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Table 1 ML estimates of the logistic ACM-ARMA model for Jack in the Box Inc. (JBX) and Halliburton Company (HAL)* Parameter JBX HAL Symmetric Non-symmetric Symmetric Non-symmetric Estimate Std. dev. Estimate Std. dev. Estimate Std. dev. Estimate Std. dev. μ1 −0.0998 0.0263 −0.1331 0.0382 −0.0355 0.0035 −0.0368 0.0036 μ2 −0.0998 0.0263 −0.1204 0.0345 −0.0355 0.0035 −0.0349 0.0035 c1 (1) 0.9116 0.0230 0.8881 0.0316 1.1412 0.0294 1.1309 0.0287 (2) c1 −0.1895 0.0292 −0.1797 0.0283 (1) a11 0.1164 0.0186 0.1367 0.0309 0.0568 0.0109 0.0934 0.0147 a12 (1) 0.0955 0.0180 0.0512 0.0219 0.2510 0.0099 0.1458 0.0135 a21 (1) 0.0955 0.0180 0.1606 0.0335 0.2510 0.0099 0.3539 0.0135 (1) a22 0.1164 0.0186 0.1124 0.0196 0.0568 0.0109 0.0253 0.0144 (2) a11 0.0473 0.0116 0.0140 0.0152 a12 (2) −0.1853 0.0100 −0.0897 0.0136 a21 (2) (2) −0.1853 0.0100 −0.2755 0.0136 a 22 0.0473 0.0116 0.0773 0.0148 log-likelihood −0.928726 −0.926585 −1.005572 −1.003333 SIC 0.932423 0.933055 1.006618 1.005126 Q(30) 132.9 (0.149) 121.1 (0.331) 302.4 (0.000) 163.6 (0.001) Q(50) 215.1 (0.179) 204.5 (0.306) 401.7 (0.000) 261.4 (0.001) Resid. mean (−0.019, 0.029) (0.000, 0.001) (−0.004, 0.012) (−0.000, −0.000) Resid. variance 0:902 0:024 0:934 0:023 0:887 0:033 0:024 1:107 0:023 1:069 0:033 1:132 LR-test on symmetry 19.514 (0.0002) 156.79 (0.0000) *Dependent variable is the direction of the price changes, D i, n = 4,566 (JBX), n = 35,021 (HAL), p-values in parenthesis 0:890 0:037 0:037 1:132 178 R. Liesenfeld et al.
Modelling financial transaction price movements: a dynamic integer count data model 179 hypothesis of absence of serial and cross-correlation in v i can be tested by the multivariate version of the Portmanteau statistic: 6 QL ð Þ ¼ n XL ‘¼1 tr v ðÞ ‘ 0 vð0Þ 1 v ðÞ ‘ vðÞ 0 1 h i ; (2.18) where v ðÞ¼ ‘ Pn i¼‘þ1 viv0 i ‘ ðn ‘ 1Þ. Under the null hypothesis, Q(L) is asymptotically χ 2 -distributed with degrees of freedom equal to the difference between four times L and the number of parameters to be estimated. The ML-estimation results for the pure time series specifications (obtained using the optimization procedure of Berndt et al. (1974) (BHHH)) and the results of the corresponding diagnostic checks are summarized in Table 1. The Schwarz criterion suggests to select an ARMA(1,1)-specification for JBX and an ARMA (2,2)-specification for HAL regardless whether symmetry on the coefficient matrices is imposed or not. All coefficient estimates are at least significant at the 5% level. The LR-test for symmetry of the coefficient matrices rejects the null of symmetric responses for both stocks. Our estimates reveal some differences in the dynamics of the price direction variable for the two stocks. For the JBX stock the estimate of 0.912 (0.888 for the non-symmetric specification) for the coefficient c1 (1) indicates a high degree of persistence in the price direction variable. Independent of the direction of the price movement, the probability of a price change is comparatively high if the probability of a price change for the previous transaction was high. Because the probability of a non-zero price change can be interpreted as a specific measure of price volatility, this finding reflects a clustering of volatility. Since under the estimated non-symmetric specification a12 (1) (1) (1) (1) < a11 and a22 < a21 we can conclude that there is no clear evidence for a bid-ask bounce. Hence, our estimates confirm the explorative findings on the cross-correlations of the price direction variable (Fig. 4) and the simple autocorrelation function of the transaction prices in Fig. 2. The results for HAL are more along the lines of previous empirical findings on the dynamics of the transaction price process. Since c1 (1) +c 1 (2) is positive and close to unity, a high degree of persistence can be found as well. Moreover, there is now evidence for a negative first-order serial cross-correlation for the price change (1) (1) (1) (1) indicators with a12 > a11 and a22 < a21 , indicating the existence of a bid-ask bounce. Our diagnostic checks show that most of the dynamics of the price direction variable is captured for the JBX data, but not for the HAL. For JBX the generalized Portmanteau statistic Q(30) with a value of 132.9 (121.1) does not reject the null hypothesis of no cross-correlations at the 10% significance level for the symmetric and the nonsymmetric specification. For the raw data xi, the corresponding value of the Q(30) statistic was found to be 303.9. For HAL the generalized Portmanteau statistics indicate that the standardized residuals are still cross-correlated, although the model reduces the value of the Q(30) statistic quite substantially from value of 3590.0 for the raw data to 163.6 (non-symmetric specification). Figure 5 depicts the cross-correlation functions of the standardized residuals v−1i and v1i. For JBX all but one correlations lie within the 99% confidence band 6 See, for example, Lütkepohl (1993).
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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 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 183: 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
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
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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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