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192 the invertibility condition holds. The proposed modified test procedure works as follows: i) Construct u u i as the probability that Yi is less than the actually observed price change yi: u u i bPr½YiyijF i 1; ZiŠ ¼ Xyi bPr½Yi¼jjF i 1; ZiŠ (4.1) j¼ 1 for each i: 1→n, and construct u i l as the probability that Yi is less than the actually observed price change minus one: u l i bPr½Yiyi1jF i 1; ZiŠ ¼ Xyi 1 bPr½Yi¼jjF i 1; ZiŠ: (4.2) j¼ 1 ii) Then use this sequence of probabilities to generate a sequence of artificial random numbers from the conditional uniform distributions on the intervals [ui l , u i u ], i.e., ui U u l i ; uu i ; i : 1 ! n: (4.3) If the model is correctly specified, the u i’s drawn under the true parameter values (to calculate u i l and ui u ) are i.i.d. following a uniform distribution on the interval [0,1] (see the Appendix). Moreover, one can map the u i’s into a standard normal distribution using u i* ≡ Φ −1 (u i). Under the correct model, the normalized u i*’s are i.i.d. standard normal distributed. JBX HAL R. Liesenfeld et al. Fig. 10 Autocorrelation function of the density forecast variable ui* for Jack in the Box Inc. (JBX) and HalliburtonpCompany ffiffi (HAL). The dashed lines mark off the approximate 99% confidence interval 2:58 n
Modelling financial transaction price movements: a dynamic integer count data model 193 JBX HAL Fig. 11 Autocorrelation function of the squared density forecast variable ui* for Jack in the Box Inc. (JBX) and Halliburton pCompany ffiffiffi (HAL). The dashed lines mark off the approximate 99% confidence interval 2:58 n Figures 10 and 11 plot the autocorrelation function for a sequence of normalized residuals u i* and of squared normalized residuals (u i*) 2 . The plots indicate that for both stocks there is nearly no significant autocorrelation left in the first and second moments. Table 6 represents summary statistics of the normalized residuals. They are computed as the corresponding sample means based on 1,000 repeated draws of the trajectory {ui*, i: 1→N}. For JBX the Jarque-Bera statistic indicates that we cannot reject the null of a normal distribution for u i*, whereas for HAL we have to reject the null at 1% significance level. The quantile–quantile (QQ) plot of a sequence of u i*’s against the standard normal distribution displayed in Fig. 12 reveals that the ICH model approximates the distributional properties of the transaction price changes for both stocks fairly well. However, the deviation from normality in the tails of the distribution of the ui*’s indicates slight difficulties characterizing extreme price changes appropriately. Table 6 Properties of the density forecast variable u i* for Jack in the Box Inc. (JBX) and Halliburton Company (HAL) JBX HAL Mean −0.003 [0.0000] −0.001 [0.0000] Variance 1.000 [0.0000] 1.002 [0.0000] Skewness 0.027 [0.0000] 0.029 [0.0000] Kurtosis 2.989 [0.0000] 3.048 [0.0000] Jarque-Bera 0.793 [0.0006] 9.910 [0.0019] p-value (0.6727) (0.007) The values of the statistics are sample means based upon 1,000 repeated draws of {u i*, i: 1→N}. Values in brackets report the sampling standard error, due to repeated sampling of {ui*, i:1→N}in the density forecast procedure
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High Frequency Financial Econometri
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Prof. Luc Bauwens CORE Voie du Roma
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vi Contents Intraday stock prices,
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2 L. Bauwens et al. component nicel
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4 L. Bauwens et al. but provides al
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Luc Bauwens . Dagfinn Rime . Genaro
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Exchange rate volatility and the mi
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32 K. Bien et al. Although economet
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34 K. Bien et al. 2.1 Copula functi
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36 K. Bien et al. and x k t ≡ (xk
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38 K. Bien et al. Fig. 3 Multivaria
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40 K. Bien et al. Bivariate model s
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42 K. Bien et al. deviation 0.0099,
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44 K. Bien et al. - Set ˆzt = Âxt
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46 K. Bien et al. % Frequency −0.
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48 K. Bien et al. References Amilon
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50 1 Introduction A. Escribano and
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52 A. Escribano and R. Pascual Jang
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54 A. Escribano and R. Pascual the
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56 The generating processes of mark
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58 with AtðLÞ ¼ 0 B @ 1 ð ÞAab
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60 A. Escribano and R. Pascual cros
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62 Hasbrouck (1991). The system is
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64 unitary seller-initiated shock (
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66 6.1 Estimation of the baseline m
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Table 2 The base-line VEC model for
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70 Table 3 Simulation of the base-l
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72 revert towards narrow levels. As
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Table 5 Impulse-response functions
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76 We also show that NYSE buyer-ini
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78 As 0 < a m < 1; L ð Þ ¼ 1 a m
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80 NYSE 2000 Stocks AOL America Onl
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82 A. Escribano and R. Pascual Madh
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84 1 Introduction S. Frey, J. Gramm
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86 develops the empirical methodolo
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Table 1 Sample descriptives Company
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90 comparability across stocks, we
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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
Page 148 and 149: Table 1 Order book characteristics
Page 150 and 151: 144 data covering the normal tradin
Page 152 and 153: 146 Table 3 Descriptive statistics
Page 154 and 155: Table 4 Fully specified ACI models
Page 156 and 157: Table 4 (continued) BHP NAB NCP TLS
Page 158 and 159: Table 5 ACI models without dynamics
Page 162 and 163: Table 6 ACI models without covariat
Page 166 and 167: 160 specification which includes or
Page 168 and 169: 162 5.2.5 The impact of the bid-ask
Page 170 and 171: 164 contrast to those of Pascual an
Page 173 and 174: Roman Liesenfeld . Ingmar Nolte . W
Page 175 and 176: Modelling financial transaction pri
Page 197: Modelling financial transaction pri
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Page 206 and 207: 200 W. B. Omrane, H. V. Oppens anal
Page 208 and 209: 202 W. B. Omrane, H. V. Oppens of s
Page 210 and 211: 204 The extrema detection method ba
Page 212 and 213: 206 price 0.8565 0.8575 0.8585 0.85
Page 214 and 215: 208 We distinguish three possible c
Page 216 and 217: 210 originates. The most active tra
Page 218 and 219: 212 Table 2 Predictability of the c
Page 220 and 221: 214 6 Conclusion Using 5-min euro/d
Page 222 and 223: 216 where σk is the standard devia
Page 224 and 225: 218 If we meet a particular case su
Page 226 and 227: 220 C.5. Triple bottom (TB) TB is c
Page 228 and 229: 222 References W. B. Omrane, H. V.
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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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