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36 K. Bien et al. and x k t ≡ (xk −1t ,xk 1t )′ ⎧ ⎨ (1,0) = ⎩ ′ if Ykt < 0 (0,0) ′ if Ykt = 0 (0,1) ′ if Ykt > 0, denotes the state vector, whether Ykt decreases, stays equal or increases at time t. Thus, ξk t represents the standardized state vector xk t . The conditional density of the size process is modelled with an at-zerotruncated Negative Binomial (NegBin) distribution: fs(|ykt||Ykt �= 0, Ft−1) ≡ Ŵ(κk +|ykt|) Ŵ(κk ��κ k + ωk t )Ŵ(|ykt|+1) κk � κ k (7) �−1� ωk t − 1 ωk t + κk �|ykt| , (8) where |ykt|∈N \{0}, κk > 0 denotes the dispersion parameter and scaling parameter ωk t is parameterized using the exponential link function with a generalized autoregressive moving average model (GLARMA(p,q)) of Shephard (1995) in the following way: ln ω k t = δ ˜Dt + ˜λ k t with ˜λ k t =˜µ + Sk (ν,τ,K)+ β1 ˜λ k t−1 + α1 ˜ξ k t−1 . where ˜Dt ∈{−1, 1} indicates a negative or positive value of Ykt at time t with the corresponding coefficient denoted by δ. ˜µ denotes the constant term. β1 as well as α1 denote coefficients and ˜ξ k t being constructed as ˜ξ k t ≡ |Ykt|−E(|Ykt||Ykt �= 0, Ft−1) , V(|Ykt||Ykt �= 0, Ft−1) 1/2 is the innovation term that drives the GLARMA model in λk t . The conditional moments of the at-zero-truncated NegBin distribution are given by E(|Ykt||Ykt �= 0, Ft−1) = ωk t 1 − ϑk , t V(|Ykt||Ykt �= 0, Ft−1) = ωk t 1 − ϑ k t � − where ϑ k t is given by ϑ k t =[κk /(κ k + ω k t )]κ . S k (ν,τ,K)≡ ν0τ + ω k t (1 − ϑ k t ) �2 � ϑ k t − 1 − ϑk t κk � , K� ν2l−1 sin(2π(2l − 1)τ) + ν2l cos(2π(2l)τ) (9) l=1 is a Fourier flexible form used to capture diurnal seasonality, where τ is the intraday time standardized to [0, 1] and ν isa2K + 1 dimensional parameter vector.
A multivariate integer count hurdle model 37 3 Bivariate modelling of exchange rate changes Data description We apply our model to 1 min mid quote changes of the EUR/GBP and the EUR/USD exchange rates. The data has been provided by Olsen Financial Technologies and contains quotes from the electronic foreign exchange interbank market. The period under study spreads between October 6 (Monday), 2003, 0:01 EST, and October 10 (Friday), 2003, 17:00 EST, resulting in 6,780 observations for both time series. The sampling frequency of 1 min is, on the one side, sufficiently high to maintain the discrete nature of the data, whereas on the other side, it is low enough to preserve a significant correlation between the two marginal processes. The histograms of the two marginal processes are presented in the Fig. 2. Both distributions reveal a fairly large support between −20 and 20 ticks for the EUR/GBP and between −30 and 30 ticks for the more volatile EUR/USD exchange rate. Thus, the discreteness of the quote changes combined with a high number of zero quote movements (about 13% for the EUR/GBP and about 7.5% for the EUR/USD) justifies the ICH-model approach of Liesenfeld et al. (2006). We associate Y1t and Y2t with the changes of the EUR/GBP and the EUR/USD currency pairs, respectively, and present in Figs. 3 and 4 the dynamic features of these variables in the form of the multivariate autocorrelograms of the vectors x 1 t and x2 t , which indicate the change of the direction of the EUR/GBP and the EUR/USD exchange rates, as defined in Eq. (7). We observe that there is a certain dynamic pattern, which should be explained by theACM part of the ICH model.As indicated by the negative first-order autocorrelation and the positive first-order cross correlation coefficients, the probability of an upward movement of each exchange rate following a downward movement is significantly more probable than two subsequent negative or positive movements. In Fig. 5 the autocorrelograms for the absolute value of the non-zero exchange rate changes are presented. The high degree of persistence characterizing the processes should be explained by the GLARMA part of the ICH model. The interdependence between the two marginal processes can be seen from Fig. 6, where we plotted the multivariate autocorrelogram of Y1t and Y2t. The two marginal processes are positively correlated, with the correlation coefficient of about 0.35. % Frequency 0 2 4 6 8 10 12 14 EUR/GBP EUR/USD % Frequency 0 1 2 3 4 5 6 7 8 −40 −30 −20 −10 0 10 20 30 40 −40 −30 −20 −10 0 10 20 30 40 Category Category Fig. 2 Histograms of the tick changes of the EUR/GBP and the EUR/USD exchange rates.
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 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 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
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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
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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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