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246 J. M. Rodríguez-Poo et al. Fig. 9 Intradaily seasonal curves, and confidence bands, for in-sample (solid lines) and out-ofsample (dashed lines). Price durations in the left box and volume durations in the right box seasonality. Hence the spline will fail to fit the out-of-sample seasonality if its pattern has changed. This is not the case of UniNW as it does not depend on parameters, other than ˆϑ1n and ˆξn, to capture the seasonality. The empirical evidence supports this intuition. Figure 9 shows the in-sample and outof-sample intradaily seasonalities. We observe that the out-of-sample seasonal patterns shift down compared with the in-sample patterns. This is especially visible for volume durations. If we use BiSp, BiNW, or UniSp to evaluate the out-of-sample density forecast, they all fail because none may capture changes in seasonality. By contrast, UniNW adapts quickly to changes in the out-of-sample and this explains why the density forecast produced by UniNW is better than for any other estimator. 4 Conclusions We propose a component model for the analysis of financial durations. The components are dynamics and seasonality. The latter is left unspecified and the former is assumed to fall within the class of (Log-)ACD models. Joint estimation of the parameters of interest and the smooth curve is performed through a local (quasi-)likelihood method. The resulting nonparametric estimator of the seasonal component shows a closed form expression. Although the methodology is applied to intradaily seasonality, it could also be used to measure relations between any other two variables. This is particularly useful when the relation is nonlinear and we are not sure about the functional link. So, for instance, the time-of-the-day may be replaced by some volatility measure, spread, or any other microstructure variables. Alternatively, the nonparametric estimator could be multivariate, including the time-of-the-day and any other variable of interest. The model is applied to the price and volume duration processes of two stocks traded on the NYSE. We show that the proposed method produces better predictions, in terms of densities, since it adapts quickly to changes in the seasonal pattern. Acknowledgements The authors acknowledge financial support from the Université catholique de Louvain (project 11000131), the Institute of Statistics at the Université Catholique de Louvain, the Dirección General de Investigación del Ministerio de Ciencia y Tecnología under research grants BEC2001-1121 and SEJ2005-05549/ECON as well as the Spanish Ministry of Education (project PB98-0140), respectively. Work supported in part by the European Community’s Human
Semiparametric estimation for financial durations 247 Potential Programme under contract HPRN-CT-2002-00232, [MICFINMA]. Thanks are due also to Luc Bauwens, Joachim Grammig, M. Paz Moral, Wendelin Schnedler, Laura Spierdijk, Jorge Yzaguirre for useful remarks, and to the seminar participants at CEMFI, University Carlos III de Madrid, the PAI Conference in Financial Econometrics in Leuven, and at the CAF conference on Market Microstructure and High-Frequency data in Finance in Aarhaus. Last, we are also grateful to the co-editor Winfried Pohlmeier, a referee for insightful remarks. Appendix A. Definitions and assumptions In order to prove the results claimed in Theorems 1 and 2, we need to establish some definitions and assumptions. (L.1) For fixed but arbitrary η1,φ + , where η ∈ �, and φ + ∈ �, let ρ � φ + ,η � � = log p � ϕ(ψ,φ + ); ξ � dF � ϕ(ψ,φ + ); ξ � . If η �= η1, then ρ (φ,η)
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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
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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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Page 208 and 209: 202 W. B. Omrane, H. V. Oppens of s
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Page 212 and 213: 206 price 0.8565 0.8575 0.8585 0.85
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Page 220 and 221: 214 6 Conclusion Using 5-min euro/d
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Page 228 and 229: 222 References W. B. Omrane, H. V.
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Page 262 and 263: 256 simply aggregated. Even after a
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Page 266 and 267: 260 together with the restrictions
Page 268 and 269: Table 3 Estimated probabilities of
Page 270 and 271: 264 A. S. Tay, C. Ting More interes
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Page 274 and 275: 268 Acknowledgements Tay gratefully
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Page 278 and 279: 272 contrast, price responses to po
Page 280 and 281: 274 Fig. 1 Continuous line is the T
Page 282 and 283: 276 the β’s can form a convex sh
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Page 288 and 289: 282 30 25 20 15 10 5 CC UNEMW ISM U
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Page 298 and 299: 292 Table A12 GDP, BI, TB and PI Re
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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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