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44 K. Bien et al. – Set ˆzt = Âxt – Set û1t = �(ˆz1t) and û2t = �(ˆz2t) where � denotes the univariate standard normal distribution function – Set ˆY1t = ˆF −1 1 (û1|Ft−1)) and ˆY2t = ˆF −1 2 (û2|Ft−1)) where ˆF1 and ˆF2 denote the estimated marginal cumulative distribution functions of the EUR/GBP and the EUR/USD changes, respectively Figure 8 contains the plots of the unconditional histograms of the simulated marginal processes. Their shapes seem to agree with those of the raw data series already presented in Fig. 2. Fig. 10 Bivariate histogram of the positive differences between the empirical and the simulated bivariate histogram of the EUR/GBP and the EUR/USD exchange rate changes. Fig. 11 Bivariate histogram of the absolute values of the negative differences between the empirical and the simulated bivariate histogram of the the EUR/GBPand the EUR/USD exchange rate changes.
A multivariate integer count hurdle model 45 The unconditional bivariate histogram of the simulated time series is presented in Fig. 9. Although the positive dependence between the marginal processes is reflected, the shape of the histogram does not correspond to the empirical one in full (see Fig. 1). In particular the frequency of the outcome (0, 0) has been considerably underestimated. We compute the differences between the histograms of the empirical and the simulated data to infer in which points (i,j) the observed and the estimated probabilities disagree. To assess these differences graphically, we plotted in Fig. 10 only positive differences and in Fig. 11 only absolute negative differences. Besides the outcome probability of (0, 0), the probabilities for points (i,j) concentrated around (0,0) are a little bit underestimated (positive differences in Fig. 10) as well, and the probabilities for points (i,j) which are a little further away from (0,0) are a little overestimated (negative differences in Fig. 11). Thus, we conclude that we underestimate the kurtosis of the empirical distribution. The real data is much more concentrated in the outcome (0,0), as well as evidencing much fatter tails. There is a clear signal for a tail dependency in the data generating process, as the extreme positive or negative movements of the exchange rates take place much more often than could be explained by a standard Gaussian copula function (see Fig. 10). Additionally, we can address the goodness-of-fit of the conditional bivariate density by considering the bivariate autocorrelation function of the residual series ˆεt = (ˆε 1 t , ˆε2 t )′ depicted in Fig. 14 and the quantile–quantile (QQ) plots of the modified density forecast test variables for the implied marginal processes in Fig. 12. We have mapped these modified density forecast test variables into a standard normal distribution, so that under the correct model specification, these normalized variables should be i.i.d. standard normally distributed. Figure 13 plots the autocorrelation functions of these normalized density forecast variables. Both plots indicate that the processes are almost uncorrelated. The deviation from normality, especially for the EUR/USD exchange rate changes and in the upper tail of the normalized density forecast variables indicated by the QQ-plots, reveals that our specification has difficulties to characterize extreme exchange rate changes appropriately. The bivariate autocorrelation function of the residual series (Fig. 14) shows significant cross-correlations at lag 1. Although, we manage to explain a large Empirical Qunatiles −5 −3 −1 1 2 3 4 5 −4 EUR/GBP EUR/USD Empirical Qunatiles −5 −3 −1 1 2 3 4 5 −2 0 1 2 3 4 5 −4 Std. Normal Quantiles Fig. 12 QQ plot of the normalized density forecast variables. −2 0 1 2 3 4 5 Std. Normal Quantiles
Page 1 and 2: High Frequency Financial Econometri
Page 3 and 4: Prof. Luc Bauwens CORE Voie du Roma
Page 5: vi Contents Intraday stock prices,
Page 8 and 9: 2 L. Bauwens et al. component nicel
Page 10 and 11: 4 L. Bauwens et al. but provides al
Page 13 and 14: Luc Bauwens . Dagfinn Rime . Genaro
Page 15 and 16: Exchange rate volatility and the mi
Page 35: Exchange rate volatility and the mi
Page 38 and 39: 32 K. Bien et al. Although economet
Page 40 and 41: 34 K. Bien et al. 2.1 Copula functi
Page 42 and 43: 36 K. Bien et al. and x k t ≡ (xk
Page 44 and 45: 38 K. Bien et al. Fig. 3 Multivaria
Page 46 and 47: 40 K. Bien et al. Bivariate model s
Page 48 and 49: 42 K. Bien et al. deviation 0.0099,
Page 52 and 53: 46 K. Bien et al. % Frequency −0.
Page 54 and 55: 48 K. Bien et al. References Amilon
Page 56 and 57: 50 1 Introduction A. Escribano and
Page 58 and 59: 52 A. Escribano and R. Pascual Jang
Page 60 and 61: 54 A. Escribano and R. Pascual the
Page 62 and 63: 56 The generating processes of mark
Page 64 and 65: 58 with AtðLÞ ¼ 0 B @ 1 ð ÞAab
Page 66 and 67: 60 A. Escribano and R. Pascual cros
Page 68 and 69: 62 Hasbrouck (1991). The system is
Page 70 and 71: 64 unitary seller-initiated shock (
Page 72 and 73: 66 6.1 Estimation of the baseline m
Page 74 and 75: Table 2 The base-line VEC model for
Page 76 and 77: 70 Table 3 Simulation of the base-l
Page 78 and 79: 72 revert towards narrow levels. As
Page 80 and 81: Table 5 Impulse-response functions
Page 82 and 83: 76 We also show that NYSE buyer-ini
Page 84 and 85: 78 As 0 < a m < 1; L ð Þ ¼ 1 a m
Page 86 and 87: 80 NYSE 2000 Stocks AOL America Onl
Page 88 and 89: 82 A. Escribano and R. Pascual Madh
Page 90 and 91: 84 1 Introduction S. Frey, J. Gramm
Page 92 and 93: 86 develops the empirical methodolo
Page 94 and 95: Table 1 Sample descriptives Company
Page 96 and 97: 90 comparability across stocks, we
Page 98 and 99: 92 subtracting the deviations from
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94 market order distribution that c
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96 Table 2 First stage GMM results
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Table 4 First stage GMM results bas
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100 S. Frey, J. Grammig quotes on e
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102 S. Frey, J. Grammig approximate
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104 To obtain the estimates in the
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106 Hence, using the liquidity stat
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108 In the main text we discuss the
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Pierre Giot . Joachim Grammig How l
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How large is liquidity risk in an a
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134 A. D. Hall, N. Hautsch In this
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136 includes order book variables,
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138 An important determinant of liq
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140 The innovation term ei is compu
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Table 1 Order book characteristics
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144 data covering the normal tradin
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146 Table 3 Descriptive statistics
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Table 4 Fully specified ACI models
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Table 4 (continued) BHP NAB NCP TLS
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Table 5 ACI models without dynamics
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Table 6 ACI models without covariat
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160 specification which includes or
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162 5.2.5 The impact of the bid-ask
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164 contrast to those of Pascual an
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Roman Liesenfeld . Ingmar Nolte . W
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Modelling financial transaction pri
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200 W. B. Omrane, H. V. Oppens anal
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202 W. B. Omrane, H. V. Oppens of s
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204 The extrema detection method ba
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206 price 0.8565 0.8575 0.8585 0.85
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208 We distinguish three possible c
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210 originates. The most active tra
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212 Table 2 Predictability of the c
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214 6 Conclusion Using 5-min euro/d
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216 where σk is the standard devia
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218 If we meet a particular case su
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220 C.5. Triple bottom (TB) TB is c
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222 References W. B. Omrane, H. V.
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Juan M. Rodríguez-Poo · David Ver
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Semiparametric estimation for finan
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254 between price changes and durat
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256 simply aggregated. Even after a
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258 is to make use of the fact that
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260 together with the restrictions
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Table 3 Estimated probabilities of
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264 A. S. Tay, C. Ting More interes
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Table 4 Estimated probabilities of
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268 Acknowledgements Tay gratefully
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270 This paper explores the effect
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272 contrast, price responses to po
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274 Fig. 1 Continuous line is the T
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276 the β’s can form a convex sh
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278 fixing some intervals around th
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280 . That is for a given absolute
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282 30 25 20 15 10 5 CC UNEMW ISM U
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Appendix Table A1 Consumer confiden
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Table A3 Non-farm payrolls • ✓
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Table A5 Weekly unemployment claims
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290 Table A8 Retail sales • ✓ 1
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292 Table A12 GDP, BI, TB and PI Re
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294 V. Voev with the problem of how
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296 V. Voev 2.1 A sample covariance
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298 V. Voev Using the equicorrelate
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300 V. Voev where �kl(t) is the (
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302 V. Voev where hkl,k ′ l ′ i
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304 V. Voev is 1.9%. From the daily
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306 V. Voev ACF ACF ACF 0.5 0.5 0.5
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308 V. Voev autocorrelated. Indeed,
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310 V. Voev 5 Conclusion Table 2 Ro
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312 V. Voev Engle R (1982) Autoregr
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