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140 The innovation term ei is computed from the integrated intensity function associated with the most recently observed process. Hence, 0 1 ei ¼ XK k¼1 @1 Z k t Nk ðÞ ti tk Nk ðÞ ti 1 k ðs; F sÞds Ay k i : (5) Under fairly weak assumptions, the integrated intensity function corresponds to an i.i.d. standard exponential variate. 7 Therefore, e i is a random mixture of exponential variates. For this reason, weak stationarity of the model depends on the eigenvalues of the matrix B. If these lie inside the unit circle, the process e i is weakly stationary. Since the intensity function has left-continuous sample paths, Ψ i also has to be a left-continuous function and predetermined, at least instantaneously before the arrival of a new event. Therefore, Ψi is known instantaneously after the occurrence of ti−1 and does not change until ti. Then kðt;F tÞ changes between ti−1 and ti only k k as a deterministic function of time according to the functions l0 (t) and s (t). The baseline intensity function l 0 k (t) is specified in terms of the backward re- currence times xkðÞ¼t t t k M k , k =1,...,K, of all processes and may be specified ðÞ t using a Weibull-type parameterization depending on the parameters ω k k and pr , k 0 t YK ðÞ¼exp !k r¼1 x r ðÞ t pkr 1 ; p k r > 0 : (6) Moreover, the seasonality functions s k (t) are parameterized as linear spline functions given by 8 s k ðÞ¼1 t þ XS j¼1 k j t j 1 ft> jg ; (7) where τj, j=1,..., S, denote the S nodes within a trading day and νj k the corresponding parameters. As a result, by denoting W as the data matrix consisting of all points and explanatory variables and denoting θ as the parameter vector of the model, the loglikelihood function of the multivariate ACI model is given by ln LðW; Þ ¼ XK X n k¼1 i¼1 Z ti ti 1 k ðs; F sÞds þ y k i ln k ti;F ti ; (8) where t 0=0 and n denotes the number of points of the pooled process. Under correct specification of the model, the resulting k-type ACI residuals ^" k i ¼ Z k ti t k i 1 ^ k ðs;FsÞds A. D. Hall, N. Hautsch 7 See Brémaud (1981) and Bowsher (2002). 8 In order to identify the constant ω k , s k (t) is set to one at the beginning of a trading day.
Order aggressiveness and order book dynamics 141 should be distributed as i.i.d. unit exponential. As a result, model diagnostics can be undertaken by evaluating the dynamical and distributional properties of these residuals. Engle and Russell (1998) have proposed ffiffiffiffiffiffiffiffiffi a test against excess dispersion based on the asymptotically normal test statistic nk p =8 ^2 " k 1 , where ^2 " k is the empirical variance of the k-type residual series and n k denotes the number of points observed for process k. 4 Data and descriptive statistics 4.1 Trading at the ASX The Australian Stock Exchange (ASX) is a continuous double auction electronic market. After a pre-opening period followed by a staggered sequence of opening call auctions, normal trading takes place continuously between 10:00 A.M. and 16:00 P.M. The market is closed with a further call auction and a late trading period. For more details regarding the daily market schedule of the ASX, see Hall and Hautsch (2004). During normal trading, orders can be entered as market orders which will execute immediately and limit orders which enter the queues. On the ASX, as orders are not allowed to walk up (down) the book, a market order with a large quoted volume will first be matched with the pending volume on the first level of the opposite queue. Trades will be generated and traded orders deleted until there is no more order volume at the posted price. The remaining part of the order enters the queue as a corresponding limit order. When a market order is executed against several pending limit orders, a trade record for each market order—limit order pair is generated. Since these multiple trades are generated by a single market order, we aggregate them into a single trade record. Limit orders are queued in the buy and sell queues according to a strict pricetime priority order. During normal trading, pending limit orders can be modified or cancelled without restrictions. 9 All trades and orders are visible to the public. Orders with a total value exceeding $200,000 can be entered with a hidden volume. However, sufficient information is available to unambiguously reconstruct all transactions. 4.2 Descriptive statistics Our empirical analysis is based on the order book data from the five most liquid stocks traded at the ASX during the period 1 July to 30 August 2002, namely Broken Hill Proprietary Limited (BHP), National Australia Bank (NAB), News Corporation (NCP), Telstra (TLS) and Woolworths (WOW). The samples are extracted from the Stock Exchange Automated Trading System and contain time stamped prices, volumes and identification attributes of all orders as well as information about opening and closing auctions. By replicating the execution engine of the ASX, with explicit consideration of all trading rules, we can fully reconstruct the individual order books at any time. Our resulting samples consist of 9 Clearly, modifying the order volume or the order price can affect the order priority. For more details, see Hall and Hautsch (2004).
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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
Page 96 and 97: 90 comparability across stocks, we
Page 98 and 99: 92 subtracting the deviations from
Page 100 and 101: 94 market order distribution that c
Page 102 and 103: 96 Table 2 First stage GMM results
Page 104 and 105: Table 4 First stage GMM results bas
Page 106 and 107: 100 S. Frey, J. Grammig quotes on e
Page 108 and 109: 102 S. Frey, J. Grammig approximate
Page 110 and 111: 104 To obtain the estimates in the
Page 112 and 113: 106 Hence, using the liquidity stat
Page 114 and 115: 108 In the main text we discuss the
Page 117 and 118: Pierre Giot . Joachim Grammig How l
Page 119 and 120: How large is liquidity risk in an a
Page 137: How large is liquidity risk in an a
Page 140 and 141: 134 A. D. Hall, N. Hautsch In this
Page 142 and 143: 136 includes order book variables,
Page 144 and 145: 138 An important determinant of liq
Page 148 and 149: Table 1 Order book characteristics
Page 150 and 151: 144 data covering the normal tradin
Page 152 and 153: 146 Table 3 Descriptive statistics
Page 154 and 155: Table 4 Fully specified ACI models
Page 156 and 157: Table 4 (continued) BHP NAB NCP TLS
Page 158 and 159: Table 5 ACI models without dynamics
Page 162 and 163: Table 6 ACI models without covariat
Page 166 and 167: 160 specification which includes or
Page 168 and 169: 162 5.2.5 The impact of the bid-ask
Page 170 and 171: 164 contrast to those of Pascual an
Page 173 and 174: Roman Liesenfeld . Ingmar Nolte . W
Page 175 and 176: Modelling financial transaction pri
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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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