has the three features that we identified earlier as desirable properties of a covariance matrix estimator: 1.    It uses high-frequency data (daily) to estimate volatilities and covariances over a longer horizon (monthly). 2.    It accommodates a correction for the existence of serial correlation in high-frequency data. 3.    It accommodates a weighting scheme that assigns a larger weight to recent observations. The estimator that we have developed is very general. In fact, the interested reader can verify that simple estimators that assume that daily returns are iid (and therefore do not adjust for correlation in daily data, and do assign equal weight to all observations) can be obtained as a special case from (16.6) by setting q = 0 and all the elements in w equal to 1. COVARIANCE MATRIX ESTIMATION: PRACTICE So far we have identified some important regularities of financial data and provided a theoretical framework to take those regularities into account when building a risk model. In this section, we discuss how to approach the problem of covariance matrix estimation in practice. Assuming that the researcher has access to a complete set of daily returns for a sufficiently long period,9 there are at least two parameters that must be estimated to produce a covariance matrix: the order of serial correlation (q in our notation) and the decay parameter for the weighting scheme (5 in our notation). As mentioned earlier, a thorough analysis of the correlation structure of the data is probably the best way to identify the appropriate value of q. However, a discussion of the time-series methodologies that accomplish this task is beyond the scope of this chapter and the interested reader should refer to a more specialized treatment of this topic.10 Here, we want to focus on the intuition behind the choice of q. How are the serial correlation components going to affect the estimated volatility? To get an insight, let us look at a special case of equation (16.2') in which the variance of the returns on asset i is estimated assuming q = 1: var[r,(m)] = p.var[r,.i(i)]+2(p-l).cov[r,.i+1("i),r,.;(i)] (16.7) 9A scenario in which a shorter history is available for some of the data is an important one. For this reason, we dedicate an entire section to that problem later in this chapter. 10See, for example, Hamilton (1994).