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306 V. Voev ACF ACF ACF 0.5 0.5 0.5 EK GE.AA GE.MO 0.4 0.4 0.4 Autocorrelation 0.1 0.2 0.3 Autocorrelation 0.1 0.2 0.3 Autocorrelation 0.1 0.2 0.3 0.0 0.0 0.0 20 24 28 32 36 0 4 8 12 16 lag −0.1 20 24 28 32 36 0 4 8 12 16 lag −0.1 20 24 28 32 36 0 4 8 12 16 lag −0.1 ACF ACF ACF 0.5 0.5 0.5 GE.AXP GE.BA GE.CAT 0.4 0.4 0.4 Autocorrelation 0.1 0.2 0.3 Autocorrelation 0.1 0.2 0.3 Autocorrelation 0.1 0.2 0.3 0.0 0.0 0.0 20 24 28 32 36 0 4 8 12 16 lag −0.1 20 24 28 32 36 0 4 8 12 16 lag 20 24 28 32 36 0 4 8 12 16 lag −0.1 ACF ACF 0.5 0.5 0.4 0.4 Autocorrelation 0.1 0.2 0.3 Autocorrelation 0.1 0.2 0.3 Autocorrelation 0.1 0.2 0.3 Fig. 2 Autocorrelation functions of the realized variance and covariance series. to the forecast will produce a good forecast of the initial series. So there is a trade-off between the possibility of including more information in the forecast and obtaining positive definite matrices on the one hand, and the distortions caused by the non-linearity of the transformation on the other. It turns out that in our case the beneficial effects outweigh the negative ones. Figure 3 shows the drc− Chol and the RiskMetrics TM forecast for the same nine variance and covariance series. From the figure it is evident that the dynamic forecasts track the true series much closer than the RiskMetrics TM forecasts, especially at the end of the period when the (co)volatilities were more volatile. The dsrc − Chol forecast looks quite similar ACF 0.5 GE.KO GE.EK GE 0.4 0.0 0.0 0.0 20 24 28 32 36 0 4 8 12 16 lag −0.1 20 24 28 32 36 0 4 8 12 16 lag −0.1 20 24 28 32 36 0 4 8 12 16 lag −0.1
Dynamic modelling of large-dimensional covariance matrices 307 GE.MO GE.AA EK 0.035 0.035 0.035 True DRC-Chol RM True DRC-Chol RM True DRC-Chol RM 0.025 0.025 0.025 0.015 0.015 0.015 0.005 0.005 0.005 100 120 140 160 180 200 220 240 260 280 −0.005 100 120 140 160 180 200 220 240 260 280 −0.005 100 120 140 160 180 200 220 240 260 280 −0.005 GE.CAT GE.AA GE.AXP 0.035 0.035 0.035 True DRC-Chol RM True DRC-Chol RM True DRC-Chol RM 0.025 0.025 0.025 0.015 0.015 0.015 Fig. 3 Comparison of the Riskmetrics TM forecast (RM) and the dynamic realized covariance forecast based on Cholesky series (DRC-Chol) against the realized covariance (True). to the drc − Chol (due to the usually small shrinkage constants), but as we shall see later the forecasts are in fact somewhat better. Turning to the statistical comparison of the forecasting methods, we first briefly present the Diebold–Mariano testing framework as in Harvey et al. (1997). Suppose a pair of l-step ahead forecasts h1 and h2, h1,h2 ∈ H have produced errors (e1t,e2t), t = 1,...,T. The null hypothesis of equality of forecasts is based on some function g(e) of the forecast errors and has the form E [g(e1t) − g(e2t)] = 0. Defining the loss differential dt = g(e1t) − g(e2t) and its average ¯d = T −1 � T t=1 dt, the authors note that ‘the series dt is likely to be 0.005 0.005 0.005 100 120 140 160 180 200 220 240 260 280 −0.005 100 120 140 160 180 200 220 240 260 280 −0.005 100 120 140 160 180 200 220 240 260 280 −0.005 GE GE.EK EK 0.035 0.035 0.035 True DRC-Chol RM True DRC-Chol RM True DRC-Chol RM 0.025 0.025 0.025 0.015 0.015 0.015 0.005 0.005 0.005 100 120 140 160 180 200 220 240 260 280 100 120 140 160 180 200 220 240 260 280 100 120 140 160 180 200 220 240 260 280
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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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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
Page 262 and 263: 256 simply aggregated. Even after a
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Page 266 and 267: 260 together with the restrictions
Page 268 and 269: Table 3 Estimated probabilities of
Page 270 and 271: 264 A. S. Tay, C. Ting More interes
Page 272 and 273: Table 4 Estimated probabilities of
Page 274 and 275: 268 Acknowledgements Tay gratefully
Page 276 and 277: 270 This paper explores the effect
Page 278 and 279: 272 contrast, price responses to po
Page 280 and 281: 274 Fig. 1 Continuous line is the T
Page 282 and 283: 276 the β’s can form a convex sh
Page 284 and 285: 278 fixing some intervals around th
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Page 290 and 291: Appendix Table A1 Consumer confiden
Page 292 and 293: Table A3 Non-farm payrolls • ✓
Page 294 and 295: Table A5 Weekly unemployment claims
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Page 300 and 301: 294 V. Voev with the problem of how
Page 302 and 303: 296 V. Voev 2.1 A sample covariance
Page 304 and 305: 298 V. Voev Using the equicorrelate
Page 306 and 307: 300 V. Voev where �kl(t) is the (
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Page 316 and 317: 310 V. Voev 5 Conclusion Table 2 Ro
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