IV. Empirical ResultsThe estimated

IV. Empirical Results
The estimated results of the P-GARCH model of spreads by using the estimated conditional P-GARCH variance of the exchange rates, ^ 2 Xt, are reported in Table 3. The Ljung–Box statistic, Q2(15), for up to 15th-order autocorrelation in the squared standardized residuals ^ "2 t=^ 2 t is less than 25, the critical value of a 215 distribution at the 5% significance level. This indicates that the estimated P-MA(1)-P-GARCH(1,1) model is sufficiently good to capture the dynamics of time-varying volatility. We also estimate the model by using the range between the highest and lowest ask rates of the exchange rates and the calculated variances of the exchange rates as proxies for exchange rate volatility. The results are quite similar and will not be reported in order to save space. The results are available upon request. The earlier studies of Brock and Kleidon (1992), Hsieh and Kleidon (1996) and Bollerslev and Domowitz (1993) have found a U-shaped pattern for the intraday spread. Jorda and Marcellino (2003) found two peaks in the Reuters FXFX Deutsche mark’s intraday spread. Danielsson and Payne (2002) found a U-shaped pattern of intraday Deutsche mark/dollar spreads in the European and North American trading times in the Reuters D2000-2 market. Ito and Hashimoto (2004) found that the width of the spread does not change much during all of the trading times, and later Ito and Hashimoto (2006) found a negative intraday correlation between the bid–ask spreads and the volatility of the JPY/ USD and USD/EUR spot exchange rates in the EBS electronic brokerage market.