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176 order serial correlation for price changes in the same directions (upper left and lower right panel), which underpins the existence of a bid-ask bounce. For JBX an analogue pattern is not observable. Moreover, for HAL the positive autocorrelations at longer lags indicate that the bounce effect will be compensated in later periods. Finally, note that the negative serial correlation caused by the bid-ask bounce is a short-run phenomenon. In order to capture the dynamics of the price direction variable, the vector of log–odds ratios Λi =(Λ −1i, Λ 1i)′ = (ln[π −1i/π 0i], ln[π 1i/π 0i])′ is specified as a multivariate ARMA process. The final form including possible explanatory variables is: i ¼ Pm i ¼ þ Pp l¼0 GlZ D i l þ i Cl i 1 þ l¼1 Pq Al i l l¼1 (2.13) with {Cl, l: 1→p} and {Al, l: 1→q} being matrices of dimension (2×2) with the elements {c (l) hk} and {a (l) D hk} and μ =(μ1, μ2)′. The vector Zi contains additional explanatory variables capturing other marks of the trading process (market microstructure variables) with {Gl, l: 0→m} as the corresponding coefficient matrix (l) and typical element {ghk}. The vector of log–odds ratios is driven by the martingale differences: i¼ð 1i; 1iÞ 0 ; with ji ¼ xji ji q ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ; j ¼ 1; 1; (2.14) ji 1 ji R. Liesenfeld et al. (2.13) which is the standardized state vector xi. In this ACM-ARMA(p,q) specification, the conditional distribution of the direction of price changes depends on lagged conditional distributions of the process and the lagged values of the standardized state vector. 4 The process is stationary if all values of z that satisfy ∣I−C1z− C2z 2 −⋯−Cpzp∣=0 lie outside the unit circle. Furthermore note, that the existence of a bid-ask bounce would imply that a (1) 12 > a (1) 11 and a (1) 21 > a (1) 22, which means that the probability of an immediate reversal of the price direction is higher than that of an unchanged price direction. 5 The log likelihood of the logistic ACM model, the 4 According to the classification by Cox (1981), our ACM model belongs to the class of observationally driven models where time dependence arises from a recursion on lagged endogenous variables. Alternatively, our model could be based on a parameter driven specification, in which the log–odds ratios Λi are determined by a dynamic latent process. However, the estimation and the diagnostics of the latter approach results in a substantially higher computational burden than for the ACM model. On the other hand, models driven by latent processes are usually more parsimonious than comparable dynamic models based on lagged dependent variables. A comparison of the two alternatives should be the subject of future research. 5 See Russel and Engle (2002) for a more detailed discussion of the stochastic properties of the ACM-ARMA(p,q) model.
Modelling financial transaction price movements: a dynamic integer count data model 177 first component of the likelihood of the overall model, takes on the familiar form presented below: L1 ¼ Xn i¼1 i ln 1i þ 0 i ln 0i þ þ i ln 1i : (2.15) Concerning the coefficient matrix Al, our empirical analysis will be based on two alternative specifications: an unrestricted one, and one including symmetry restrictions as suggested by Russel and Engle (2002). In particular, we impose the (1) (1) symmetry restriction a12=a21. This implies that the marginal effect of a negative price change on the conditional probability of a future positive price change is of the same size as the marginal effect of a positive change on the probability of a future negative change. Moreover, we impose the symmetry restriction a (1) 11 = a (1) 22 which guarantees that the impact of a negative change on the probability of a future negative change is the same as the corresponding effect for positive price changes. The symmetry of impacts on the conditional price direction probabilities will also be imposed for all lagged values of the probabilities and normalized state variables. Following Russel and Engle (2002), we set in the model with symmetry restrictions c2 (l) =0, ∀l, which implies that shocks in the log–odds ratios vanish at an exponential (l) rate determined by the diagonal element c1 . This simplifies the ARMA specification (2.13) for the symmetric model to: ¼ 1 2 ; Cl ¼ l c ðÞ 1 0 0 c l ! ; Al ¼ ðÞ 1 l a ðÞ 1 a l ðÞ 2 a l ðÞ 2 a l ðÞ 1 ! : (2.16) Although the reasoning behind these restrictions seems appropriate due to the explorative evidence of the state variable xi, the validity of these restrictions can, of course, be easily tested by standard ML based tests. 2.2 Empirical results for the ACM model In search of the best specification, we use the Schwarz information criterion (SIC) to determine the order of the ARMA process. For the selected specification, its standardized residuals will be subject to diagnostic checks. For the estimates of the conditional expectations and the variances Ê½xijF i 1Š ¼ î and ^V½xijF i 1Š ¼ diagðîÞ î ^0 i , respectively, the standardized residuals can be computed as: vi ¼ ðv1i; v1iÞ 0 1=2 ¼ ^V xijF i 1 h i xi Ê xijF i 1 ; (2.17) where ^V½xijF i 1Š 1=2 is the inverse of the Cholesky factor of the conditional variance. For a correctly specified model, the standardized residuals evaluated at the true parameter values should be serially uncorrelated in the first two moments with the following unconditional moments: E[vi]=0 and E[vivi′ ]=I. The null
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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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Page 131 and 132: How large is liquidity risk in an a
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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 146 and 147: 140 The innovation term ei is compu
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
Page 181: 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
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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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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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