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46 K. Bien et al. % Frequency −0.10 −0.00 0.10 EUR/GBP EUR/USD % Frequency −0.10 −0.00 0.10 1 4 7 10 14 18 22 26 1 4 7 10 14 18 22 26 Category Category Fig. 13 Autocorrelation function of the normalized density forecast variables. Fig. 14 Multivariate autocorrelation function for residuals of the EUR/GBP and the EUR/USD tick changes. Upper left panel: corr(ε1 t ,ε1 t−l ); upper right panel: corr(ε1 t ,ε2 t−l ); lower left panel: corr(ε2 t−l ,ε1 t ) and lower right panel: corr(ε2 t ,ε2 t−l ). The dashed lines mark the approximate 99% confidence interval ±2.58/ √ T . part of the correlation structure of the processes for the exchange rate changes (compare Fig. 6), there is some room to improve the model specification. These results are also emphasized by the multivariate Ljung-Box statistics for the bid and ask change process and its residuals in Table 3.
A multivariate integer count hurdle model 47 4 Conclusion Table 3 Multivariate Ljung-Box statistic for the residuals of the simulated bivariate process Real exchange rate changes Residuals Q(20) 473.6279 159.8679 Q(30) 521.8745 207.2940 Q(50) 588.0909 296.7522 In this paper we propose an approach that is capable of modelling complex multivariate processes for discrete random variables. Combining the approach by Cameron et al. (2004) for copulas of discrete random variables with the ICH model by Liesenfeld et al. (2006), we model the joint process for two integer count variables. As an illustration of the explanatory power of our approach we estimate the joint distribution of the EUR/GBP and the EUR/USD exchange rate changes at the 1 min level. Even without detailed specification search, our model describes the exchange rate dynamics fairly well. Moreover, the marginal distributions which are characterized by inflated outcomes are also estimated satisfactorily. In order to pick up the obvious excess kurtosis in the joint empirical distribution, we have tried out more flexible parametric alternatives to the Gaussian copula, such as the t-student copula, which allows for symmetric lower and upper tail dependency and an excessive concentration in (0,0) and the symmetrized Joe– Clayton copula, which has a quite parsimonious functional form and allows for asymmetric tail dependence. Although both specifications improve the goodnessof-fit of our model in some aspects the application of the t-student copula or the symmetrized Joe–Clayton copula has been by no means clearly superior to the simple Gaussian copula, so that we conclude that simply applying more flexible copula functions is not the proper remedy to capture the large excess kurtosis. An obvious alternative path of future research is to keep the Gaussian copula and to inflate the outcome (0,0) along the lines of zero inflated count data models. Last but not least, the potential merits of the approach should be checked in the light of real world applications such as the measurement of multivariate conditional volatilities and the quantification of liquidity or value-at-risk applications. Obviously, our approach can easily be extended to the most general case of mixed multivariate distributions for continuous and discrete random variables. For financial market research at the high frequency level, such an extension is attractive for the joint analysis of several marks of the trading process (volumes, price and volume durations, discrete quote changes, etc.). Acknowledgements The work is supported by the European Community’s Human Potential Program under contract HPRN-CT-2002-00232, Microstructure of Financial Markets in Europe; and by the Fritz Thyssen Foundation through the project ‘Dealer-Behavior and Price-Dynamics on the Foreign Exchange Market’. We thank Richard Olsen and Olsen Financial Technologies for providing us with the data.
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 50 and 51: 44 K. Bien et al. - Set ˆzt = Âxt
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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Page 98 and 99: 92 subtracting the deviations from
Page 100 and 101: 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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