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214 6 Conclusion Using 5-min euro/dollar mid-quotes for the May 15 through November 14, 2001 time period, we shed light on the predictability and profitability of some chart patterns. We compare results according to two extrema detection methods. The first method (M1), traditionally used in the literature, considers only prices which occur at the end of each time interval (they are called close prices). The second method (M2) takes into account both the highest and the lowest price of each interval of time. To evaluate the statistical significance of the results, we run a Monte Carlo simulation. We conclude on the apparent existence of some technical patterns in the euro/ dollar intra-daily foreign exchange rate. More than one half of the detected patterns, according to M1 and M2, seem to have some significant predictive success. Nevertheless, only two out of twelve patterns present significant profitability, which is however too small to cover the transaction costs. We also show that the extrema detection method using high and low prices provides higher but riskier profits than those provided by the M1 method. To summarize, chart patterns seems to really exist in the euro/dollar foreign exchange market at the 5 min level. They also show some power to predict future price trends. However, trading rules based upon them seem unprofitable. Acknowledgements While remaining responsible for any error in this paper, we thank Luc Bauwens, Winfried Pohlmeier and David Veredas (the editors of the special issue) and two anonymous referees for helpful comments which improved the results in the paper. We thank also Eric Debodt, Nihat Aktas, Hervé Alexandre, Patrick Roger and participants at the 20th AFFI International Conference (France) and SIFF 2003 seminar (France). This paper presents the results of research supported in part by the European Community Human Potential Programme under contract HPRN-CT-2002-00232, Microstructure of Financial Markets in Europe. Appendices A. Price curve estimation Before adopting the Nadaraya–Watson kernel estimator, we tested the cubic splines and polynomial approximations but we conclude empirically that the appropriate smoothing method is the kernel. Because the two first methods carry out too smoothed results and they are not flexible as the kernel method. From the complete series of the price, Pt (t =1,...,T), we take a window k of l regularly spaced time intervals, 13 such that: Pj;k fPtjktkþl1g; (8) j =1,...,l and k=1,...,T−l+1. For each window k, we consider the following relation: Pj;k ¼ mXPj;k þ Pj;k ; (9) where Pj;k is a white noise and mXPj;k is an arbitrarily fixed but unknown non linear function of a state variable XPj;k . Like Lo et al. (2000) to construct a smooth 13 We fix l at 36 observations. W. B. Omrane, H. V. Oppens
The performance analysis of chart patterns 215 function in order to approximate the time series of prices Pj,k, we set the state variable equal to time, XPj;k m(x) may be expressed as: ¼ t: For any arbitrary x, a smoothing estimator of ^mðxÞ ¼ 1 l X l j¼1 !jðxÞPj;k; (10) where the weight ωj(x) is large for the prices Pj,k with XPj;k near x and small for those with XPj;k far from x. For the kernel regression estimator, the weight function ωj(x) is built from a probability density function K(x), also called a kernel: KðxÞ 0; Z þ1 1 KðuÞdu ¼ 1: (11) By rescaling the kernel with respect to a parameter h > 0, we can change its spread: 1 KhðuÞ h Kðu=hÞ; Zþ1 KhðuÞdu ¼ 1 (12) and define the weight function to be used in the weighted average (10) as: 1 !j;h Kh x XPj;k =ghðxÞ (13) ghðxÞ 1 l X l j¼l Kh x XPj;k : (14) Substituting (14) into (10) yields the Nadaraya–Watson kernel estimator ^mhðxÞ of m(x): ^mhðxÞ ¼ 1 l X l j¼l !j;hðxÞPj;k ¼ Pl j¼1 Kh x XPj;k Pj;k Pl j¼1 Kh : (15) x XPj;k If h is very small, the averaging will be done with respect to a rather small neighborhood around each of the XPj;k ’s. If h is very large, the averaging will be over larger neighborhoods of the XPj;k’s. Therefore, controlling the degree of averaging amounts to adjusting the smoothing parameter h, also known as the bandwidth. Choosing the appropriate bandwidth is an important aspect of any local-averaging technique. In our case we select a Gaussian kernel with a bandwidth, hopt,j , computed by Silverman (1986): KhðxÞ ¼ 1 h ffiffiffiffiffi p e 2 x2 hopt;k ¼ 4 3 1=5 2h 2 (16) kl 1=5 ; (17)
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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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Page 206 and 207: 200 W. B. Omrane, H. V. Oppens anal
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Page 212 and 213: 206 price 0.8565 0.8575 0.8585 0.85
Page 214 and 215: 208 We distinguish three possible c
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Page 262 and 263: 256 simply aggregated. Even after a
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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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