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174 specify the parametric form of the p.d.f. for the price direction and the absolute size of the price changes. 2.1 Dynamics of the price direction The parametric model for the direction of the transaction price change Di=j,(j=−1, 0, 1) is taken from the class of logistic ACM (autoregressive conditional multinomial) models suggested by Russel and Engle (2002). In order to relate the probability ji ¼ Pr ½Di¼jjF i 1Š for the occurrence of price direction j to subsets of F i 1 (and further explanatory variables), we use a logistic link function. This leads to a multinomial logit model of the form: ji ¼ exp ji P 1 j¼ 1 exp ji ; j ¼ 1; 0; 1; (2.10) where Λji represents a function of some subset of F i 1 to be specified below. As a normalizing constraint, we use Λ0i=0, ∀i. Due to the observed dynamic behavior of the transaction price changes associated with the bid-ask bounce or the volatility clustering, one can expect that the process of the price direction also exhibits serial dependence. In order to shed light on this serial dependence, which has to be taken into account when modelling the conditional distribution of the price direction, we define the following state vector xi ¼ ðx1i; x1iÞ 0 ð1; 0Þ ¼ 0 if Yi < 0 ð0; 0Þ 0 if Yi ¼ 0 ð0; 1Þ 0 8 < (2.11) : if Yi > 0; and consider its corresponding sample autocorrelation matrix. For a lag length ‘, this matrix is given by: with ðÞ¼D ‘ 1 1 ðÞ¼ ‘ n ‘ 1 ðÞD ‘ 1 ; ‘ ¼ 1; 2; ...; (2.12) X n ðxixÞ xi ‘ x i¼‘þ1 ð Þ 0 : R. Liesenfeld et al. D denotes a diagonal matrix containing the standard deviations of x −1i and x 1i. Figure 4 below depicts the cross-correlation function of up to 30 lagged transactions. The significant, but not very large, first order cross-correlations provide empirical support for the existence of a bid-ask bounce: The probability of a price reduction is significantly (HAL) positively correlated with the price increase in the previous period (upper right panel), and also significant (both stocks), a price increase is more likely if a negative price change is observed for the previous transaction (lower left panel). The cross-correlation effects turn out to be asymmetric, in the sense that the correlation of a negative price change with a previous positive one is smaller than the effect vice versa. For HAL we observe negative first
Modelling financial transaction price movements: a dynamic integer count data model 175 JBX HAL Fig. 4 Multivariate autocorrelation function for the price change directions for Jack in the Box Inc. (JBX) and Halliburton Company (HAL). Upper left panel: corrðx1i; x 1i ‘ Þ; upper right panel: corrðx1i; x1i ‘ Þ; lower left panel: corrðx1i ‘; x1iÞ and lower right panel: corr x1i; x1i pffiffiffi ð ‘ Þ. The dashed lines mark the approximate 99% confidence interval 2:58 n
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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 129 and 130: 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 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 179: Modelling financial transaction pri
Page 203: Modelling financial transaction pri
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.
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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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