0.31-1--- -1-1-

0.25

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0.3 r-0.25 -

0.2 -

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FIGURE 6.9 Sample autocorrelations for the USD-DEM and USD-JPY for the 5-min absolute returns of (a) USD-DEM absolute returns and (b) USD-JPY absolute returns from October I. 1992. through SeDtember 29. 1993.

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Lags (days)

Lags (days)

FIGURE 6.10 Sample autocorrelations for the wavelet filtered 5-min absolute returns of (a) USD-DEM and (b) USD-JPY from October I, 1992 through September 29, 1993. The dotted line is the autocorrelogram for the estimated hyperbolic decay rate for d = 0.40- that is, A:-20 where is the number of lags.

findings indicate that the wavelet method is more successful in filtering out intraday seasonalities relative to the method presented in Andersen and Bollerslev (1997a). The persistence of volatility in further lags is also much smaller in Gencay et al. (2001a) relative to the Andersen and Bollerslev (1997a). However, the seasonality filters of both Gencay et al. (2001a) and Andersen and Bollerslev (1997a) suffer from the fact that the decay of the volatility persistence is slow in the immediate lags relative to the method of Dacorogna et al. (1993).

REALIZED VOLATILITY DYNAMICS

7.1 introduction

High-frequency returns no longer exhibit the seasonal behavior of volatility when investigated in deseasonalized form. Therefore, well-known stylized facts start to be visible in the deseasonalized returns and the corresponding absolute returns. Deseasonalization can be achieved by taking returns regularly spaced in #-time. Absolute returns are just one form of realized volatility whose general definition is given by Equation 3.8.

Realized volatility has a considerable statistical error, which can be reduced by taking returns over short time intervals. This leads to a high number of observations within a given sample.1 Unfortunately, the choice of a small return interval also leads to a bias caused by microstructure effects. This bias is explained in Section 5.5.3 as a consequence of biased quoting, which leads to a bouncing effect of quotes within a range related to the bid-ask spread. In Section 5.5.3, the bias is treated as a component of the measurement error. In Section 7.2, we study the bias empirically and propose a simple bias correction method that applies to the bias caused by any microstructural effect, not only bid-ask bouncing. Bias-corrected realized volatility has a smaller error than the error attainable without correction.

Using overlapping returns is also helpful, as explained in Section 3.2.8.