda, combined with the availability of highfrequency data (provided by, most notably, the Olsen group), lead several authors, particularly Torben Andersen and Tim Bollerslev, to explore empirically the issue of nonparametric measurement of instantaneous variance. They obviously ran into the problem of microstructure effects, especially the intraday periodicity (see, e.g., Andersen and Bollerslev 1997). At the same time, another research strand was developed under the leadership of Robert Engle with the goal of extracting the information on volatility contained in the durations between consecutive trades (see, e.g., Engle 2000). Closer to the current literature, an important breakthrough can be attributed to Andersen and Bollerslev (1998), as well as Barndorff-Nielsen and Shephard (2001). For instance, Andersen and Bollerslev (1998) clearly showed the importance of measuring daily integrated variance by summing squared intradaily returns. Moving from measuring instantaneous variance to integrated variance was theoretically successful due to the availability of a central limit theorem (Jacod and Protter 1998; Barndorff-Nielsen and Shephard 2002). This move was also empirically successful because intraday periodicity plays a less important role. Moving from instantaneous to integrated variance is indeed a temporal aggregation issue, and it is well known from the macroeconometric literature that aggregating helps solve the seasonality problem. The empirical success of this approach was clearly demonstrated by Andersen, Bollerslev, Diebold, and Labys (2001, 2003). We finish this section with some historical notes. Andersen and Bollerslev (1997) gave a presentation at the World Congress of the Econometric Society in Tokyo (1995). At the same congress, Éric Renault gave an invited lecture on financial econometrics and ended his talk by saying that the financial econometrics lecture at the next World Congress should focus on the problems related to microstructure effects (see Renault 1997). In fact, it took 10 years to have lectures on the topic, by Yacine Aït-Sahalia and Neil Shephard, at the last World Congress in London. Engle (2000) gave the Fisher–Schultz invited lecture of the European meeting of the Econometric Society in Istanbul in 1996. Also note that at the end of Aït-Sahalia and Shephard’s talks, Engle made the comment that the iid assumption of noise clearly is not empirically supported by the data, because durations (i.e., the time between two consecutive trades) contain information on volatility. The rest of this comment is organized as follows. Section 2 discusses several issues about statistical inference when one faces microstructure noise. Section 3 studies the time series properties of the realized variance under the presence of microstructure noise. The last section discusses the economic importance of accounting and correcting for microstructure noise and identifies the questions for which it may be relevant to do so.