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40 K. Bien et al. Bivariate model specification The copula concept allows one to model the bivariate density without forcing the direction of the dependence upon the data generating process. We choose the standard Gaussian copula function since its single dependency parameter can easily be estimated and it allows for a straightforward sampling algorithm of variables from the bivariate conditional density, which is necessary to assess the goodnessof-fit of our specification. The Gaussian copula is given by C(ut,vt; ρ) = � �−1 (ut) � �−1 (vt) −∞ −∞ 1 2π � � 2ρuv − u2 − v2 exp 1 − ρ2 2(1 − ρ2 � dudv, ) (10) where ut = F(y1t|Ft−1), vt = F(y2t|Ft−1) and ρ denotes the timeinvariant parameter of the Gaussian copula, which is the correlation between � −1 (ut) and � −1 (vt). Since ρ is chosen to be fixed over time C(F(y1t|Ft−1), F(y2t|Ft−1)|Ft−1) = C(F(y1t|Ft−1), F(y2t|Ft−1)) and the conditional bivariate density of Y1t and Y2t can be inferred from Eq. (3) as f(y1t,y2t|Ft−1) = C(F(y1t|Ft−1), F(y2t|Ft−1)) − C(F(y1t − 1|Ft−1), F(y2|Ft−1)) − C(F(y1t|Ft−1), F(y2t − 1|Ft−1)) + C(F(y1t − 1|Ft−1), F(y2t − 1|Ft−1)). (11) The cumulative distribution function F(y1t|Ft−1) (and analogously F(y2t|Ft−1)) can be written as F(y1t|Ft−1) = y1t � k=−50 π 1 −1t 1{k0} · fs(|k||k �= 0, Ft−1) (1−1{k=0}) where we set the lower bound of the summation to −50 and where the probabilities of the downward, zero and upward movement of the exchange rate are specified with the logistic link function, as shown in Eq. (4), and the density for the absolute value of the change is specified along the conditional NegBin distribution, as presented in Eq. (8). Estimation and simulation results Our estimates are obtained by a one-step maximum likelihood estimation, whereas the log-likelihood function is taken as a logarithm of the bivariate density presented in the Eq. (11). Estimation results for the ACM part of ICH model are presented in Table 1 and for the GLARMA part of the ICH model in Table 2. The estimate of the dependency parameter ˆρ for the Gaussian copula equals to 0.3588 with standard
A multivariate integer count hurdle model 41 Table 1 ML estimates of the ACM-ARMA part of ICH model. Multivariate Ljung-Box statistic for L lags, Q(L), is computed as Q(L) = n � L ℓ=1 tr � Ŵ(ℓ) ′ Ŵ(0) −1 Ŵ(ℓ)Ŵ(0) −1� , where Ŵ(ℓ) = � ni=ℓ+1 νtν ′ t−ℓ /(n − ℓ − 1). Under the null hypothesis, Q(L) is asymptotically χ 2 -distributed with degrees of freedom equal to the difference between 4 times L and the number of parameters to be estimated EUR/GBP EUR/USD Parameter Estimate Standard deviation Estimate Standard deviation µ 0.0639 0.0177 0.0837 0.0222 b (1) (11) b 0.6583 0.0856 0.4518 0.0426 (1) (12) a 0.2910 0.0540 0.5054 0.0635 (1) 11 a 0.1269 0.0324 0.2535 0.0465 (1) 12 a 0.2059 0.0323 0.3739 0.0472 (1) 21 a 0.2009 0.0271 0.3350 0.0466 (1) 22 0.0921 0.0312 0.2586 0.0477 Resid. mean Resid. variance (−0.003, 0.002) � � 0.655 0.803 0.803 2.631 (0.003, 0.009) � � 1.413 2.306 2.306 4.721 Resid. Q(20) 72.359 (0.532) 89.054 (0.111) Resid. Q(30) 102.246 (0.777) 122.068 (0.285) Log-lik. −6.2125 Table 2 ML estimates of the GLARMA part of ICH model EUR/GBP EUR/USD Parameter Estimate Standard deviation Estimate Standard deviation κ 0.5 0.7862 0.0192 0.7952 0.0130 ˜µ 0.3363 0.0438 0.7179 0.0814 β1 0.6567 0.0335 0.6085 0.0428 α1 0.1675 0.0100 0.1455 0.0097 ν0 0.0981 0.0633 −0.0396 0.0510 ν1 −0.0712 0.0117 −0.0430 0.0100 ν2 −0.0060 0.0091 0.0388 0.0099 ν3 −0.0501 0.0105 −0.0258 0.0093 ν4 0.0852 0.0238 0.0954 0.0215 ν5 −0.0100 0.0129 −0.0234 0.0120 ν6 0.0449 0.0115 0.0297 0.0108 Resid. mean 0.013 0.007 Resid. variance 1.001 1.025 Resid. Q(20) 26.408 (0.067) 42.332 (0.001) Resid. Q(30) 64.997 (0.000) 87.641 (0.000) Log-lik. −6.2125
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 48 and 49: 42 K. Bien et al. deviation 0.0099,
Page 50 and 51: 44 K. Bien et al. - Set ˆzt = Âxt
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
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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
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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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