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54 A. Escribano and R. Pascual the trade indicator (x t). Therefore, the expected impact of a buyer-initiated shock is exactly the reverse of a seller-initiated shock. So as to allow for asymmetric dynamics, next section modifies the structural model used by Hasbrouck (1991) to motivate his VAR model. The empirical counterpart of this most flexible structural model will be a VEC model for ask and bid revisions in response to buyer and seller-initiated shocks, which generalizes Eq. (2.1). Given that ask and bid quotes have a common non-stationary long-run component, the efficient stock price, they must be co-integrated time series (see Hasbrouck 1995). The VEC model is the most common efficient parameterization of vector autoregressive models with co-integrated variables (e.g., Engle and Granger 1987). In this case, the co-integration relationship is known a priori, which lets setting a very general parameterization of the model. We will also allow quote revisions after trade-related shocks to follow non-linear patterns due to trade features, such as size and durations, and market conditions, such as volatility and liquidity. Our approach connects with other econometric applications in microstructure research. Hasbrouck (1995) uses a common-trend representation to simultaneously model the quotes of both the NYSE and the regional markets. The model has an associated VEC representation. Hasbrouck is aimed to measure relative contributions to price discovery. Pascual et al. (2005) build on the model introduced in the next sections to incorporate the markets’ trading processes into Hasbrouck’s (1995) methodology. In this way, they are able to isolate, for each market, the traderelated contribution from the trade-unrelated contribution. Hasbrouck (1999b) estimates an unobserved-components model for the best market quotes. In this model, ask and bid quotes have a common random walk component, and the respective transitory terms are modeled as two unobserved and identical first-order autoregressive processes. This model features discreteness, clustering, and stochastic volatility effects. However, it does not incorporate the trading process, and the transitory components of ask and bid quotes are assumed mutually independent. This analysis does not deal with asymmetric dynamics either. In a recent paper, Zhang et al. (2005) use Hasbrouck’s (1999b) methodology to decompose the bid–ask spread of a single stock (General Electric) into its ask and bid exposure costs constituents. They show that ask and bid components of the spread change asymmetrically about the efficient price. Our findings, based on a less sophisticated but more widespread econometric approach, are totally consistent. Even closer to the purpose of this paper is the independent study by Engle and Patton (2004). These authors (henceforth, EP) also estimate an error correction model for ask and bid quotes using data on a large set of NYSE-listed stocks. There are, however, remarkable differences between both empirical specifications. In EP’s model, the trading process is exogenous. Thus, they model the dynamics of ask and bid quotes, but not the feedback from quotes to trades. As shown by Hasbrouck (1991), to accurately measure the informativeness of trades, we need to model not only how quotes evolve after the trade, but also how trading responds to the progressive adjustment in quotes. Since we are aimed to compare the information content of buyer and seller-initiated trades, we propose a model that accommodates a broader set of dynamic interactions between quotes and trades than EP’s model. Moreover, EP’s model is quote-driven, meaning that there is a new observation each time there is a change in quotes. Since we are interested in the price impact of trades, it makes sense to define our model in trade time. In this manner, we filter those quote changes that are not directly linked to the trading
Asymmetries in bid and ask responses to innovations in the trading process 55 process. 6 These technical disparities may explain the discrepant findings we will report later on regarding the information content of buys versus sells. Nevertheless, in our opinion, EP’s paper and the present paper are complementary, since both evidence the relevance of modeling ask and bid prices jointly rather than averaging them through the quote midpoint. 3 The model 3.1 A structural dynamic model of quote formation In this subsection, we build on Hasbrouck (1991) to develop a dynamic model for ask and bid quotes. The model allows for asymmetric adjustment paths going after trades. Two main features differentiate our structural model from those previously found in the literature. First, ask and bid prices share a common long-run component, the efficient price, which is updated due to trade-related and tradeunrelated informative shocks. The empirical evidence previously revised, however, suggests that buyer and seller-initiated trades (henceforth, “buys” and “sells”) may not be equally informative. To accommodate this empirical observation, we will distinguish between trade-related shocks to buy and trade-related shocks to sell. Second, quotes result from adding or subtracting a transitory component (wt), due to market frictions and market-making costs, to the efficient price (mt). Since the evidence at hand points to asymmetric short-term adjustments of the ask quote versus the bid quote, in our specification we will allow the short-term components a b of ask and bid quotes to differ (Δwt ≠Δwt ). We use the same notation as in Hasbrouck (1991). The model is defined in trade time. Thus, the subscript t denotes the t-th trade in the chronological sequence of trades. Hereafter, the superscript a means “ask quote,” b means “bid quote,” B refers to buys, and S refers to sells. mt is the efficient price after the t-th trade, which B S could be either a buy (xt ) or a sell (xt ). Similarly, at and bt are the quotes posted right after the t-th trade. The adjustment in the posted quotes after the t-th trade are Δat=a t−a t −1 and Δbt=b t−b t −1. The efficient price follows the random walk process in Eq. (3.1). Three types of stochastic shocks update mt: trade-unrelated shocks (v1,t), and trade-related shocks B S due to buyer-initiated trades (v2,t ) or seller-initiated trades (v2,t). We let v1,t be B S B S mutually and serially uncorrelated with v2,t and v2,t, while v2,t and v2,t are serially uncorrelated but, perhaps, mutually correlated. The parameters B and S measure the average amount of private information (adverse selection costs) conveyed by buys and sells, respectively. If B = S buy shocks would have the same information content than sell shocks. mt ¼ mt 1 þ B v B 2;t þ S v S 2;t þ v1;t: (3.1) 6 Another minor difference is that, unlike EP’s model, the properties of our empirical specification are derived from a theoretical framework presented in the next section. The empirical model we derive from the structural model is an “extended” VECM, that is, it incorporates lagged values of the error correction term. The EP’s model is a standard VEC.
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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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Page 13 and 14: Luc Bauwens . Dagfinn Rime . Genaro
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Page 38 and 39: 32 K. Bien et al. Although economet
Page 40 and 41: 34 K. Bien et al. 2.1 Copula functi
Page 42 and 43: 36 K. Bien et al. and x k t ≡ (xk
Page 44 and 45: 38 K. Bien et al. Fig. 3 Multivaria
Page 46 and 47: 40 K. Bien et al. Bivariate model s
Page 48 and 49: 42 K. Bien et al. deviation 0.0099,
Page 50 and 51: 44 K. Bien et al. - Set ˆzt = Âxt
Page 52 and 53: 46 K. Bien et al. % Frequency −0.
Page 54 and 55: 48 K. Bien et al. References Amilon
Page 56 and 57: 50 1 Introduction A. Escribano and
Page 58 and 59: 52 A. Escribano and R. Pascual Jang
Page 62 and 63: 56 The generating processes of mark
Page 64 and 65: 58 with AtðLÞ ¼ 0 B @ 1 ð ÞAab
Page 66 and 67: 60 A. Escribano and R. Pascual cros
Page 68 and 69: 62 Hasbrouck (1991). The system is
Page 70 and 71: 64 unitary seller-initiated shock (
Page 72 and 73: 66 6.1 Estimation of the baseline m
Page 74 and 75: Table 2 The base-line VEC model for
Page 76 and 77: 70 Table 3 Simulation of the base-l
Page 78 and 79: 72 revert towards narrow levels. As
Page 80 and 81: Table 5 Impulse-response functions
Page 82 and 83: 76 We also show that NYSE buyer-ini
Page 84 and 85: 78 As 0 < a m < 1; L ð Þ ¼ 1 a m
Page 86 and 87: 80 NYSE 2000 Stocks AOL America Onl
Page 88 and 89: 82 A. Escribano and R. Pascual Madh
Page 90 and 91: 84 1 Introduction S. Frey, J. Gramm
Page 92 and 93: 86 develops the empirical methodolo
Page 94 and 95: Table 1 Sample descriptives Company
Page 96 and 97: 90 comparability across stocks, we
Page 98 and 99: 92 subtracting the deviations from
Page 100 and 101: 94 market order distribution that c
Page 102 and 103: 96 Table 2 First stage GMM results
Page 104 and 105: Table 4 First stage GMM results bas
Page 106 and 107: 100 S. Frey, J. Grammig quotes on e
Page 108 and 109: 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
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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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