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236 J. M. Rodríguez-Poo et al. certain threshold. We define the threshold as $0.125. Following Engle and Russell (1998), the price is defined as the mid-quote. A volume duration is defined as the time interval needed to observe an accumulated change in volume greater than a given number of shares. The threshold is defined to be 25,000 shares. The data sample covers September, October, and November 1996, and the stocks are Boeing for price durations and Disney for volume durations. The choice of these two stocks and its time horizon is motivated by the fact that Bauwens et al. (2004) show, in a density forecast analysis, that they are difficult to model, both in terms of expectation and density. Price and volume durations provide an instantaneous overview of two important market features. Price durations are strongly linked to the instantaneous volatility process, see Engle and Russell (1998) and Gerhard and Hautsch (2002). By computing the conditional expectation of the duration, it is possible to compute the instantaneous volatility process. Volume durations are appealing as they convey information about two of the three dimensions of the liquidity: time and volume. Therefore, price and volume durations provide measures of the instantaneous volatility and the liquidity of the market. Prior to estimation we follow Engle and Russell (1998) and two transformations are performed: (1) Trades and bid/ask quotes recorded before 09:30 am and after 4 pm are ignored and (2) the time gaps between market closing and opening and weekends are also ignored. 3.2 Descriptive analysis Table 1 shows some basic statistics. There are 1,778 and 2,160 price and volume durations, respectively. The first two-thirds of the sample are used for estimation (in-sample), while the last third of the sample is used for diagnosis and prediction (out-of-sample). Price and volume durations show different properties. Price durations are overdispersed (the ratio of standard deviation to mean is 1.49) while volume durations are underdispersed (0.81). The proportions of observations below the mode (% < mod) are 11% and 24% for price and volume durations, respectively. These high proportions translate into humps in the density, even very close to the origin, as it is the case of price durations (see Fig. 1). Furthermore, there are large durations, specially for price durations, inducing a long right tail. A hump close to the origin and long right tails are important insights that help to choose the density function. Regarding seasonality, we estimate a preliminary nonparametric regression, allowing for differences between the days of the week. For the sth day we define ˆφs(t ′ 0 ) = 1 nh 1 nh �⌊n/5⌋ �ni=1 j=1 K � ⌊n/5⌋ j=1 Table 1 Information on duration data � t ′ 0 −t ′ i h �ni=1 K � � t0−ti h I � � I ⌊ t−to � + 1⌋=js di tc−to � ⌊ t−to � , s = 1, ··· , 5, + 1⌋=js tc−to n nin nout Mean sd mode % < mod min max Price (Boeing) 2,160 1,426 734 647 966 70.6 0.11 3 9,739 Volume (Disney) 1,778 1,173 605 801 648 304 0.24 6 4,621 Durations are measured in seconds. n denotes the total number of observations, nin the in-sample number of observations,nout the out-of-sample number of observations, sd the standard deviation, %
Semiparametric estimation for financial durations 237 Fig. 1 Kernel marginal densities for Boeing price durations (left box), and Disney volume durations (right box). The kernel is gamma, see Chen (2000), with optimal bandwidth (0.9sN −0.2 ) 2 where N is the number of observations and s is the sample standard deviation. Seconds 100 400 700 1100 1500 Seconds 100 400 700 1100 1500 9 10 11 12 13 14 15 16 Hours 9 10 11 12 13 14 15 16 Hours Seconds 100 400 700 1100 1500 Seconds 100 400 700 1100 1500 9 10 11 12 13 14 15 16 Hours 9 10 11 12 13 14 15 16 Hours Fig. 2 Intradaily seasonal patterns (middle line) for the days of the week and 95% confidence bands (side lines) for Boeing price durations. The straight line represents the mean of each curve.
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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 206 and 207: 200 W. B. Omrane, H. V. Oppens anal
Page 208 and 209: 202 W. B. Omrane, H. V. Oppens of s
Page 210 and 211: 204 The extrema detection method ba
Page 212 and 213: 206 price 0.8565 0.8575 0.8585 0.85
Page 214 and 215: 208 We distinguish three possible c
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
Page 222 and 223: 216 where σk is the standard devia
Page 224 and 225: 218 If we meet a particular case su
Page 226 and 227: 220 C.5. Triple bottom (TB) TB is c
Page 228 and 229: 222 References W. B. Omrane, H. V.
Page 231 and 232: Juan M. Rodríguez-Poo · David Ver
Page 233 and 234: Semiparametric estimation for finan
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Page 260 and 261: 254 between price changes and durat
Page 262 and 263: 256 simply aggregated. Even after a
Page 264 and 265: 258 is to make use of the fact that
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
Page 282 and 283: 276 the β’s can form a convex sh
Page 284 and 285: 278 fixing some intervals around th
Page 286 and 287: 280 . That is for a given absolute
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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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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