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180 JBX HAL R. Liesenfeld et al. Fig. 5 Multivariate autocorrelation function for the residuals of the logistic ACM model for Jack in the Box Inc. (JBX) and Halliburton Company (HAL) up to 30 lagged transactions. The correlations are the following: upper left panel: corrðv1i; v 1i ‘ Þ, upper right panel: corrðv1i; v1i ‘ Þ, lower left panel: corrðv1i ‘; v1iÞ and lower right panel: corr v1i; v1i pffiffi ð ‘ Þ. The dashed lines mark off the approximate 99% confidence interval 2:58 n
Modelling financial transaction price movements: a dynamic integer count data model 181 and for HAL all but two correlations lie inside the 99% band. The means of standardized residuals reported in Table 1 are close to zero, which should be expected from a well specified model. However, the estimated variance–covariance matrix of the standardized residuals deviate slightly from the identity matrix. This may hint to a distributional misspecification or a misspecification of log–odds ratios Λi, which is not fully compatible with the variation in the observed variation of price change direction. 2.3 Dynamics of the size of price changes In order to analyze the size of the non-zero price changes, we use a GLARMA (generalized linear autoregressive moving average) model based on a truncated-atzero Negative Binomial (Negbin) distribution. The choice of a Negbin in favor of a Poisson distribution is motivated by the fact, that the unconditional distributions of the non-zero price changes show over-dispersion for both stocks. For JBX (HAL) the dispersion coefficient 7 is given by 3.770 (2.911). Moreover, note, that an atzero-truncated Poisson distribution would allow only for under-dispersion. Similar to the ACM model, the dynamic structure of this count data model rests on a recursion on lagged observable variables. A comprehensive description of this class of models can, for instance, be found in Davis et al. (2003). Note that the time scale for absolute price changes (defined by transactions associated with non-zero price changes) is different from the one of the ACM model for the direction of the price changes, which is defined on the ticktime scale. Let u be a random variable following a Negbin distribution with the p.d.f. 8 fðuÞ ¼ ð þ uÞ ðÞ ðuþ1Þ þ ! ! ! þ u ; u ¼ 0; 1; 2;:::; (2.19) with E(u)=ω > 0 and Var(u)=ω+ω 2 /κ. The overdispersion of the Negbin distribution depends on parameter κ >0. As κ→∞, the Negbin collapses to a Poisson distribution. The corresponding truncated-at-zero Negbin distribution is obtained as h(u)=f (u)/[1−f (0)], (u = 1, 2, 3, ...), with f (0) = [κ/(κ+ω)] κ . This flexible class of distributions will be used to model the size of non-zero price changes conditional on filtration F i 1 and price direction D i. Thus, for S i∣S i >0,D i, F i 1 we assume the following p.d.f.: hsijDi; ð F i 1Þ ¼ ð þ siÞ ðÞ ðsiþ1Þ with the conditional moments: h þ i !i 1 1 !i !i þ !i ESijSi ½ > 0; Di; F i 1Š ¼ Si ¼ 1 #i 7 Computed as variance over mean. 8 See, for example, Cameron and Trivedi (1998) (Ch. 4.2.2.). si ; si ¼ 1; 2; ...; (2.20) (2.21)
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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 135 and 136: 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 185: 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.
Page 231 and 232: Juan M. Rodríguez-Poo · David Ver
Page 233 and 234: Semiparametric estimation for finan
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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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