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240 J. M. Rodríguez-Poo et al. where (·) + = max (·, 0), G is the number of knots, and πg is the gth knot. θj,j = 1, ··· , 4, and δg, g = 1, ··· ,G, are the parameters of the spline to be estimated. Further details on the derivation of this form can be found in Eubank (1988, p 354). Knots are set at every hour with an additional knot in the last half hour, as in Engle and Russell (1998). The two remaining estimators are two steps estimators, in the sense that they are not estimated jointly with the finite dimensional parameters but independently: First the seasonal curve is estimated, then durations are adjusted by seasonality and finally the parameters are estimated using the deseasonalized durations. This procedure is often followed in the literature (see, for instance, Engle and Russell (1998) and Bauwens and Giot (2000)). The first of these two estimators is the plain Nadaraya–Watson estimator ˆφ(t ′ 0 ) = 1 �ni=1 nh K 1 nh � ni=1 K � t ′ 0−t ′ i h � t ′ 0−t ′ i h � di � , (23) which we denote by BiNW—standing for two steps and Nadaraya–Watson. The second two-step estimator is the one used by Engle and Russell (1998); it is the seasonal component that is estimated by averaging the durations over 30 min intervals, and smoothing the resulting piece-wise constant function via cubic splines. We denote this estimator by BiSp. To construct pointwise confidence bands for the seasonal curve in UniNW, we need to estimate the empirical counterparts of Eqs. (16) and (17): �φ�ϑ1,�ξ (t′ 0 ) ± z1− α � � � � �K� 2 2 2 �f(t ′ 0 )�I(�φ�ϑ1,�ξ ,t′ 0 ), (24) where �I(�φ�ϑ1,�ξ ,t′ 0 ) = �f(t ′ 1 0 ) = nh 1 �ni=1 nh K n� K i=1 � t ′ 0−t ′ � i h ⎡ ⎣�γ � t ′ 0 − t ′ i h ⎛� ⎝ 1 �ni=1 nh K � , di � exp ψ(�ϑ1)+�φ�ϑ 1 ,�ξ (t′ 0 ) � � t ′ 0−t ′ i h � �γ ⎞⎤ 2 −�ν ⎠⎦ � , z α 1− is the 2 α 2 -quantile of the standard normal distribution, and �K�2 2 is a known constant that depends on the kernel. For the quartic kernel, �K�2 2 = 5 7 . We can also compute consistent estimators of the variance–covariance matrix of the parameters. For the other three cases, no results in this direction are available and, therefore, the standard errors we present for these three cases have unknown properties. Nonetheless, we present them for the sake of comparison. Table 2 presents the estimation results of the four specifications for price and volume durations. Comparing UniNW with the other specifications we conclude: The estimated parameters of the dynamic component are very similar under the exponential and the generalized gamma distribution but the standard deviations are smaller under the generalized gamma distribution. This supports the theory of ML and GLM in the sense that the
Semiparametric estimation for financial durations 241 Table 2 Estimation results Boeing (price) Disney (volume) BiNW BiSp UniNW UniSp BiNW BiSp UniNW UniSp �ω 0.0954 0.2375 − 0.5867 0.0309 0.0894 − 1.5461 [0.0171] [0.0457] [0.0738] [0.0103] [0.0233] [0.0490] �α 0.1436 0.2418 0.1598 0.1657 0.1054 0.1799 0.0875 0.1226 [0.0185] [0.0258] [0.0203] [0.0187] [0.0279] [0.0341] [0.0260] [0.0931] �β 0.7591 0.5290 0.6309 0.5144 0.8255 0.6471 0.8875 0.6886 [0.0735] [0.0942] [0.0581] [0.0901] [0.0543] [0.0829] [0.0451] [0.0710] �α + �β 0.9027 0.7708 0.7907 0.6801 0.9309 0.8270 0.9750 0.8112 [0.0820] [0.1183] [0.0801] [0.0997] [0.0824] [0.1154] [0.0711] [0.1638] �ω 0.0501 0.2115 − 1.4121 0.0306 0.0896 − 1.5361 [0.0135] [0.0211] [0.0654] [0.0069] [0.0163] [0.0244] �α 0.0611 0.1596 0.1761 0.1401 0.1003 0.1799 0.0875 0.1216 [0.0185] [0.0175] [0.0128] [0.0141] [0.0183] [0.0237] [0.0185] [0.0910] �β 0.8039 0.5672 0.6834 0.5899 0.8236 0.6459 0.8798 0.7786 [0.0417] [0.0404] [0.0297] [0.0494] [0.0388] [0.0583] [0.0379] [0.0545] �γ 0.2693 0.2900 0.2527 0.0675 1.4356 1.0180 1.3959 1.0653 [0.0605] [0.0579] [0.0518] [0.0401] [0.1328] [0.0972] [0.1328] [0.2376] �ν 10.807 8.7329 10.332 17.852 1.2468 1.9952 1.2774 1.7702 [3.7263] [3.3737] [3.1208] [2.4329] [0.1912] [0.3373] [0.2020] [0.2453] �α + �β 0.8650 0.7268 0.8595 0.7300 0.9239 0.8258 0.9673 0.9002 [0.0611] [0.0590] [0.0415] [0.0538] [0.0561] [0.0818] [0.0549] [0.1459] Entries are GLM estimates—using the exponential distribution—(top part of the table) and ML estimates—using a generalized gamma distribution—(bottom part) for the Log-ACD. Numbers in brackets are heteroskedastic-consistent standard errors. exponential density cannot fit the empirical density, which implies inefficient estimates with respect to the ML ones. Second, the estimated parameters under BiSp and UniSp are very similar, confirming the results shown in Engle and Russell (1998, p 1137), who do not find very different results for BiSp and UniSp. By contrast, there are substantial differences between the NW (UniNW and BiNW) and the Sp (UniSp and BiSp) groups, meaning that the parameters and the nonparametric curve are not orthogonal when estimating with kernels. Third, volume durations estimates have, in general, smaller �α and bigger �β than price durations estimates. This is due to the persistence (see Spearman’s ρ in Fig. 5) and the underdispersion of volume durations. Note that the constant of the dynamic component is not present in UniNW as it is replaced by the seasonal curve. As for the nonparametric curves (see Fig. 6), results in terms of smoothness are rather different for UniSp and UniNW. UniSp curves are sharper with small humps and, for volume durations, we also observe a rough increase (decrease) at the beginning (end) of the day. This finding can be explained by the fact that UniNW provides a data-driven method to compute the bandwidth, whereas the UniSp does not (location and number of
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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 212 and 213: 206 price 0.8565 0.8575 0.8585 0.85
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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
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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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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
Page 272 and 273: Table 4 Estimated probabilities of
Page 274 and 275: 268 Acknowledgements Tay gratefully
Page 276 and 277: 270 This paper explores the effect
Page 278 and 279: 272 contrast, price responses to po
Page 280 and 281: 274 Fig. 1 Continuous line is the T
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Page 284 and 285: 278 fixing some intervals around th
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Page 288 and 289: 282 30 25 20 15 10 5 CC UNEMW ISM U
Page 290 and 291: Appendix Table A1 Consumer confiden
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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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