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58 with AtðLÞ ¼ 0 B @ 1 ð ÞAabðLÞAaB;tðLÞAaS;tðLÞ ð ÞAbbðLÞAbB;tðLÞAbS;tðLÞ C ð ÞABbðLÞABB;tðLÞABS;tðLÞA ð ÞASbðLÞASB;tðLÞASS;tðLÞ : Aaa L Aba L ABa L ASa L This model echoes the main features of the structural model in the previous subsection. First, the bid–ask spread s t=a−b t is the error correction term. Second, the matrix on the left-hand side of Eq. (3.7) reflects that the theoretical model is tradedriven. Thus, trades have a contemporaneous effect on ask and bid quotes. The reverse, however, is not true. Third, the matrix of autoregressive polynomials A t (L) depicts the dynamical structure of the theoretical model. Moreover, A ij (L), for all i, j2{a,b,B,S}, has its roots outside the unit circle. Thus, the influence of past quotes and trades decays with time. Finally, the polynomials A ij,t(L) are time-varying because they depend on a set of exogenous variables (MC t) and trading-time dummies (D t). The following expression makes explicit the type of dependence, Aij;t L ð Þxt1 ¼ A B ij L B ð Þf ð Þx B t 1 þ ASij L S ð Þf ð Þx S ij MCt 1; Dt 1 A. Escribano and R. Pascual ij MCt 1; Dt 1 B S The polynomials Aij,t(L) and Aij,t (L) have all the roots outside the unit circle. Finally, Aij,t *=−Aij,t(0). A salient feature of the VEC model Eq. (3.7) is the extra lags in the error correction term. This type of specification is called an extended vector error correction (EVEC) model. Arranz and Escribano (2000) show that extended error correction models are robust to the presence of structural breaks under partial co-breaking. Co-breaks represent those situations characterized by having breaks (level shifts, changes in trend etc.) occurring simultaneously in some variables, so that certain linear combinations of those variables have no breaks. The common lung-run trend jointly with their discrete type of moves makes at and bt the perfect example of co-integrated time series that are partially cobreaking. Thus, this property of the model is consistent with the properties of EC the time series of ask and bid prices. The error correction terms γa (L)st−1 and EC EC EC γb (L)st−1 should be such that γa (1)−γb (1)
Asymmetries in bid and ask responses to innovations in the trading process 59 j fi (MCt,Dt)=1 for all i and j. In this case, the matrix of autoregressive polynomials is time invariant, At(L)=A(L), and the impact of trades on quotes is perfectly linear. We will show that this model suffices to illustrate the essentials of the dynamic relationship between trades and quotes. However, some other aspects of this relationship can only be captured by considering the more general case. Following Hasbrouck (1991), we characterize the trading processes using indicator variables. Namely, xt B S equals one for buys and zero otherwise, and xt equals one for sells and zero otherwise. The discreteness of these variables, however, may introduce some problems in the estimation process. 10 To control for these potential problems, we also estimate Eq. (3.7) using the trade size ex i t to characterize each transaction. In particular, we define ex i t ¼ xit log ðVtÞ , where Vt is the size of the t-th trade in shares. 4 Data The database comprises high frequency data on trades and quotes from two markets with remarkably different microstructures: the NYSE and the SSE. The NYSE is a peculiar mixture of microstructure types. It combines an electronic limit order book, only partially transparent, with monopolist market makers, and an intensive trading activity at the floor market. The SSE, on the contrary, is a representative example of an electronic order-driven venue. Liquidity provision depends exclusively on a fully transparent open limit order book. Twenty levels of the book are nowadays visible in real time for all market participants. There are no market makers, no floor trading, price improvements are not possible, and all the orders are submitted through vendor feeds, and stored or matched electronically. We use data on two different markets to show that asymmetric dynamics between ask and bid quotes in response to trades are not exclusive of the NYSE. In addition, trades in the SSE always involve a market order (or equivalent), the initiating side, and one or more limit orders stored on the book. Therefore, trades are straightforwardly classified as either buyer or seller-initiated by simply identifying the side of the book the market order hits. Thus, with the SSE data we do not bear the ambiguity and misclassification problems that appear when traditional trade-direction algorithms, such as Lee and Ready (1991), are applied to NYSE data (see Ellis et al. 2000, and Odders-White 2000). Finally, using Spanish data we do not have reporting delays neither in trades nor in quotes since the book and trade files are updated simultaneously and in real time. Therefore, we avoid the use ad hoc rules to match trades and quotes, like the classical “five-second rule” applied to NYSE data. 11 NYSE data is obtained from the TAQ database. We consider two different sample periods, January to March 1996 and 2000. Several details in the mi- 10 Our model is nonlinear and well behaved around the mean (nonlinear). Like standard linear probability models (LPM), only in the extremes it can give predictions out of the zero and one interval. The corresponding estimation theory for dynamic models with weakly dependent variables is covered in White (1994) and Wooldridge (1994). Park and Phillips (2000) extend it to cover nonlinear cointegration cases with limited dependent variables. 11 Blume and Goldstein (1997) shows that the “five-second rule” could not be generalized to all sample periods and markets. However, Odders-White (2000) shows that this rule does not seem to explain much of the bias induced by the Lee and Ready’s (1991) algorithm.
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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
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 52 and 53: 46 K. Bien et al. % Frequency −0.
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 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
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
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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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