Intraday exchange rate volatility: ARCH, news and seasonality effects

The Quarterly Review of Economics and Finance 47 (2007) 135–158

Intraday exchange rate volatility: ARCH, news and seasonality effects Yin-Feng Gau ∗ , Mingshu Hua Department of International Business Studies, National Chi Nan University, 1 University Rd., Puli, Nantou 545, Taiwan Received 28 October 2003; received in revised form 12 April 2005; accepted 19 April 2005 Available online 18 December 2006

Abstract This paper examines how the calendar seasonality in terms of intraday New Taiwan dollar/U.S. dollar (NTD/USD) exchange rate volatility is impacted by public news arrivals and the unexpected volume shocks. Incorporating counts of Taiwan and the U.S news releases, unexpected volume of trading, and explicit time-of-day seasonality into the framework of GARCH model, we find that the pronounced periodicity of intraday volatility can be partly captured by the augmented model, whereas the spikes of volatility at the market closing and at the opening of the afternoon trading session are not successfully explained by time-of-day factors, public news, unexpected volume of trading, and lagged squared return innovations. © 2006 Board of Trustees of the University of Illinois. All rights reserved. JEL classification: F31; G14 Keywords: GARCH; Intraday volatility; Public news arrivals; Trading volume

1. Introduction The market volatility is related to information releases (Ross, 1989). The use of high-frequency intraday data allows us to examine the link between the variation of intraday volatility and information arrivals during a day. However, to interpret the impact of intraday information arrivals on the volatility, we have to adjust for intraday volatility seasonality to avoid compounded results. The seasonality of volatility has been found in intradaily and intraweekly returns in the foreign exchange (FX) markets, stock markets, and other exchange traded instruments. A typically U∗

Corresponding author. Tel.: +886 49 2910960x4921; fax: +886 49 2912595. E-mail address: [email protected] (Y.-F. Gau).

1062-9769/$ – see front matter © 2006 Board of Trustees of the University of Illinois. All rights reserved. doi:10.1016/j.qref.2005.04.004

136

Y.-F. Gau, M. Hua / The Quarterly Review of Economics and Finance 47 (2007) 135–158

shaped pattern is often observed in intraday volatility,1 even a doubly U-shaped pattern is found in exchanges where the daily trading schemes are interrupted by a lunch break (e.g., Andersen, Bollerslev, and Cai, 2000; Gau, 2005; Gau & Hua, 2004; Ito & Lin, 1992; Tang & Lui, 2002). The substantial periodic clustering variation in intraday returns is often explained by the arrival of information. Mitchell and Mulherin (1994) apply daily counts of news reported by Dow Jones on the Broadtape to investigate the link between news arrivals and stock prices. Their results indicate a significant relation between information arrivals and trading volumes, but only a weak link between news counts and stock returns. Berry and Howe (1994) employ the numbers of news headlines crossing the Reuters news screen as the proxy of information arrivals and find a positive relation between news arrivals and trading volume but an insignificant relation with stock return volatility. Moreover, they find that public information arrives seasonally, and it exhibits a distinctively inverted U-shaped pattern across trading days. Low and Muthuswamy (1996), Melvin and Yin (2000), and Chang and Taylor (2003) use the numbers of news reported in Reuters News pages as the information proxy and discuss the link between public information arrivals and exchange rate volatility. As argued in Andersen and Bollerslev (1998), Ederington and Lee (2001) also point out the inappropriate use of the traditional ARCH-GARCH (i.e., Autoregressive Conditional Heteroskedastic and Generalized Autoregressive Conditional Heteroskedastic; see Bollerslev, 1986; Engle, 1982) models for estimating the intraday periodicity and persistence in the volatility of high-frequency returns. Ederington and Lee (2001) observe that the typically U-shaped pattern of intraday volatility completely disappears after controlling for effects of scheduled macroeconomic announcements. By contrast, Andersen and Bollerslev (1998) and Han, Kling, and Sell (1999) find that public news arrivals cannot explain the intraday periodicity fully, implying that there are some other important factors that affect the periodicity of intraday volatility. On the other hand, the dealers’ liquidity demand and private information could influence the exchange rate volatility as well. As discussed in Flood (1994) and Lyons (1995, 1996, 2001), the hot-potato hypothesis or inventory-control hypothesis implies that dealers in the FX market tend to pass undesired positions along to another, thus giving rise to temporary misallocations of currency inventories. Moreover, as argued in Lyons (2001), order flow is an ideal variable to measure dealers’ belief or uncommon-knowledge information. However, due to the unavailability of inventory and order flow data for the New Taiwan dollar/U.S. dollar (NTD/USD) exchange rate, we utilize the unexpected volume of trading as a proxy variable that corresponds to the combined effects of inventory adjustments and uncommon-knowledge information. As new information flows into the market, the expected volume changes in response to common-knowledge information and the unexpected volume reflects the disagreement or uncommon-knowledge information among dealers. If the dealers adjust trading volumes just for inventory control, the trading volume will change even when no new information flows into the FX market and the expected volume remains unchanged. The discrepancy between the actual volume and expected volume of trading therefore can work as a proxy variable for the combined effects of inventory control and private information. However, to handle the intraday seasonality in high-frequency return volatility, some researchers deseasonalize or filter out the seasonality in the data before analyzing the time-varying and persistent intraday volatility. This two-stage approach is taken by, for example, Andersen and

1 For example, Baillie and Bollerslev (1991), Harvey and Huang (1991), Dacorogna, Muller, Nagler, Olsen, and Pictet (1993), Cornett, Schwarz, and Szakmary (1995), Bollerslev and Ghysels (1996), and Andersen and Bollerslev (1998).

Y.-F. Gau, M. Hua / The Quarterly Review of Economics and Finance 47 (2007) 135–158

137

Bollerslev (1998) (with the flexible Fourier transformation), and Taylor and Xu (1997) (with the set of multiplicative factors). The other approach is a one-stage procedure that incorporates the periodicity and volatility persistence at the same time. For example, Ederington and Lee (2001) employ dummy variables indicating announcements and time-of-day within the GARCH framework. Bollerslev and Ghysels (1996), Gau and Hua (2004) and Gau (2005) use the periodic GARCH model to capture the repetitive seasonal variations in the volatility by allowing state-dependent ARCH coefficients in the equation of conditional variance. In this paper, we examine the seasonality in the volatility of intraday NTD/USD exchange rate and study factors that influence for the periodicity in terms of intraday volatility. Different from the two-stage approach that uses deseasonalized return to study the impact of news arrivals, as in Melvin and Yin (2000) and Chang and Taylor (2003), we apply a one-stage approach that incorporates the ARCH, news effects, unexpected volume innovations, and time-of-day seasonality simultaneously, as in Ederington and Lee (2001). However, Ederington and Lee only discuss the effect of scheduled announcements releases on the intraday volatility of foreign exchange rate, ignoring the influences of inventory control and uncommon-knowledge information on the intraday volatility. In this paper, we consider both effects of public information and unexpected volume that is linked to inventory control and non-public information, allowing for seasonality and autocorrelation in the intraday volatility. To capture the seasonal and time-varying intraday volatility, we estimate 15-min NTD/USD exchange rate volatility within the framework of the GARCH model.2 Different from the finding of Ederington and Lee (2001) that the U-shaped patterns completely disappear after controlling for the scheduled announcement effects, we find that the arrivals of public information and unexpected volume of trading can only explain for the increased volatility at the market opening, but not for the spike of volatility at the market closing. This suggests another possible factors other than macroeconomic news announcements, uncommon-knowledge information and inventory control reflected in the unexpected volume of trading. A possible source attributing to the intraday variation of exchange rate is the intervention from the central bank. Chang and Taylor (1998) and Dominguez (1998, 2003) show that interventions from central banks generally increase the exchange rate volatility. Nevertheless, the central bank in Taiwan does not reveal any data about the FX intervention. The only available information is the news reports on the next day after the central bank explicitly bought or sold USD in the Taipei FX market. To investigate the impacts of central bank intervention operations on the daily volatility of the NTD/USD exchange rate, we calculate the realized volatility by the sum of 15-min deseasonalized squared-changes (Andersen, Bollerslev, Diebold, & Labys, 2003). The estimation results, based on the binary indicator variable of the central bank intervention operations reported in the newspapers, show that the central bank intervention has a positive and significant effect on the daily NTD/USD realized volatility. The remainder of this paper is organized as follows. Section 2 introduces the trading of the Taipei FX market and documents the intraday periodicity in absolute changes and trading volumes of NTD/USD. Section 3 presents specifications of the GARCH model that simultaneously consider 2 Actually, we have tried to estimate a periodic GARCH model with the explanatory variable of unexpected volume and dummy variables of announcements in another earlier study. However, the estimation results are sensitive to the number of periodic states and the choice of state numbers is not testable. Besides, the periodic cycle in the data studied in this paper is regular (at length of 20 periods). Therefore, we employ the simpler dummy-variable approach and use time-of-day dummy variables to identify the periodic variation across all 15-min intervals in this paper, as the way used in Ederington and Lee (2001).

138

Y.-F. Gau, M. Hua / The Quarterly Review of Economics and Finance 47 (2007) 135–158

explicit time-of-day factors, numbers of news headlines related to Taiwan and the U.S. reported on the Bloomberg Headline News screen, and unexpected volume of trading. Section 4 explains the estimation results and explores to what extent the periodicity in the intraday NTD/USD volatility is captured by the model proposed in this paper. Section 5 concludes. 2. The data and seasonality The data of actual intraday transaction prices and trading volume on the spot NTD/USD exchange rate every 15 min, covering the period from January 4, 2001 to December 31, 2001, are obtained from the Taipei Foreign Exchange Brokerage Inc., the larger of two brokerage firms at the Taipei FX market. During the period studied in this paper, the Taipei FX market opens from 9:00 to 16:00 h Taipei time, with a lunch break from 12:00 to 14:00 h, from Mondays to Fridays. The NTD/USD prices and volumes data also appear on the screens of Reuters, Telerate, and Bloomberg real-time quotation systems.3 The trading volume at the Taipei Foreign Exchange Brokerage Inc. accounts for about 70% of the total trade in the Taipei interbank FX market. Let Pt,k and Vt,k denote the spot exchange rate and trading volume of NTD/USD, respectively, for the kth 15-min interval of day t. The exchange rate change can be calculated by rt,k = 100 × [ln(Pt,k ) − ln(Pt,k−1 )]. From the opening of the market at 9:00 h Taipei time through the closing at 16:00 h, with a lunch break from 12:00 to 14:00 h, it yields 20 observations of (Pt,k , Vt,k ) during a trading day.4 In the literature, the seasonality of volatility has been found in intradaily and intraweekly frequencies. We at first examine the intradaily and intraweekly seasonality in volatility in terms of absolute changes of NTD/USD. Fig. 1 plots the average changes, average absolute changes and average trading volume across every 15-min trading period (k = 1, 2, . . ., 11, 12, 21, 22, . . ., 27, 28). One can observe occurrences of peaks in the intraday volatility at periods k = 1, 21, and 28, corresponding to close-to-9:15, 12:00-to-14:15, and 15:45-to-16:00 absolute changes, respectively. Regarding the intraday volume of trading, peaks occur at 9:15, 11:00, 14:15, and 16:00 h. In the presence of seasonal heteroskedasticity, autocorrelation coefficients are significantly higher for time lags that are integer multiples of the seasonal period than for the other lags. The autocorrelations in rt,k , |rt,k | and Vt,k for up to 200 lags are presented in Fig. 2. We observe that the autocorrelograms of |rt,k | and Vt,k have frequent peaks for lags that are multiples of 20. This indicates a cyclical seasonality in 15-min volatility and trading volume of NTD/USD at length of 20, the number of total 15-min trading intervals during a trading day at the Taipei FX market. To test the equality of NTD/USD intraday volatility across different times of day based on the data sampled at 15-min intervals, we calculate a joint F test statistic from a regression of absolute changes |rt,k | against time-of-day dummy variables Tj,k : Tj,k = 1 if interval k is the jth 15-min 3

The data used are from the Page 6161 of the Telerate real-time quotation system. In calculating the 15-min changes of NTD/USD, we use the price at the 15-min mark. We do not use the prices right at the openings of 9:00 (for the morning session) and 14:00 (for the afternoon session) because opening prices may contain more noise and tend to produce autocorrelated returns, as noted in Stoll and Whaley (1990) and Amihud and Mendelson (1991). Furthermore, transaction volumes at 9:00 (the opening of the morning session) and 14:00 (the opening of the afternoon session) are not available from the data provided by the Taipei Foreign Exchange Brokerage, Inc. Therefore, k = 1 refers to the time mark at 9:15. For the tth trading day, k = 1, 2, . . ., 11, 12, 21, 22, . . ., 27, 28, denoting time marks at 9:15, 9:30, . . ., 11:45, 12:00, 14:15, 14:30, . . ., 15:45, 16:00. The overnight or close-to-open changes for day t, i.e., rt,1 , is calculated by rt,1 = 100 × [ln(Pt,1 ) − ln(Pt−1 ,28)], or close-to-9:15 changes. The morning-close-to-afternoon-open or 12:00-to-14:15 change is rt,21 = 100 × [ln(Pt,21 ) − ln(Pt,12 )]. 4

Y.-F. Gau, M. Hua / The Quarterly Review of Economics and Finance 47 (2007) 135–158

139

Fig. 1. Average changes, average absolute changes, and average trading volume of intraday NTD/USD exchange rates (January 4, 2001 to December 31, 2001). Notes: The kth 15-min period corresponds to each 15-min mark during 9:00–16:00 h. For k = 1, 2, . . ., 11, 12, 21, 22, . . ., 27, and 28, it denotes time marks at 9:15, 9:30, . . ., 11:45, 12:00, 14:15, 14:30, . . ., 15:45, and 16:00 h, respectively.

period, 0 otherwise, where j = 1, 2, . . ., 11, 12, 21, . . ., 28. The null hypothesis, H0 : coefficients on Tj,k , where j = 1, 2, . . ., 11, 12, 21, . . ., 28, are all the same, is equivalent to the null hypothesis that there is no difference in average absolute changes across all intervals. Table 1 reports the estimation results of this regression based on time-of-day dummy variables. Based on to the robust t statistics calculated from the Newey–West HAC (heteroskedasticity-autocorrelation-consistent, Newey & West, 1987) standard errors, the results of the positively significant coefficient on each single Tj,k (for j = 1, 2, . . ., 11, 12, 21, 22, . . ., 27, 28) indicate that, for each 15-min interval, average absolute change is significantly larger than zero. To test whether the intraday volatility of NTD/USD is in fact U-shaped or even has a more complicated shape, we examine several joint hypotheses on the equality of average absolute return across different intervals. The bottom panel of Table 1 indicates three peaks in the 15-min volatility of NTD/USD: the volatilities are relatively higher at

140

Y.-F. Gau, M. Hua / The Quarterly Review of Economics and Finance 47 (2007) 135–158

Fig. 2. Autocorrelograms of NTD/USD changes, absolute changes, and trading volumes (January 4, 2001 to December 31, 2001).

intervals k = 1, k = 21, and k = 28, associated with the close-9:15, 12:00–14:15, and 15:45–16:00 h periods, respectively. Therefore, the pattern of intraday volatility of the NTD/USD exchange rate is more like a W shape (or a distorted doubly-U shape) rather than a U-shape. Furthermore, we employ the regression based on the weekday dummy variables to test if there exist intraweekly variations in the intraday volatility. Table 2 reports the inference results of the regression of absolute change (|rt,k |) against the day-of-week dummy variables D,j,k : Dj,k = 1 if interval k is on the jth weekday, 0 otherwise, where j = 1, 2, 3, 4, and 5.5 The results of tests on 5

Weekdays 1, 2, 3, 4 and 5 refer to Monday, Tuesday, Wednesday, Thursday and Friday, respectively.

Y.-F. Gau, M. Hua / The Quarterly Review of Economics and Finance 47 (2007) 135–158

141

Table 1 Tests of intraday seasonality of absolute changes (January 4, 2001, to December 31, 2001) Time dummy variable (Tj,k )

Coefficient estimate

HAC standard error

Robust t

T1,k (close-to-9:15) T2,k (9:15–9:30) T3,k (9:30–9:45) T4,k (9:45–10:00) T5,k (10:00–10:15) T6,k (10:15–10:30) T7,k (10:30–10:45) T8,k (10:45–11:00) T9,k (11:00–11:15) T10,k (11:15–11:30) T11,k (11:30–11:45) T12,k (11:45–12:00) T21,k (12:00–14:15) T22,k (14:15–14:30) T23,k (14:30–14:45) T24,k (14:45–15:00) T25,k (15:00–15:15) T26,k (15:15–15:30) T27,k (15:30–15:45) T28,k (15:45–16:00)

0.085249*** 0.024845*** 0.021242*** 0.019619*** 0.016673*** 0.015133*** 0.017369*** 0.020248*** 0.017894*** 0.014305*** 0.012314*** 0.012198*** 0.026048*** 0.016806*** 0.015290*** 0.015481*** 0.015819*** 0.015745*** 0.017649*** 0.047724***

0.007483 0.001881 0.001637 0.001947 0.001563 0.001363 0.002166 0.002014 0.001431 0.001293 0.001089 0.001019 0.001748 0.001344 0.001175 0.001467 0.001613 0.001272 0.002168 0.010976

11.39206 13.21055 12.97231 10.07579 10.67062 11.10400 8.01930 10.05581 12.50078 11.06296 11.30544 11.96585 14.89990 12.50779 13.01046 10.54950 9.80987 12.38153 8.14243 4.34818

Tests of coefficients c1 = c2 = c3 = ··· = c11 = c12 = c21 = c22 = ··· = c27 = c28 c1 = c2 c2 = c3 = ··· = c11 = c12 c10 = c11 = c12 c21 = c22 c22 = c23 = c24 = c25 = c26 = c27 c27 = c28

12

Wald F statistic

P-value

F(19,4894) = 10.97 F(1,4894) = 67.46 F(10,4894) = 5.27 F(2,4894) = 1.52 F(1,4894) = 26.69 F(5,4894) = 0.37 F(1,4894) = 10.04

0.00 0.00 0.00 0.22 0.00 0.87 0.00

28

|rt,k | = c T + c T + εt,k , Tj,k = 1 if interval k is the jth 15-min period, 0 otherwise. j=1 j j,k j=21 j j,k Notes: For the tth trading day, k = 1, 2, . . ., 11, 12, 21, 22, . . ., 27, and 28, denoting time intervals close-to-9:15, 9:15–9:30, . . ., 11:30–11:45, 11:45–12:00, 12:00–14:15, 14:15–14:30, . . ., 15:30–15:45, and 15:45–16:00 h, respectively. The overnight or close-to-open changes for day t, i.e., rt,1 , is calculated by rt,1 = 100 × [ln(Pt,1 ) − ln(Pt−1,28 )], or closeto-9:15 changes. The morning-close-to-afternoon-open or 12:00-to-14:15 change is rt,21 = 100 × [ln(Pt,21 ) − ln(Pt,12 )]. *, **, and *** indicate the significance at the 10%, 5%, and 1% levels of significance, respectively. HAC standard errors denote the Newey–West heteroskedasticity-autocorrelation-consistent standard errors.

mean equality in the volatility across weekdays, reported in the lower panel of Table 2, indicate that the intraweekly seasonality in the NTD/USD volatility (measured by absolute changes) is not statistically significant. Finally, we analyze the weekend effects in the intraday NTD/USD volatility by examining if the absolute change is higher at the market closing on Friday and market opening on Monday. Table 3 reports the results of the regression of absolute changes against the interaction variables of D1,k × T1,k and D5,k × T28,k , which can test whether the volatility at the opening on Monday or at the closure on Friday is different from the volatilities of other intervals. The fact of insignificant b2 and b4 in Table 3 implies that the intraday volatility is not significantly larger at the opening on Monday or at the closing on Friday than at other intervals.

142

Y.-F. Gau, M. Hua / The Quarterly Review of Economics and Finance 47 (2007) 135–158

Table 2 Tests of weekly seasonality of absolute changes (January 4, 2001 to December 31, 2001) Weekday dummy variable (Dj,t )

Coefficient estimate

HAC standard error

Robust t

D1,t D2,t D3,t D4,t D5,t

0.025631*** 0.019825*** 0.023648*** 0.021040*** 0.021942***

0.004703 0.001371 0.001908 0.001475 0.001675

5.45033 14.46214 12.39616 14.26494 13.09804

(Monday) (Tuesday) (Wednesday) (Thursday) (Friday)

Tests of coefficients a1 = a2 = a3 = a4 = a5

Wald F statistic

P-value

F(4,4909) = 1.08

0.37

5

|rt,k | = a D + εt,k , Dj,t = 1 if day t is the jth weekday, 0 otherwise. j=1 j j,t Notes: Weekdays 1, 2, 3, 4, and 5 refer to Monday, Tuesday, Wednesday, Thursday, and Friday, respectively. The HAC standard errors denote the Newey–West heteroskedasticity-autocorrelation-consistent standard errors. *, **, and *** indicate the significance at the 10%, 5%, and 1% levels of significance, respectively. Table 3 Tests of weekend effects of absolute changes (January 4, 2001 to December 31, 2001) Coefficient

Estimate

HAC standard error

Robust t

b0 b1 b2 b3 b4

0.017480*** 0.063228*** 0.023180 0.032605** −0.011618

0.000637 0.005440 0.030922 0.013480 0.015457

27.4382 11.6217 0.7496 2.4187 −0.7516

|rt,k | = b0 + b1 T1,k + b2 D1,t T1,k + b3 T28,k + b4 D5,t T28,k + εt,k , T1,k = 1 if interval k is the interval of 9:00–9:15, 0 otherwise; T28,k = 1 if interval k is the interval of 15:45–16:00, 0 otherwise; D1,t = 1 if day t is Monday, 0 otherwise; D5,t = 1 if day t is Friday, 0 otherwise. Notes: The HAC standard errors denote the Newey–West heteroskedasticity-autocorrelation-consistent standard errors. *, **, and *** indicate the significance at the 10%, 5%, and 1% levels of significance, respectively.

We also examine the equality of NTD/USD trading volume across all 15-min intervals by regressing the trading volume (Vt,k ) against time-of-day dummy variables Tj,k and report the inference results in Table 4. By the rejection of mean equality across different 15-min periods, we detect significant peaks at 9:15, 11:00, 14:15, and 16:00 h. However, based on Tables 5 and 6, the intraweekly pattern and weekend effects are not significant for the trading volume, at the 1% significance level. Data on numbers of news related to Taiwan and the U.S. during every 15-min interval are collected from news headlines reported on the Bloomberg real-time news screen from the Bloomberg Professional Service. We consider counts of all news instead of only exchange-rate relevant news.6 The data consist of all news releases sent to the Bloomberg News Services during a 1-year time period, from January 2001 to December 2001. The database contains all information events, not only firm specific information, over the full 24-h day. Actually, it cannot avoid the inclusion of company specific announcements with little direct connection to the exchange rate. Nevertheless, due to the data availability, other studies on the link between public information arrivals and intraday exchange rate volatility employ total counts of news items reported in Reuters 6 We have tried to collect only exchange rate relevant news (with keyword FRX) but find the numbers of such news in a 15-min period are mostly 0 and the associated estimation results are implausible.

Y.-F. Gau, M. Hua / The Quarterly Review of Economics and Finance 47 (2007) 135–158

143

Table 4 Tests of intraday seasonality of trading volume (January 4, 2001 to December 31, 2001) Time dummy variable (Tj,k )

Coefficient estimate

HAC standard error

Robust t

T1,k (9:00–9:15) T2,k (9:15–9:30) T3,k (9:30–9:45) T4,k (9:45–10:00) T5,k (10:00–10:15) T6,k (10:15–10:30) T7,k (10:30–10:45) T8,k (10:45–11:00) T9,k (11:00–11:15) T10,k (11:15–11:30) T11,k (11:30–11:45) T12,k (11:45–12:00) T21,k (14:00–14:15) T22,k (14:15–14:30) T23,k (14:30–14:45) T24,k (14:45–15:00) T25,k (15:00–15:15) T26,k (15:15–15:30) T27,k (15:30–15:45) T28,k (15:45–16:00)

39.86327*** 23.32653*** 19.07755*** 18.24082*** 16.61224*** 16.04490*** 17.43902*** 30.36585*** 23.48171*** 15.20122*** 14.00813*** 14.85366*** 32.38415*** 22.03049*** 17.87602*** 17.22764*** 17.03659*** 20.27033*** 21.92683*** 62.50203***

2.638929 1.739814 1.171127 1.318326 1.087286 1.141173 1.286737 1.464625 1.202340 1.037977 0.972637 0.903999 1.831481 1.417384 1.021653 1.015375 1.039010 1.270116 1.407624 4.334806

15.10585 13.40748 16.28991 13.83635 15.27864 14.06000 13.55290 20.73286 19.53001 14.64505 14.40222 16.43106 17.68195 15.54306 17.49715 16.96678 16.39694 15.95943 15.57719 14.41865

Tests of coefficients c1 = c2 = c3 = ··· = c11 = c12 = c22 = ··· = c27 = c28 c1 = c2 c2 = c3 = ··· = c11 = c12 c10 = c11 = c12 c21 = c22 c22 = c23 = c24 = c25 = c26 = c27 c27 = c28

12

Wald F Statistic

P-value

F(19,4894) = 22.37 F(1,4894) = 47.51 F(10,4894) = 17.25 F(2,4894) = 0.54 F(1,4894) = 33.97 F(5,4894) = 3.17 F(1,4894) = 91.12

0.00 0.00 0.00 0.58 0.00 0.01 0.00

28

Vt,k = c T + c T + νt,k , Tj,k = 1 if interval k is the jth 15-min period, 0 otherwise. j=1 j j,k j=21 j j,k Notes: The kth 15-min period corresponds to each 15-min trading interval during 9:00 to 16:00. For example, Vt,1 , Vt,12 , Vt,21 , and Vt,28 denote the trading volume during intervals 9:00–9:15, 11:45–12:00, 14:00–14:15, and 15:45–16:00 h, respectively. The HAC standard errors denote the Newey–West heteroskedasticity-autocorrelation-consistent standard errors. *, **, and *** indicate the significance at the 10%, 5%, and 1% levels of significance, respectively.

or Bloomberg News Screens as well (e.g., Low & Muthuswamy, 1996; Melvin & Yin, 2000). Moreover, most of scheduled U.S. macroeconomic announcements and market information about the U.S. are released during the midnight (Taipei time) when the trading is halted in Taipei, total headline news counts still reflect the tendency of news flows during a day. In addition, Taiwan is an export-oriented economy and the U.S. is one of its major targeted markets, any news related to the U.S. economy, even the political news, may have more or less influence on Taiwan. TW Let NEWSUS t,k and NEWSt,k denote counts of news headlines related to the U.S. and Taiwan, respectively, crossing the Bloomberg news screen during the kth 15-min interval on day t. For the interval k = 1, the counts of news for this period consist of the number of overnight news arrivals and the number of news arrivals during 9:00 opening and 9:15. For the interval k = 21,

144

Y.-F. Gau, M. Hua / The Quarterly Review of Economics and Finance 47 (2007) 135–158

Table 5 Tests of weekly seasonality of trading volume (January 4, 2001 to December 31, 2001) Weekday dummy variable (Dj,t )

Coefficient estimate

HAC standard error

Robust t

D1,t D2,t D3,t D4,t D5,t

21.57386*** 20.72823*** 24.50821*** 24.59500*** 23.49550***

0.823253 0.665610 0.957676 1.116467 0.847895

26.20562 31.14171 25.59133 22.02931 27.71038

(Monday) (Tuesday) (Wednesday) (Thursday) (Friday)

Tests of coefficients a1 = a2 = a3 = a4 = a5 a1 = a3 a1 = a2 a3 = a4 = a5

Wald F statistic

P-value

F(4,4909) = 3.41 F(2,4909) = 5.40 F(2,4909) = 0.64 F(2,4909) = 0.44

0.01 0.02 0.43 0.64

5

Vt,k = a D + νt,k , Dj,t = 1 if day t is the jth weekday, 0 otherwise. j=1 j j,t Notes: Weekdays 1, 2, 3, 4, and 5 refer to Monday, Tuesday, Wednesday, Thursday, and Friday, respectively. The HAC standard errors denote the Newey–West heteroskedasticity-autocorrelation-consistent standard errors. *, **, and *** indicate the significance at the 10%, 5%, and 1% levels of significance, respectively.

the number of news includes the number of news arrivals during lunch hours (12:00–14:00 h) and 14:00–14:15 h (afternoon-opening-to-14:15). Fig. 3 plots the average number of news related to Taiwan and U.S. for every 15-min interval. Table 7 reports the inference results of the average counts of news arrivals across times of day, via a regressions of news counts against time-of-day dummy variable Tj,k and day-of-week dummy variables Dj,k . The results of the significance of single coefficient, shown in the upper panel of Table 7, indicate that, for each interval, average counts of Taiwan news and the U.S. news are both significantly larger than zero. We observe that the average counts of Taiwan and the U.S. news are the greatest during the interval of close-to-9:15, and the secondly larger during the interval of 12:00–14:15 (i.e., morning-close-to-afternoon-opening). Because the count of news during the opening interval (k = 1) consists of overnight news from 16:00 on the previous trading day through 9:15, and the count for the afternoon-opening interval (k = 21) includes news occurred during the period from 12:00 to 14:15, the two counts are numbers of news accumulated over more than one non-trading 15-min period. By comparing each single 15-min trading period, during the morning session from 9:15 to 12:00 and the afternoon session from 14:15 to 16:00, we observe Table 6 Tests of weekend effects of trading volume (January 4, 2001 to December 31, 2001) Coefficient

Estimate

HAC standard error

Robust t

b0 b1 b2 b3 b4

19.85711*** 22.74949*** 2.940089 42.03064*** 3.022245

0.482793 2.969195 5.415213 5.069942 8.973033

41.12969 7.66184 0.54293 8.29016 0.33681

Vt,k = b0 + b1 T1,k + b2 D1,t T1,k + b3 T28,k + b4 D5,t T28,k + νt,k , T1,k = 1 if interval k is the interval of 9:00–9:15 h, 0 otherwise; T28,k = 1 if interval k is the interval of 15:45–16:00 h, 0 otherwise; D1,t = 1 if day t is Monday, 0 otherwise; D5,t = 1 if day t is Friday, 0 otherwise. Notes: The HAC standard errors denote the Newey–West heteroskedasticity-autocorrelation-consistent standard errors. *, **, and *** indicate the significance at the 10%, 5%, and 1% levels of significance, respectively.

Y.-F. Gau, M. Hua / The Quarterly Review of Economics and Finance 47 (2007) 135–158

145

Fig. 3. Average Numbers of macroeconomic news crossing the Bloomberg screen in 15-min periods (January 4, 2001 to December 31, 2001). Notes: Data on counts of news arrivals in Taiwan and U.S. every 15-min interval are collected from the Bloomberg realtime news screen. For the interval k = 1, the counts of news for this period consist of the number of overnight news arrivals and the number of news arrivals during 9:00 opening and 9:15. For the interval k = 21, the number of news includes the number of news arrivals during lunch hours (12:00–14:00 h) and 14:00–14:15 h (afternoon-opening-to-14:15).

that the counts of Taiwan and the U.S. news start low in the early morning (9:15–9:30); reaches US daily peaks in the late morning (10:45–11:00 for NEWSTW t,k and 10:00–10:15 for NEWSt,k ); declines slightly till the closing of the morning session. A similar pattern occurs for the afternoon session: the counts of news start low in the early afternoon (14:15–14:30), increase as time goes by, and end low again at the closing of the afternoon session. It turns out a distorted M-shaped pattern in the total counts of Taiwan and the U.S. news across every 15-min trading period during a day, which is not the same as the inverted U-shaped pattern found by Berry and Howe (1994). 3. The GARCH model with seasonal dummy variables To capture the volatility seasonality, volatility persistence, news effects, the response to nonpublic information shocks and inventory control, we incorporate explicit time-of-day dummy variables, numbers of news announcements related to the U.S. and Taiwan, and unexpected volume of trading into a GARCH model. Since the time span of seasonality is regular in the data studied in this paper, a well-specified GARCH model with exogenous dummy variables allows us to

146

Y.-F. Gau, M. Hua / The Quarterly Review of Economics and Finance 47 (2007) 135–158

Table 7 Tests of intraday seasonality in numbers of news (January 4, 2001 to December 31, 2001) Time dummy variable (Tj,k )

T1,k (close-to-9:15) T2,k (9:15–9:30) T3,k (9:30–9:45) T4,k (9:45–10:00) T5,k (10:00–10:15) T6,k (10:15–10:30) T7,k (10:30–10:45) T8,k (10:45–11:00) T9,k (11:00–11:15) T10,k (11:15–11:30) T11,k (11:30–11:45) T12,k (11:45–12:00) T21,k (12:00–14:15) T22,k (14:15–14:30) T23,k (14:30–14:45) T24,k (14:45–15:00) T25,k (15:00–15:15) T26,k (15:15–15:30) T27,k (15:30–15:45) T28,k (15:45–16:00)

NEWSTW t,k

NEWSUS t,k

Coefficient estimate

HAC standard error

Coefficient estimate

HAC standard error

199.7061*** 5.5633*** 8.0041*** 9.9918*** 11.0408*** 8.9143*** 11.0732*** 11.8130*** 10.4756*** 9.8293*** 10.1138*** 11.4959*** 74.8333*** 5.7358*** 7.6585*** 7.2033*** 6.6016*** 6.1667*** 5.9309*** 6.3049***

4.7908 0.2447 0.4723 0.3342 0.3419 0.3125 0.4698 0.3912 0.3656 0.3999 0.3658 0.4233 1.9521 0.2419 0.3035 0.3568 0.3233 0.2992 0.2427 0.2743

4029.3840*** 22.6041*** 33.8571*** 37.1225*** 44.9674*** 37.9061*** 32.3333*** 28.4187*** 21.0854*** 19.0569*** 22.3618*** 20.5041*** 218.7398*** 14.9715*** 18.0081*** 19.3821*** 18.2236*** 17.9431*** 18.1504*** 13.5122***

66.8168 3.2636 5.4402 5.7058 7.5091 6.2719 6.2289 5.9438 4.7740 5.0941 6.0180 5.5644 23.5248 2.7388 5.1448 5.0252 4.3595 4.5428 5.4230 2.1917

Tests of coefficients (H0 ): c1 = c2 = c3 = ··· = c11 = c12 = c21 = c22 = ··· = c27 = c28 . Dependent variable

Wald F statistic

P-value

NEWSTW t NEWSUS t

F(19,4894) = 165.11 F(19,4894) = 195.20

0.00 0.00

12



28 c T + c T + ut,k , i = TW, US, Tj,k = 1 if interval k is the jth 15-min period, 0 otherwise. j=1 j j,k j=21 j j,k US TW NEWSt,k and NEWSt,k denote numbers of news headlines related to the U.S. and Taiwan, respectively, crossing

NEWSit,k =

Notes: the Bloomberg screen during the kth 15-min interval on day t. For the interval k = 1, the counts of news for this period consist of the number of overnight news arrivals and the number of news arrivals during 9:00 opening and 9:15 h. For the interval k = 21, the number of news includes the number of news arrivals during lunch hours (12:00–14:00) and 14:00–14:15 (afternoon-opening-to-14:15). The HAC standard errors denote the Newey–West heteroskedasticityautocorrelation-consistent standard errors. *, **, and *** indicate the significance at the 10%, 5%, and 1% levels of significance, respectively.

examine how the intraday volatility shifts in response to the news announcements and unexpected volume innovations.7 Given the exchange rate changes (rt,k ) and trading volume (Vt,k ) of the kth 15-min interval on day t, we consider time-of-day dummy variables Tj,k : Tj,k = 1 if interval k is the jth 15-min period, 0 otherwise; j = 1, 2, . . ., 11, 12, 21, . . ., 28, denoting the periodic cycle at time interval k on day t. The variable vt,k is denoted by the unexpected volume of trading and plays the role of a proxy variable that corresponds to the combined effects of inventory adjustments and 7 If the time span of seasonality is irregular, we may employ a periodic GARCH (P-GARCH) model to identify the complicated cycle of seasonality. However, before specifying a state-dependent P-GARCH model, one has to identify the number of states of interest and then specifies a coherent P-GARCH model.

Y.-F. Gau, M. Hua / The Quarterly Review of Economics and Finance 47 (2007) 135–158

147

US uncommon-knowledge information. NEWSTW t,k and NEWSt,k are defined by numbers of news headlines related to Taiwan and the U.S., respectively, that are crossing the Bloomberg news screen during the kth 15-min interval on day t. The simultaneous GARCH model is specified as follows:

rt,k = μ + εt,k +

s 

θi εt,k−i

i=1 2 = σt,k

12  j=1

wj Tj,t +

28 

wj Tj,t +

q 

αi ε2t,k−i +

j=21 i=1 TW +λ1 NEWSt,k + λ2 NEWSUS t,k

p  i=1

2 βi σt,k−i + γvt,k

(1)

2 ), v where εt,k |Ωt,k−1 ∼ N(0, σt,k t,k = Vt,k − E(Vt,k |Ωt,k−1 ), Ωt,k−1 is the information available at interval k − 1 on day t. The optimal lag s of the MA(s) specification in the equation of conditional mean is chosen to be 1 based on the Akaike information criterion (AIC) and Schwarz information criterion (SIC). The optimal lags of ARCH and GARCH terms, i.e., q and p, are determined by the LR (likelihood ratio) test of overfitting parameters. For the purpose of comparison, we also estimate a benchmark model of GARCH without thetime-of-day  factors, announcement q q 2 2 2 =w + variables, and unexpected volume as follows: σt,k ε + 0 i=1 βi σt,k−i . i=1 t,k−i If wj ’s are different across time of the day, it implies that there is pronounced seasonality in the intraday volatility. Parameters αi ’s (where i = 1, . . ., q) capture the impacts of lagged squared return 2 . To ensure the estimated innovations ε2t,k−i (i = 1, . . ., q) on the current conditional volatility σt,k 2 to be positive, we have to restrict values of w (j = 1, 2, . . ., 11, 12, 21, . . ., 28), α value of σt,k j i (i = 1, 2, . . ., q) and βi (i = 1, . . ., p) to be positive. To satisfy the covariance stationarity of the p q volatility process, parameters are constrained to satisfy 0 ≤ i=1 αi + i=1 βi < 1. Parameters γ, λ1 , and λ2 measure the influences on the intraday volatility from the unexpected volume, the Taiwan news announcements, and the U.S. news announcements, respectively. To examine the effects of inventory control, the order flow (or quote flow) of dealers is an ideal explanatory variable since it may indicate the inventory position of dealers. However, since the data of actual inventories of NTD/USD are not available, we can only employ the unexpected volume of trading as the proxy for the inventory control effects, as in Bessembinder (1994) and Jorion (1996).8 Actually, the unexpected volume of trading works as a proxy variable that corresponds to the combined effects of inventory adjustments and uncommon-knowledge information. As new information flows into the market, the expected volume changes in response to common-knowledge or public information, and the unexpected volume reflects the disagreement or uncommon-knowledge information among dealers. If the dealers adjust trading volumes just for inventory control, the trading volume will change even when no new information flows into the FX market, and the expected volume remains unchanged. The explanatory variable vt,k , defined by the discrepancy between actual volume and expected volume of trading, therefore can work as a proxy variable for the mixed effects of inventory control and uncommon-knowledge information. In practice, we also consider the intraday seasonality in estimating the expected volume, as we observe intraday seasonality in the trading volume. Utilizing the ARMA (p, q) model with

8 Bessembinder (1994) incorporates the unexpected trading volume, i.e., the deviation of actual trading volume from the expected volume, to measure the link between risk and information asymmetry. Jorion (1996) also applies unexpected volume to capture the effects of inventory risk.

148

Y.-F. Gau, M. Hua / The Quarterly Review of Economics and Finance 47 (2007) 135–158

time-of-day dummy variables, we can specify the expected volume as follows: E(Vt,k |Ωt,k−1 ) =

12  j=1

τj Tj,k +

28 

τj Tj,k +

j=21

p  i=1

φi Vt,k−i +

q 

θi νt,k−i

(2)

i=1

where vt,k is a white noise with mean zero and constant variance. The optimal lags p and q can be determined by the AIC and SIC criteria. 4. Empirical results To estimate the GARCH model specified above, we utilize the quasi-maximum likelihood estimation (QMLE) method and report the Bollerslev–Wooldridge robust t statistics (Bollerslev & Wooldridge, 1992). Although the data studied in this paper exhibit significant skewness and kurtosis, in that the assumption of conditional normality in the GARCH model may be violated, the QMLE estimates remain consistent. For large sample sizes, the QMLE-based inference procedure is generally reliable. The unexpected volume of trading is used to reflect the risk associated to the unexpected or uncommon-knowledge information and inventory adjustments. Employing an ARMA (p, q) framework with explicit time-of-day periodicity (Tj,k ), we obtain the unexpected volume of trading vt,k by vt,k = Vt,k − Vˆ t,k , where Vˆ t,k is the predicted volume based on the information set Ωt,k−1 . The estimation results of the trading volume are reported in Table 8. According to the AIC and SIC criteria, an ARMA (2,1) specification is chosen. Table 9 reports the estimation results of the GARCH models. Model 1 is the benchmark model that only considers the volatility clustering. Model 2 takes into account the volatility clustering and time-of-day seasonality. Model 3 gauges the volatility clustering with public announcements and unexpected volume of trading. Model 4 is the simultaneous model that incorporates the volatility clustering, intraday seasonality, macroeconomic announcements effects, and the influence of unexpected trading volume simultaneously. For each model, we employ the LR (likelihood ratio) test on overfitting parameters to determine the optimal lags of ARCH and GARCH terms. Specifications of GARCH (1,2), GARCH (1,1), ARCH (3), and ARCH (3) are determined for Models 1, 2, 3, and 4, respectively. The resulting AIC provides a measure of in-sample predictive ability, and a lower value of AIC indicates a better goodness of fit. According to the log likelihood and AIC, we can conclude that Model 4 is the best model that explains the dynamics in intraday volatility of NTD/USD exchange rate. With only lagged squared shocks and lagged volatility in the information set, it turns out that the ARCH effect is estimated to be stronger than the GARCH effect in Model 1. Once the time-of-day dummy variables are included in the information set, the ARCH effect becomes smaller, implying that adding implicit periodicity into the model of intraday volatility adjusts the impact of past return innovations to be lower. By comparing Models 1 and 3, we find that the ARCH effect is also reduced as the effects of Taiwan and the U.S. public announcements and unexpected volume shocks are incorporated into the model. Similarly, the estimated ARCH effect of Model 4 is weaker than that in Model 1, indicating that the simultaneous consideration of intraday seasonality, public announcements effects, and unexpected volume innovations mitigates the exaggerated ARCH effects of an intraday GARCH model. Moreover, the coefficients of lagged return innovations decline monotonically in Models 3 and 4, implying shocks of up to last 45 min affect the NTD/USD volatility with a monotonically decreasing size.

Y.-F. Gau, M. Hua / The Quarterly Review of Economics and Finance 47 (2007) 135–158

149

Table 8 Estimation results of trading volume (Vt,k ): ARMA (2,1) (January 4, 2001 to December 31, 2001) Parameter

Coefficient

HAC standard error

Robust t-statistic

τ1 τ2 τ3 τ4 τ5 τ6 τ7 τ8 τ9 τ 10 τ 11 τ 12 τ 21 τ 22 τ 23 τ 24 τ 25 τ 26 τ 27 τ 28 φ1 φ2 θ1

52.723***

9.104 2.083 1.556 1.638 1.421 1.468 1.660 1.769 1.515 1.352 1.318 1.246 2.717 1.685 1.324 1.297 1.274 1.536 1.582 5.214 0.035 0.032 0.017

5.794 11.294 12.399 11.274 11.875 11.388 10.612 17.236 15.566 11.303 10.697 11.977 12.072 13.114 13.549 13.326 13.415 13.232 13.886 11.869 30.863 −3.467 −54.515

23.523*** 19.295*** 18.467*** 16.871*** 16.375*** 17.611*** 30.489*** 23.577*** 15.287*** 14.096*** 14.927*** 32.799*** 22.095*** 17.937*** 17.289*** 17.091*** 20.319*** 21.962*** 61.879*** 1.083*** −0.111*** −0.907***

12

28

p

q

Vt,k = τ T + τ T + φV + θν + νt,k , where νt,k is a white noise with mean zero j=1 j jk j=21 j jk i=1 i t,k−i i=1 i t,k−i and constant variance. Notes: Tj,k = 1 if interval k is the jth 15-min period, 0 otherwise. For example, T1,k = 1 if interval k is the interval of 9:00–9:15, 0 otherwise; T8,k = 1 if interval k is 10:45–11:00, 0 otherwise; T21,k = 1 if interval k is 14:00–14:15, 0 otherwise; T28,k = 1 if interval k is 15:45–16:00, 0 otherwise. The HAC standard errors denote the Newey–West heteroskedasticityautocorrelation-consistent standard errors. *, **, and *** indicate the significance at the 10%, 5%, and 1% levels of significance, respectively.

Based on the estimated coefficients on the time-of-day dummy variables in Model 4, we can significantly reject the null hypothesis that individual wk is zero by the large value of robust t statistic. This implies that the average volatility is significantly different from zero by time of day, after controlling for the effects of public announcements and unexpected volume innovations. By testing the null hypothesis, H0 : w1 = w2 = · · · = w11 = w12 = w21 = w22 = · · · = w27 = w28 , we examine whether the average volatility is different from each other. Given the corresponding F statistics, F19,4887 = 575.0727 (with P-value 0) for Model 2 and F19,4884 = 153.5252 (with P-value 0) for Model 4, we can reject the above null hypothesis and conclude that the average volatility is indeed different across time of day. The estimates of wj ’s (j = 1, 2, . . ., 11, 12, 21, 22, . . ., 27, 28) in Model 4 suggest the relation of w1 > w28 > w21 > wk (k = 1, 21, 28), implying that the average volatility is highest at the open, followed by the volatility at the close, then the volatility at the opening of the afternoon session, and lastly the midday volatility. To test if w1 , w21 , and w28 are different with each other, we test the following null hypothesis, H0 : w1 = w21 = w28 . The associated F statistic is F2,4884 = 99.4739 (with P-value 0), implying a rejection of the null of w1 = w21 = w28 . Since dealers’ inventory adjustments, private or uncommon-knowledge information, and public announcements or common-knowledge information could influence the exchange rate volatility

150

Y.-F. Gau, M. Hua / The Quarterly Review of Economics and Finance 47 (2007) 135–158

Table 9 Estimation results of GARCH models (January 4, 2001 to December 31, 2001) Parameter

μ θ1 α1 α2 α3 β1 w0 × 103 w1 × 103 w2 × 103 w3 × 103 w4 × 103 w5 × 103 w6 × 103 w7 × 103 w8 × 103 w9 × 103 w10 × 103 w11 × 103 w12 × 103 w21 × 103 w22 × 103 w23 × 103 w24 × 103 w25 × 103 w26 × 103 w27 × 103 w28 × 103 γ × 105 λ1 × 105 λ2 × 105

Model 1

Model 2

Model 3

Model 4

Estimate

Robust t

Estimate

Robust t

Estimate

Robust t

Estimate

Robust t

0.001*** −0.164*** 0.617*** 0.230*** – 0.050*** 0.884*** – – – – – – – – – – – – – – – – – – – – – – –

3.503 −7.310 5.358 4.406 – 3.228 7.794 – – – – – – – – – – – – – – – – – – – – – – –

0.000 −0.104*** 0.116** – – 0.809*** – 7.846*** 0.276*** 0.198*** 0.009 0.009 0.010 0.002 0.406*** 0.315*** 0.016** 0.012** 0.022*** 0.577*** 0.281*** 0.122*** 0.051*** 0.046*** 0.035*** 1.376*** 3.537*** – – –

1.550 −8.201 9.185 – – 33.032 – 8.928 13.818 6.427 0.671 0.731 1.091 0.259 30.260 26.468 2.051 2.048 3.579 11.134 6.578 10.258 3.699 4.091 3.280 67.670 47.374 – – –

0.000 −0.048 0.337*** 0.266* 0.029* – 0.320*** – – – – – – – – – – – – – – – – – – – – 0.687*** 0.138*** 0.199***

0.014 −1.122 3.217 1.767 1.813 – 10.084 – – – – – – – – – – – – – – – – – – – – 162.189 6.779 7.619

0.001*** −0.002 0.138** 0.049*** 0.048** – – 4.620*** 0.233*** 0.311*** 0.333*** 0.334*** 0.318*** 0.369*** 0.764*** 0.310*** 0.265*** 0.219*** 0.234*** 0.837*** 0.261*** 0.354*** 0.591*** 0.286*** 0.315*** 1.026*** 2.682*** 1.070*** 0.186** 0.357***

4.300 −0.057 2.347 4.072 2.497 – – 10.756 7.775 14.636 16.834 10.700 23.823 19.579 13.192 14.452 17.414 28.190 8.729 7.914 21.360 20.225 19.956 25.114 36.008 18.332 61.017 321.195 2.302 5.334

LL AIC rt,k = μ + εt,k +

9016.883 −3.667

s

θε , i=1 i t,k−i US vt,k + λ1 NEWSTW t,k + λ2 NEWSt,k

10741.88 −4.362 2 =w + σt,k 0

12 j=1

wj Tj,t +

10380.44 −4.223

28

2 ), N(0, σt,k

j=21

wj Tj,t +

10944.33 −4.444

q

α ε2 i=1 i t,k−i

+

p

β σ2 i=1 i t,k−i

+γ ·

where εt,k |Ωt,k−1 ∼ vt,k = Vt,k = E(Vt,k |Ωt,k−1 ). Notes: LL denotes the log likelihood. AIC denotes the Akaike information criterion. Robust t statistics are the Bollerslev–Wooldridge robust t values. *, **, and *** indicate the significance at the 10%, 5%, and 1% level of significance, respectively.

as well, we add unexpected volume shocks to Model 4 to capture the joint effects of inventory adjustments and private information, and combine with the counts of Taiwan news and U.S. news to account for the impacts of public announcements. The estimate of parameter γ is significantly different from zero at the 1% level of significance, suggesting a positive response in the volatility to the unexpected shocks in trading volume. The parameters λ1 and λ2 estimate the influences of public information arrivals from Taiwan and the U.S., respectively. We see that both Taiwan and the U.S. news variables have positive and significant impacts on the intraday NTD/USD volatility at the 5% level of significance.

Y.-F. Gau, M. Hua / The Quarterly Review of Economics and Finance 47 (2007) 135–158

151

To see how the volatility periodicity is captured by different models, we examine the periodicity pattern existed in the volatility forecast and squared standardized residuals from each model. If a model can successfully capture the periodicity in the intraday volatility, then the corresponding volatility forecasts should have a shape similar to that of absolute changes or squared changes, whereby the associated squared standardized residuals have no pronounced periodicity remained. Table 10 reports the average volatility forecasts and average squared standardized 2 residuals across periods k. r¯k2 is the average squared changes, and σ¯ˆ k is the average volatility forecast, across days t for each k, where k = 1, 2, . . ., 11, 12, 21, 22, . . ., 27, 28, denoting intervals close-to-9:15, 9:15–9:30, . . ., 11:30–11:45, 11:45–12:00, 12:00–14:15, 14:15–14:30, . . ., 15:30–15:45, 15:45–16:00, respectively. According to Panel A in Table 10, the null hypotheses 2 of zero r¯k2 and zero σ¯ˆ k , for each k, can be rejected because of the significant robust t values that have been adjusted by the Newey–West heteroskedasticity-autocorrelation-consistent (HAC) standard errors. The joint F statistic is used to test the null hypothesis of mean equal2 ity across different r¯k2 and σ¯ˆ k , where k = 1, 2, . . ., 11, 12, 21, 22, . . ., 27, 28. For the squared 2 = r¯ 2 = r¯ 2 = r¯ 2 = · · · = r¯ 2 = r¯ 2 changes, the null hypothesis of H0 : r¯12 = r¯22 = · · · = r¯11 12 21 22 27 28 can be rejected, indicating the squared changes are not the same across different periods k. Regarding the volatility forecasts obtained from Models 2–4, we find that the null hypotheses, 2 2 2 2 2 2 2 2 H0 : σ¯ˆ 1 = σ¯ˆ 2 = · · · = σ¯ˆ 11 = σ¯ˆ 12 = σ¯ˆ 21 = σ¯ˆ 22 = · · · = σ¯ˆ 27 = σ¯ˆ 28 , are rejected at the 1% significance level, whereas the volatility forecasts from Model 1 (i.e., GARCH (1,1) without time-of-day dummies and other explanatory variables) are not significantly different across periods k, at the 1% level of significance. This finding is consistent with the property that the GARCH model without explicit time-of-day calendar dummies implies that after a shock, volatility returns to virtually normal levels too quickly (Ederington & Lee, 2001). Hence, this indicates that a traditional GARCH model is not appropriate to capture the dynamics in the intraday volatility. 2 )= The results in Panel B of Table 10 show that the null hypotheses H0 : Avg(ˆε2t,k /σˆ t,k 0, for k = 1, 2, . . . , 12, 21, 22, . . . , 28, can be rejected because of the significant robust t values 2 ) is the average of squared standardized residor HAC-adjusted t values, where Avg(ˆε2t,k /σˆ t,k uals across days t for each k. For Models 1 and 3, the significantly large values of the F statistic for testing the equality of squared standardized residuals imply a rejection of the null 2 ) = Avg(ˆ 2 ) = · · · = Avg(ˆ 2 ) = Avg(ˆ 2 )= hypothesis H0 : Avg(ˆε2t,1 /σˆ t,1 ε2t,2 /σˆ t,2 ε2t,11 /σˆ t,11 ε2t,12 /σˆ t,12 2 ) = Avg(ˆ 2 ) = · · · = Avg(ˆ 2 ) = Avg(ˆ 2 ) at the 1% ε2t,22 /σˆ t,22 ε2t,27 /σˆ t,27 ε2t,28 /σˆ t,28 · · · = Avg(ˆε2t,21 /σˆ t,21 level of significance. This means that neither the information set that only includes past volatility and past returns innovations (associated to Model 1) nor the information set that covers past returns innovations, unexpected volume innovations, and counts of public news of Taiwan and the U.S. (associated to Model 3) is sufficient to capture all the seasonality in the intraday volatility of the NTD/USD exchange rate. On the other hand, the small values of the F statistic for the squared standardized residuals obtained from Models 2 and 4 suggest that the information set that simultaneously incorporates explicit time-of-day dummy variables, past squared changes, unexpected volumes, and counts of public news of Taiwan and the U.S. is better in explaining for the periodicity and time-varying clustering in the intraday volatility. Furthermore, Figs. 4 and 5 show the time-of-day variations in average volatility forecasts and average of squared standardized residuals, respectively, obtained from Models 1–4. Fig. 4 indicates that Models 1–4 are able to capture the high volatility at the opening, whereas only Models 2 and 4 that incorporate explicit time-of-day dummy variables can resemble the peak of volatility at the closing to some extent. However, the four models fail to forecast the high volatility at the opening of the afternoon session. Fig. 5 shows that the squared standardized

152

Period

Squared changes (¯rk2 )

Panel A. Average of fitted volatilitya 1 0.0209*** (4.20) 2 0.0015*** (6.75) 3 0.0011*** (5.07) 4 0.0013*** (2.98) 5 0.0009*** (3.14) 6 0.0007*** (5.00) 7 0.0015** (2.18) 8 0.0014*** (3.47) 9 0.0008*** (5.98) 10 0.0006*** (3.81) 11 0.0004*** (2.75) 12 0.0004*** (2.95) 21 0.0014*** (5.95) 22 0.0007*** (5.66) 23 0.0006*** (5.65) 24 0.0008*** (3.42) 25 0.0009** (3.51) 26 0.0006*** (5.32) 27 0.0015* (1.69) 28 0.0318** (2.23) F19,4894

2.77** [0.00]

2

2

2

2

Model 1 σ¯ˆ k

Model 2 σ¯ˆ k

Model 3 σ¯ˆ k

Model 4 σ¯ˆ k

0.0233** (2.30) 0.0158** (2.44) 0.0051*** (3.85) 0.0025*** (7.88) 0.0022*** (6.85) 0.0017*** (8.66) 0.0016*** (14.74) 0.0020*** (4.59) 0.0021*** (6.20) 0.0017*** (13.03) 0.0015*** (12.74) 0.0014*** (10.69) 0.0014*** (10.92) 0.0020*** (12.23) 0.0017*** (15.70) 0.0015*** (18.55) 0.0016*** (10.15) 0.0016*** (8.85) 0.0015*** (16.27) 0.0020*** (3.52)

0.0244*** (4.58) 0.0058* (1.81) 0.0047* (1.87) 0.0039* (1.86) 0.0033* (1.95) 0.0028** (2.00) 0.0023** (2.07) 0.0025*** (2.68) 0.0018** (2.45) 0.0016*** (2.61) 0.0014*** (2.77) 0.0011*** (2.84) 0.0015*** (4.71) 0.0011*** (4.21) 0.0009*** (4.00) 0.0008*** (4.55) 0.0007*** (4.56) 0.0007*** (5.10) 0.0020*** (17.45) 0.0053*** (38.44)

0.0201* (2.22) 0.0188 (1.57) 0.0089*** (2.57) 0.0019*** (7.07) 0.0013*** (7.55) 0.0012*** (5.53) 0.0010*** (7.48) 0.0012*** (4.91) 0.0014*** (4.00) 0.0012*** (6.02) 0.0010*** (9.68) 0.0008*** (7.86) 0.0012*** (11.06) 0.0010*** (10.26) 0.0011*** (9.97) 0.0009*** (11.85) 0.0009*** (9.63) 0.0010*** (5.59) 0.0009*** (7.63) 0.0011*** (3.69)

0.0206*** (2.99) 0.0048* (1.92) 0.0031* (1.86) 0.0016*** (3.65) 0.0006*** (10.00) 0.0005*** (9.54) 0.0010*** (24.87) 0.0006*** (6.50) 0.0006*** (7.32) 0.0005*** (8.57) 0.0004*** (10.72) 0.0004*** (12.27) 0.0010*** (27.82) 0.0005*** (12.92) 0.0005*** (18.48) 0.0008*** (26.96) 0.0005*** (13.27) 0.0005*** (9.53) 0.0012*** (34.75) 0.0030*** (23.13)

1.73** [0.02]

4.84*** [0.00]

2.82*** [0.00]

5.35*** [0.00]

Y.-F. Gau, M. Hua / The Quarterly Review of Economics and Finance 47 (2007) 135–158

Table 10 Tests of mean equality across different periods

Period (k)

2 ) Model 1 Avg(ˆε2t,k /σˆ t,k

F19,4894

8.85*** [0.00]

2 ) Model 3 Avg(ˆε2t,k /σˆ t,k

2 ) Model 4 Avg(ˆε2t,k /σˆ t,k

1.0307*** (8.21) 0.9879*** (5.64) 0.9396*** (5.95) 0.8492*** (5.45) 0.7970*** (4.23) 0.8114*** (4.75) 1.4264*** (2.36) 0.8505*** (2.67) 0.9037*** (7.70) 0.7118*** (6.14) 0.7523*** (4.70) 0.7616*** (6.84) 1.1256*** (7.13) 0.9389*** (4.34) 1.0075*** (7.50) 1.1677*** (4.40) 1.2175*** (7.44) 1.1206*** (7.05) 0.8664 (1.40) 2.0362** (2.02)

1.4655*** (5.51) 0.4772*** (6.35) 0.3186*** (6.44) 0.7213*** (4.33) 0.5589*** (5.31) 0.6220*** (6.70) 1.2829** (2.43) 1.0417*** (4.70) 0.6928*** (6.94) 0.4587*** (6.40) 0.4038*** (7.94) 0.3946*** (7.61) 1.1333*** (8.00) 0.7076*** (5.97) 0.5542*** (4.77) 0.9843*** (2.90) 0.5665*** (8.24) 0.7363*** (6.52) 1.4576* (1.98) 5.4019*** (3.12)

1.0187*** (8.59) 1.0023*** (6.75) 0.7738*** (7.66) 0.8562*** (4.66) 0.8868*** (6.11) 0.8776*** (7.55) 0.8879*** (2.86) 1.2910*** (6.38) 1.1128*** (9.24) 0.8071*** (6.43) 0.7312*** (9.10) 0.7172*** (8.15) 1.1712*** (7.73) 1.1358*** (7.57) 0.8595*** (5.28) 0.8057*** (3.30) 0.9808*** (7.09) 1.0927*** (5.76) 0.7771* (2.08) 2.1182** (2.32)

0.78 [0.73]

5.68*** [0.00]

0.92 [0.44]

2 and σ 2 denote the squared change and volatility forecast for the kth 15-min period, respectively; k = 1, 2, . . ., 11, 12, 21, 22, . . ., 27, and 28, ˆ t,k For the tth trading day, rt,k denoting intervals close-to-9:15, 9:15–9:30, . . ., 11:30–11:45, 11:45–12:00, 12:00–14:15, 14:15–14:30, . . ., 15:30–15:45, and 15:45–16:00 h, respectively. r¯k2 is the average 2 of Models 1–4 across days t for each k and denote as σ ¯ˆ 2k . (.) denotes the robust t statistic for testing the squared changes across days t for each k. We calculate the average σˆ t,k significance of average values, adjusted by the Newey–West heteroskedasticity-autocorrelation-consistent (HAC) standard errors. The F statistic, F19,4894 , can be used to test the equality of average squared changes and equality of volatility forecasts across periods. [.] denotes the P-values of F19,4894 . *, **, and *** indicate the significance at the 10%, 5%, and 1% levels of significance, respectively. 2 denotes the squared standardized residuals for the kth 15-min period; k = 1, 2, . . ., 11, 12, 21, 22, . . ., 27, and 28, denoting intervals b For the tth trading day, ε ˆ 2t,k /σˆ t,k 2 ) is the average squared close-to-9:15, 9:15–9:30, . . ., 11:30–11:45, 11:45–12:00, 12:00–14:15, 14:15–14:30, . . ., 15:30–15:45, and 15:45–16:00, respectively. Avg (ˆε2t,k /σˆ t,k standardized residuals across days t for each k. (.) denotes the robust t statistic for testing the significance of average values, adjusted by the Newey–West heteroskedasticityautocorrelation-consistent (HAC) standard errors. The F statistic, F19,4894 , can be used to test the equality of average squared standardized residuals across periods. [.] denotes the P-values of F19,4894 . *, **, and *** indicate the significance at the 10%, 5%, and 1% levels of significance, respectively. a

Y.-F. Gau, M. Hua / The Quarterly Review of Economics and Finance 47 (2007) 135–158

Panel B. Average of squared standardized residualsb 1 6.7908*** (6.32) 2 0.3389*** (5.93) 3 0.3146*** (5.71) 4 0.4777*** (4.30) 5 0.3152*** (5.45) 6 0.3891*** (5.48) 7 1.1661* (1.80) 8 0.6536*** (3.64) 9 0.3790*** (6.00) 10 0.3182*** (4.10) 11 0.2429*** (6.94) 12 0.2177*** (6.88) 21 1.1006*** (5.94) 22 0.3829*** (5.18) 23 0.3229*** (6.61) 24 0.5591*** (2.88) 25 0.3439*** (7.16) 26 0.4091*** (6.15) 27 1.2661*** (1.40) 28 4.0138** (2.23)

2 ) Model 2 Avg(ˆε2t,k /σˆ t,k

153

154

Y.-F. Gau, M. Hua / The Quarterly Review of Economics and Finance 47 (2007) 135–158

Fig. 4. Average of fitted volatility across all 15-min periods (January 4, 2001 to December 31, 2001). Notes: The kth 15-min period corresponds to each 15-min mark during 9:00–16:00 h. For k = 1, 2, . . ., 11, 12, 21, 22, . . ., 27, and 28, it denotes time marks at 9:15, 9:30, . . ., 11:45, 12:00, 14:15, 14:30, . . ., 15:45, and 16:00 h, respectively. 2 2 = w + α ε2 Model 1: σt,k 1 t,k−1 + β1 σt,k−1 0 2 = Model 2: σt,k

Model 3: Model 4:

12 

wj Tj,k +

28

2 w T + α1 ε2t,k−1 + α2 ε2t,k−2 + β1 σt,k−1 j=21 j j,k TW 2 2 2 = w0 + α1 εt,k−1 + α2 εt,k−2 + α3 εt,k−3 + γvt,k + λ1 NEWSt,k + λ2 NEWSUS t,k 12 28 2 2 2 = w T + w T + α ε + α ε + α ε + γv + λ1 NEWSTW j j,k j j,k 1 2 3 t,k t,k t,k−1 t,k−2 t,k−3 j=1 j=21 US λ2 NEWSt,k

2 σt,k 2 σt,k

j=1



+

residuals from the simple GARCH model (i.e., Model 1) remains the similar shape as the absolute changes shown in Fig. 1. Once the explicit time-of-day seasonality is considered into Model 2, the squared standardized residuals no longer appear high at the opening, whereas they still remain slightly high at the close and at the open of the afternoon session. If we consider only the effects of unexpected volume innovations and public announcements from Taiwan and the U.S., without considering the time-of-day seasonality in Model 3, the resulting squared standardized residuals drop off at the market open, but continue to be similar to the shape associated with Model 1 for the remaining time of the day. After incorporating the ARCH terms, multiplicative time-of-day dummies, unexpected volume shocks, and counts of Taiwan and U.S. news announcements into Model 4, the resulting squared standardized residuals stay smooth for most of the time, with the exception of a small peak at the close of the market. The above evidence suggests that, other than lagged return innovations, unexpected volume shocks, public news, and explicit time-of-day periodicity, there remain some factors that could influence the intraday NTD/USD exchange rate volatility. For example, previous studies have concluded that central bank interventions can affect the exchange rate volatility (cf. Chang & Taylor,

Y.-F. Gau, M. Hua / The Quarterly Review of Economics and Finance 47 (2007) 135–158

155

Fig. 5. Average of squared standardized residuals across all 15-min periods (January 4, 2001 to December 31, 2001). Notes: The kth 15-min period corresponds to each 15-min mark during 9:00–16:00 h. For k = 1, 2, . . ., 11, 12, 21, 22, . . ., 27, and 28, it denotes time marks at 9:15, 9:30, . . ., 11:45, 12:00, 14:15, 14:30, . . ., 15:45, and 16:00 h, respectively. 2 = w + α ε2 2 Model 1: σt,k 0 1 t,k−1 + β1 σt,k−1 2 = Model 2: σt,k

Model 3: Model 4:

12 

wj Tj,k +

28

2 w T + α1 ε2t,k−1 + α2 ε2t,k−2 + β1 σt,k−1 j=21 j j,k TW 2 2 2 = w0 + α1 εt,k−1 + α2 εt,k−2 + α3 εt,k−3 + γvt,k + λ1 NEWSt,k + λ2 NEWSUS t,k 12 28 = w T + w T + α1 ε2t,k−1 + α2 ε2t,k−2 + α3 ε2t,k−3 + γvt,k + λ1 NEWSTW t,k j=1 j j,k j=21 j j,k λ2 NEWSUS t,k

2 σt,k 2 σt,k

j=1



+

1998; Dominguez, 1998, 2003). Intervention operations from the Central Bank of China (CBC) are very frequently seen at the Taipei FX market. However, the data of exact timing and intraday transaction volumes of the CBC are not officially released and cannot be observed publicly. The only possible source of information about CBC intervention operations is the reports from the newspapers on the next day after the CBC bought or sold USD at the Taipei FX market. There may be reporting errors attributed to wrong market information about the concealed operations of CBC interventions. The CBC has been notoriously intervened the exchange rate with actively open operations in the FX market. The newspapers reports are matched with open operations but cannot reveal the secret transactions of the CBC. Due to the unavailability of intraday data on the central bank intervention operations, we are not able to analyze the response of intraday NTD/USD volatility to the CBC interventions. However, we can investigate how the central bank interventions affect the daily NTD/USD volatility. Using daily observations on news reports about the CBC intervention operations, we create a binary indicator variable that equals 1 as the CBC intervention operations are reported by the newspapers; 0 otherwise. We calculate the daily volatility using the realized volatility (Andersen et al., 2003),

156

Y.-F. Gau, M. Hua / The Quarterly Review of Economics and Finance 47 (2007) 135–158

Table 11 Impacts of Central Bank intervention operations on the realized volatility of NTD/USD (January 4, 2001 to December 31, 2001) Coefficient

Estimate

HAC standard error

Robust t

c0 c1 c2

0.046*

0.022 0.032 0.022

2.090 1.688 13.455

0.054* 0.296***

s

12

28

c σ 2 + υt where σt2 = rˆ 2 + rˆ 2 , Interventiont = 1 if the newspaσt2 = c0 + c1 Interventiont + i=1 i+1 t−i k=1 t,k k=21 t,k pers report that central bank interventions are operated on day t, 0 otherwise. υt is an i.i.d. white noise. Notes: The associated Akaike information criterion = 1.107031, Schwarz information criterion = 1.149904. The HAC standard errors denote the Newey–West heteroskedasticity-autocorrelation-consistent standard errors. *, **, and *** indicate the significance at the 10%, 5%, and 1% levels of significance, respectively.

that is, summing deseasonalized squared-changes during day t to obtain the volatility  all 15-min 28 2 + 2 r ˆ of day t: σt2 = 12 k=1 t,k k=21 rˆt,k . Table 11 reports the estimation results based on the binary indicator variable of the central bank intervention reported in the newspapers. We find that the central bank intervention operations reported by the newspapers essentially have a positive and significant effect on the daily NTD/USD realized volatility. 5. Conclusion By comparing with other simpler models with alone information sets, we find that the simultaneous GARCH model, that incorporates explicit time-of-day seasonality factors, lagged squared return innovations, counts of news related to the U.S. and Taiwan, and unexpected volume innovations, performs best in capturing the time-varying dynamics of the intraday NTD/USD exchange rate volatility. However, after the news effects and response to the unexpected volume shocks are controlled for, the two subdued but still significant spikes of volatility at the market closing and at the opening of the afternoon trading session are still observed. This indicates that some other factors like, for example, the central bank intervention operations, may have significant influence on the intraday NTD/USD volatility. We separate news events into categories by countries and find that both counts of news related to the U.S. and Taiwan, respectively, have significant and positive impacts on the intraday NTD/USD volatility. Although the total news count measures some less relevant reports, it is the most comprehensive news variable available. The results of estimation show that the quantitative impact of the count of news related to the U.S. is larger than that related to Taiwan. There is an interesting question of the NTD/USD exchange rate volatility related to central bank intervention operations in the Taipei FX market. Although the intraday intervention data are not available from the central bank, we collect the daily news reports about the central bank intervention operations and examine the impact of central bank intervention based on the daily realized volatility. The results indicate that the central bank intervention operations in the Taipei FX market have a significantly positive influence on the daily NTD/USD realized volatility. Acknowledgement The authors would like to thank the editors and an anonymous referee for their valuable comments and suggestions. Any errors or omissions are our responsibility.

Y.-F. Gau, M. Hua / The Quarterly Review of Economics and Finance 47 (2007) 135–158

157

References Amihud, Y., & Mendelson, H. (1991). Volatility, efficiency, and trading: Evidence from the Japanese stock market. Japan and the World Economy, 1, 341–370. Andersen, T. G., & Bollerslev, T. (1998). DM-Dollar volatility: Intraday activity patterns, macroeconomic announcements, and longer run dependencies. Journal of Finance, 53, 219–265. Andersen, T. G., Bollerslev, T., & Cai, J. (2000). Intraday and interday volatility in the Japanese stock market. Journal of International Financial Markets, Institutions and Money, 10, 107–130. Andersen, T. G., Bollerslev, T., Diebold, F. X., & Labys, P. (2003). Modeling and forecasting realized volatility. Econometrica, 71, 525–579. Baillie, R., & Bollerslev, T. (1991). Intraday and intermarket volatility in foreign exchange rates. Review of Economic Studies, 58, 565–585. Berry, T. D., & Howe, K. M. (1994). Public information arrival. Journal of Finance, 49, 1331–1346. Bessembinder, H. (1994). Bid-ask spreads in the interbank foreign exchange markets. Journal of Financial Economics, 35, 317–348. Bollerslev, T. (1986). Generalized autoregressive conditional heteroscedasticity. Journal of Econometrics, 31, 307–327. Bollerslev, T., & Ghysels, E. (1996). Periodic autoregressive conditional heteroscedasticity. Journal of Business and Economic Statistics, 14, 139–151. Bollerslev, T., & Wooldridge, J. (1992). Quais-maximum likelihood estimation and inference in dynamic models with time varying covariance. Econometric Reviews, 11, 143–172. Chang, Y.-C., & Taylor, S. J. (1998). Intraday effects of foreign exchange intervention by the bank of Japan. Journal of International Money and Finance, 17, 191–210. Chang, Y.-C., & Taylor, S. J. (2003). Information arrivals and intraday exchange rate volatility. Journal of International Financial Markets, Institutions and Money, 13, 85–112. Cornett, M. M., Schwarz, T. V., & Szakmary, A. C. (1995). Seasonalities and intraday return patterns in the foreign currency futures market. Journal of Banking and Finance, 19, 843–869. Dacorogna, M. M., Muller, U. A., Nagler, R. J., Olsen, R. B., & Pictet, O. V. (1993). A geographical model for the daily and weekly seasonal volatility in the foreign exchange market. Journal of International Money and Finance, 12, 413–438. Dominguez, K. M. (1998). Central bank intervention and exchange rate volatility. Journal of International Money and Finance, 17, 161–190. Dominguez, K. M. (2003). The market microstructure of central bank intervention. Journal of International Economics, 59, 25–45. Ederington, L. H., & Lee, J. H. (2001). Intraday volatility in interest-rate and foreign-exchange markets: ARCH, announcement, and seasonality effects. Journal of Futures Markets, 21, 517–552. Engle, R. F. (1982). Autoregressive conditional heteroskedasticity with estimates of the variance of U.K. inflation. Econometrica, 50, 987–1008. Flood, M. D. (1994). Market structure and inefficiency in the foreign exchange market. Journal of International Money and Finance, 13, 131–158. Gau, Y.-F. (2005). Intraday volatility in the Taipei FX market. Pacific-Basin Finance Journal, 13, 471–487. Gau, Y.-F., & Hua, M. (2004). Public information, private information, inventory control, and volatility of intraday NTD/USD exchange rates. Applied Economics Letters, 11, 263–266. Han, L.-M., Kling, J. L., & Sell, C. W. (1999). Foreign exchange futures volatility: Day-of-the-week, intraday, and maturity patterns in the presence of macroeconomic announcements. Journal of Futures Markets, 19, 665–693. Harvey, C. R., & Huang, R. D. (1991). Volatility in the foreign currency futures market. Review of Financial Studies, 4, 543–569. Ito, T., & Lin, W.-L. (1992). Lunch break and intraday volatility of stock returns. Economics Letters, 39, 85–90. Jorion, P. (1996). Risk and turnover in the foreign exchange market. In J. Frankel, G. Galli, & A. Giovannini (Eds.), The microstructure of foreign exchange markets (pp. 19–40). Chicago: University of Chicago Press. Low, A., & Muthuswamy, J. (1996). Information flows in high frequency exchange rates. In C. Dunis (Ed.), Forecasting financial markets (pp. 1–30). Sussex: John Wiley and Sons Ltd. Lyons, R. K. (1995). Tests of microstructural hypotheses in the foreign exchange market. Journal of Financial Economics, 39, 321–351. Lyons, R. K. (1996). Foreign exchange volume: Sound and fury signifying nothing? In J. Frankel, G. Galli, & A. Giovannini (Eds.), The microstructure of foreign exchange markets (pp. 183–206). Chicago: University of Chicago Press. Lyons, R. K. (2001). The microstructure approach to exchange rates. Cambridge: MIT Press.

158

Y.-F. Gau, M. Hua / The Quarterly Review of Economics and Finance 47 (2007) 135–158

Melvin, M., & Yin, X. (2000). Public information arrivals, exchange rate volatility and quote frequency. Economic Journal, 100, 644–661. Mitchell, M. L., & Mulherin, J. H. (1994). The impact of public information on the stock market. Journal of Finance, 49, 923–949. Newey, W., & West, K. (1987). A simple, positive semi-definite, heteroskedasticity and autocorrelation consistent covariance matrix. Econometrica, 55, 703–708. Ross, S. A. (1989). Information and volatility: The no-arbitrage martingale approach to timing and resolution irrelevancy. Journal of Finance, 46, 1–17. Stoll, H., & Whaley, R. (1990). Stock market structure and volatility. Review of Financial Studies, 3, 37–71. Taylor, S. J., & Xu, X. (1997). The incremental volatility information in one million foreign exchange quotations. Journal of Empirical Finance, 4, 317–340. Tang, G., & Lui, D. (2002). Intraday and intraweek volatility patterns of Hang Seng index and index futures, and a test of the wait-to-trade hypothesis. Pacific-Basin Finance Journal, 10, 475–495.