3 1. 2. 3. 4. 5. 1 3 3 3 2008 3 2008 2008 3 2008 2008, 1
5 Lo and MacKinlay (1990a) de Jong and Nijman (1997) Cohen et al. (1983) Lo and MacKinlay (1990a b) Cohen et al. (1983) de Jong and Nijman (1997) de Jong and Nijman (1997) Parzen (1963) Cohen et al. (1983) Robinson (1985) Lo and Mackinlay (1990a b) Conley et al. (1995) Ghysels et al. (1995) 2 3 3 3 3 2 3 2005 10 12 3 2 1 3 2
3 3 6 3 1 10 50 2005 10 12 3 1 200 1 600 1 200 3 9 11 12 30 3 30 9 2 9 10 2 2 2005 10 12 3 3 6 6 6 2008 1 6 ( 1a-1c, 1a-1c, 2a-2c) 3 3 6 3
3 3 1a-1c 2a-2c 3 6 5 1 2 3 6 5 3 6 5 75 90 ( 3a-3c) 3 6 3a-3c 3 2008 2008 1 3 1 3 ( 2a-2c, 4a-4c, 5a-5c) 2a-2c 4a-4c 3 30 5a-5c 3 30 30 4
1 30 50 5 30 ( 6a-6c) 6a-6c 3 30 1 3 30 30 2008 2008 30 13 00 30 30 1 30 30 2008 30 1 30 30 30 30 30 30 30 2 3 5 6 1 4 3 de Jong and Nijman (1997) de Jong and Nijman (1997) 2 2 p t q t p t i q t j p t 2 p ti+1 p ti = t i+1 t=t i +1 Δp t (1) 5
Δp t = p t p t 1 (1) t i i 2 y ij (p ti+1 p ti )(q tj+1 q tj )= t i+1 t=t i +1 t j+1 Δp t s=t j +1 Δq s (2) (deterministic) 2 E[y ij ]=E[ t i+1 t=t i +1 t j+1 Δp t t=t j +1 Δq s ]= t i+1 t j+1 t=t i +1 s=t j +1 γ t s (3) γ k = Cov[Δp t, Δq t k ]=E[Δp t Δq t k ] Δq t k = q t k q t k 1 3 γ k x ij (k) x ij (k) =max(0,min(t i+1,t j+1 + k) max(t i,t j + k)) (4) x ij (k) x ij (k) y ij E[y ij x ij ]= K k= K x ij (k)γ k (5) K -K 5 2K+1 γ k γ x ij (2K+1 x ij (k) y ij x ijγ + e ij (6) γ y ij x ij 2 y ij 1 γ γ k = γ k x ij Δp t Δq t γ k γ k ρ k = ( γ p (7) 0 γq 0) 1/2 γ p 0 γ q 0 Δp t Δq t γ p 0 γ q 0 t 3.1 6
7a-7c 3 K) 5 10 K=6,1 K=15,de Jong and Nijman (1997) S & P 500 K 5 10 K=8,10, 1 K=20,25 ( 7a) 5 10 5 10 k=3 10 1 k=1 5 de Jong and Nijman (1997) S & P 500 k=1 bid-ask bounce) k=8 10 5 ( 7b) 5 10 5 k=1 1 k=3 2 1 3 1 t k=14 t 10 ( 7c) 7
5 10 5 k=1 10 10 1 k=9 2 1 3 k=9 3 2 8a-8c 3 K) 5 10 K=6,1 K=15 5 10 K=8,10, 1 K=20,25 ρ k = Cov[Δp t, Δq t k ]/(γ0γ p 0) q 1/2 p q k k k k 8b 8c 2 2 ( 8a) 5 k= 1 0 1 k=0 t 10 k=0 1 5 0 t 10 5 1 k= 2 4 5 6 8
5 10 k k=5 8 11 12 13 14 5 10 6 4 2 5 k=0 10% ( 8b) 5 k= 1 0 k= 1 t t k=0 10 k=, 1 0, 6 k= 1 5 10 10 1 k= 4 2 0 k=1 4 2 1 k= 4 2 0 5 ( 8c) 5 k= 4, 1,0,1 t k= 0 10 k= 4,0,1 k=0 k=1 10 k=0 5 10 k=1 5 1 k= 9, 8, 2, 8 k= 9, 2 k= 8,8 1 2 9
1 5 10 5 k=0 1 k= 2 5 k= 1 1 k= 9 1 k= 8 1 k=8 5 k=1 1 k=0 4 3 2008 2003 2 2004 2 13 2005 10 12 3 (2008), 3 1 5 10 1 5 10 3 ρ k = γ k ρ (γ p k = γ k 0 γq 0 )1/2 ( γ 0 γq p 0 )1/2 γ 0, p γ q 0 γ k γ k γ k γ p 0 γ p 0 White (1980) γ q 0 γ q 0 y ij x ij (k) y X 6 y = Xγ + e (8) 2 1 y p ij (p ti+1 p ti )(p tj+1 p tj ) (9) 10
y q ij (q ti+1 q ti )(q tj+1 q tj ) (10) y p ij y q ij 8 y p = X p γ p + e p (11) y q = X q γ q + e q (12) y p X p y p ij y p ij x p ij(k) y q X q y q ij y q ij x q ij(k) ( γ γ) AV [( γ γ)] = (X X) 1 X E[ee ]X(X X) 1 (13) AV [ ] ( γ p γ p ) ( γ q γ q ) AV [( γ p γ p )] = (X p X p ) 1 X p E[e p e p ]X p (X p X p ) 1 (14) AV [( γ q γ q )] = (X q X q ) 1 X q E[e q e q ]X q (X q X q ) 1 (15) ( γ γ) ( γ p γ p ) ACOV [( γ γ), ( γ p γ p )] = (X X) 1 X E[ee p ]X p (X p X p ) 1, (16) ( γ γ) ( γ q γ q ) ACOV [( γ γ), ( γ q γ q )] = (X X) 1 X E[ee q ]X q (X q X q ) 1, (17) ( γ p γ p ) ( γ q γ q ) ACOV [( γ p γ p ), ( γ q γ q )] =(X p X p ) 1 X p E[e p e q ]X q (X q X q ) 1, (18) 16 γ γ γ p γ p ( γ γ) ( γ p γ p ) γ k γ k γ p 0 γ p 0 13 18 Ω γ q 0 γ q 0 ( ρ k ρ k ) delta method ( Hayashi (2000) ) ρ k γ k,γ0,γ p q 0 ρ k f(γ k,γ0,γ p 0) q ρ k γ k,γ0,γ p q 0 11
F (γ k,γ0,γ p 0) q ( F (γ k,γ0,γ p 0) q ρk, ρ k γ k γ p, ρ ) k 0 γ q 0 ( ) 1 = (γ0γ p 0) q, 1 γ k 1/2 2 (γ0) p 3/2 (γ0) q, 1 γ k 1/2 2 (γ0) p 1/2 (γ0) q 3/2 (19) ( ρ k ρ k ) AV [( ρ k ρ k )] = F (γ k,γ0,γ p 0)ΩF q (γ k,γ0,γ p 0) q (20) ( ρ k ρ k ) ÂV [( ρ k ρ k )] = F ( γ k, γ 0, p γ 0) q ΩF ( γ k, γ 0, p γ 0) q (21) ρ k 21 2008. 11 1, 33-59. Cohen, K., Hawawimi, G., Maier, S., Schwartz, R., Whitcomb, D., 1983. Friction in the trading process and the estimation of systematic risk. Joumal of Financial Economics 12, 263-278. Conley, T., Hansen, L.P., Luttmer, E., Scheinkman, J., 1995. Short term interest rates as subordinated diffusions. Unpublished working paper. de Jong, F., Nijman, T., 1997. High frequency analysis of lead-lag relationships between financial markets, Journal of Empirical Finance 4, 259-277. Ghysels, E., Gourieroux. C., Jasiak, J., 1995. Market time and asset price movements: Theory and estimation. Discussion paper CIRANO and CREST. Hayashi, F., 2000. Econometrics, Princeton University Press, Princeton. 12
Lo, A., MacKinlay, A.C., 1990a. An econometric analysis of infrequent trading. Journal of Econometrics 45,181-211. Lo, A., MacKinlay, A.C., 1990b. When are contrarian profits due to stock market overreaction?. Review of Financial Studies 3, 175-205. Parzen, E., 1963. On spectral analysis with missing observations and amplitude modulation. Shankya, series A 25, 383-392. Robinson, P.M., 1985. Testing for serial correlation in regression with missing observations. Joumal of the Royal Statistical Society B 47, 429-437. White, H., 1980, A hetoroskedasticity-consistent covariance matrix estimator and a direct test for heteroskedasticity, Econometrica 48, 817-838. 1a 60000 120000 50000 100000 40000 80000 30000 60000 20000 40000 10000 20000 0 0 051004 051102 051202 051230 6 13
1b 60000 60000 50000 40000 40000 30000 20000 20000 10000 0 0 051004 051102 051202 051230 6 1c 45000 15000 40000 35000 30000 10000 25000 20000 15000 5000 10000 5000 0 0 051004 051102 051202 051230 6 14
2a 30 400 350 300 250 9:00 9:30 10:00 10:30 12:30 13:00 13:30 14:00 14:30 15:00 200 150 100 50 0 No. 1 No. 2 No. 3 (a) 1 3 6000 5000 4000 9:00 9:30 10:00 10:30 12:30 13:00 13:30 14:00 14:30 15:00 3000 2000 1000 0 No. 1 No. 2 No. 3 No. 4 No. 5 No. 6 (b) 1 6 15
2b 30 300 250 200 9:00 9:30 10:00 10:30 12:30 13:00 13:30 14:00 14:30 15:00 150 100 50 0 No. 1 No. 2 No. 3 (a) 1 3 2500 2000 1500 9:00 9:30 10:00 10:30 12:30 13:00 13:30 14:00 14:30 15:00 1000 500 0 No. 1 No. 2 No. 3 No. 4 No. 5 No. 6 (b) 1 6 16
2c 30 60 50 40 9:00 9:30 10:00 10:30 12:30 13:00 13:30 14:00 14:30 15:00 30 20 10 0 No. 1 No. 2 No. 3 (a) 1 3 900 800 700 600 500 9:00 9:30 10:00 10:30 12:30 13:00 13:30 14:00 14:30 15:00 400 300 200 100 0 No. 1 No. 2 No. 3 No. 4 No. 5 No. 6 (b) 1 6 17
1a 60 59 60 60 56095.7932 0.0002 71148.3333 3974452488.2333 2809.4014 0.0199 22615.5295 1249166353.1300 62043.0327 0.0483 104772.0000 5759777466.7928 51581.7556 0.0499 2338.0000 138643400.0000 6 1b 60 59 60 60 52319.4253 0.0005 26654.3167 1396735739.9346 3371.4075 0.0211 8366.6447 467798470.7706 59050.0616 0.0498 44679.0000 2391110149.2444 46985.5326 0.0431 1969.0000 108806940.0000 6 1c 60 59 60 60 40022.3660 0.0005 7100.1833 284976809.8565 1116.7117 0.0157 2210.2090 92783437.3483 42815.5159 0.0326 12176.0000 499040961.5672 38383.6885 0.0290 754.0000 30408820.0000 6 18
2a :% 2005 10 11 12 No. 1 0.6 0.6 0.9 No. 2 1.3 0.8 1.7 No. 3 2.1 2.2 5.4 No. 4 6.9 17.2 8.3 No. 5 41.5 18.6 21.3 No. 6 47.7 60.6 62.4 2b :% 2005 10 11 12 No. 1 2.2 2.4 2.4 No. 2 3.8 2.9 4.0 No. 3 3.9 5.9 7.2 No. 4 8.1 13.8 9.9 No. 5 30.5 24.3 24.8 No. 6 51.5 50.8 51.7 2c :% 2005 10 11 12 No. 1 1.3 4.9 3.1 No. 2 1.0 1.7 1.3 No. 3 1.8 3.3 2.3 No. 4 7.0 5.4 5.6 No. 5 31.8 25.3 23.7 No. 6 57.0 59.4 64.0 19
3a (h:m:s) No. 1 9 : 01 10 : 53 60 12 : 42 15 : 29 60 No. 2 9 : 02 10 : 58 60 12 : 35 15 : 28 60 No. 3 9 : 04 10 : 59 60 12 : 37 15 : 29 60 No. 4 9 : 06 10 : 59 60 12 : 39 15 : 28 60 No. 5 9 : 08 10 : 59 60 12 : 41 15 : 29 60 No. 6 9 : 10 10 : 59 60 12 : 43 15 : 29 60 3b (h:m:s) No. 1 9 : 00 10 : 53 60 12 : 42 15 : 26 60 No. 2 9 : 02 10 : 57 60 12 : 35 15 : 24 60 No. 3 9 : 04 10 : 58 60 12 : 37 15 : 24 60 No. 4 9 : 06 10 : 58 60 12 : 39 15 : 28 60 No. 5 9 : 08 10 : 59 60 12 : 41 15 : 28 60 No. 6 9 : 10 10 : 59 60 12 : 42 15 : 29 60 3c (h:m:s) No. 1 9 : 05 10 : 23 60 12 : 54 15 : 15 60 No. 2 9 : 04 10 : 28 60 12 : 40 15 : 11 60 No. 3 9 : 05 10 : 46 60 12 : 38 15 : 20 60 No. 4 9 : 06 10 : 52 60 12 : 39 15 : 28 60 No. 5 9 : 08 10 : 58 60 12 : 41 15 : 28 60 No. 6 9 : 10 10 : 59 60 12 : 43 15 : 29 60 20
4a 30 9:00 9:30 10:00 10:30 12:30 13:00 13:30 14:00 14:30 15:00 No. 1 117 40 60 37 75 33 39 34 33 53 No. 2 157 94 73 74 117 70 61 59 62 102 No. 3 388 266 210 169 281 193 141 130 144 171 No. 4 1372 1099 890 711 890 641 569 503 588 702 No. 5 3272 2719 2203 1863 1957 1834 1580 1483 1425 1639 No. 6 5879 5625 4551 3808 3641 3642 3309 3227 3211 3535 4b 30 9:00 9:30 10:00 10:30 12:30 13:00 13:30 14:00 14:30 15:00 No. 1 186 51 50 53 88 50 42 42 49 70 No. 2 190 93 88 79 127 76 67 68 74 106 No. 3 279 176 146 111 202 122 110 113 99 141 No. 4 522 370 307 245 333 244 184 182 229 260 No. 5 1230 941 747 649 750 598 542 479 532 605 No. 6 2271 1792 1458 1278 1356 1141 1092 1050 1191 1286 4c 30 9:00 9:30 10:00 10:30 12:30 13:00 13:30 14:00 14:30 15:00 No. 1 54 7 10 9 9 19 8 6 5 10 No. 2 18 12 9 11 13 7 8 11 9 11 No. 3 30 12 22 14 25 15 14 10 13 23 No. 4 65 38 43 40 50 30 28 31 32 51 No. 5 323 212 176 135 178 120 102 86 93 161 No. 6 807 573 554 429 498 411 295 319 309 646 21
5a 30 9:00 9:30 10:00 10:30 12:30 13:00 13:30 14:00 14:30 15:00 No. 1 23.4 7.6 11.8 7.1 14.2 6.0 7.3 6.4 6.2 9.9 No. 2 18.2 11.0 8.6 8.7 13.7 7.5 6.9 6.8 7.0 11.6 No. 3 18.8 12.9 10.0 8.2 13.5 9.0 6.6 6.2 6.7 8.2 No. 4 17.4 14.0 11.3 9.0 11.1 7.9 7.1 6.2 7.2 8.7 No. 5 16.6 13.6 11.0 9.3 9.7 8.7 7.9 7.4 7.2 8.4 No. 6 14.7 14.1 11.3 9.5 8.9 8.9 8.1 7.9 7.8 8.6 1 100 5b 30 9:00 9:30 10:00 10:30 12:30 13:00 13:30 14:00 14:30 15:00 No. 1 28.5 7.7 7.0 7.6 12.8 7.1 6.0 6.1 7.1 10.0 No. 2 19.8 10.0 9.3 8.5 13.1 7.7 6.8 6.9 7.5 10.4 No. 3 19.3 12.0 10.0 7.6 13.6 7.9 7.2 7.2 6.4 8.8 No. 4 18.6 13.1 10.7 8.5 11.6 8.3 6.4 6.2 7.6 9.0 No. 5 17.7 13.4 10.6 9.3 10.5 8.4 7.5 6.6 7.3 8.6 No. 6 16.5 13.0 10.6 9.3 9.7 8.1 7.8 7.5 8.5 9.1 1 100 5c 30 9:00 9:30 10:00 10:30 12:30 13:00 13:30 14:00 14:30 15:00 No. 1 54.1 4.8 5.7 6.0 7.6 3.4 4.2 3.5 2.5 8.2 No. 2 21.1 10.2 7.1 7.9 14.7 6.0 6.2 9.9 6.1 10.9 No. 3 18.5 7.0 12.5 7.5 15.5 7.5 6.9 5.2 6.8 12.5 No. 4 16.9 10.0 10.4 9.9 12.8 6.9 6.5 6.8 7.3 12.5 No. 5 21.2 13.8 10.9 8.6 11.3 7.1 6.1 5.4 5.5 10.2 No. 6 16.6 12.0 11.6 9.0 10.2 8.4 6.0 6.6 6.3 13.3 1 100 22
6a 30 x1,000 9:00 9:30 10:00 10:30 12:30 13:00 13:30 14:00 14:30 15:00 No. 1 4.598 5.587 2.871 3.161 3.911 2.793 2.370 2.240 1.979 2.583 No. 2 5.385 5.169 2.974 3.143 3.378 3.803 2.269 2.430 1.923 2.862 No. 3 4.915 5.110 3.573 2.893 3.085 3.577 2.466 2.219 1.973 3.444 No. 4 6.011 5.301 4.244 3.568 2.696 3.816 2.453 2.853 2.107 3.890 No. 5 6.683 5.404 4.168 3.614 3.496 4.450 2.819 3.191 2.386 3.945 No. 6 8.290 5.532 4.386 3.936 3.615 4.696 3.017 3.416 2.341 4.335 900 9:00-9:29 2 6 30 6b 30 x1,000 9:00 9:30 10:00 10:30 12:30 13:00 13:30 14:00 14:30 15:00 No. 1 4.743 3.562 3.051 3.141 3.170 2.413 2.617 2.755 2.384 2.753 No. 2 5.257 4.814 3.428 3.570 3.122 3.183 2.520 2.729 2.187 2.697 No. 3 5.810 5.169 4.018 2.846 2.974 3.545 2.581 2.861 2.137 3.202 No. 4 7.160 5.772 4.393 3.372 3.124 4.489 2.712 2.942 2.733 3.440 No. 5 7.963 5.542 4.767 4.110 3.611 4.661 2.884 2.860 2.815 4.539 No. 6 9.757 5.596 5.104 4.128 4.018 5.314 3.525 3.311 2.705 4.535 900 9:00-9:29 2 6 30 6c 30 x1,000 9:00 9:30 10:00 10:30 12:30 13:00 13:30 14:00 14:30 15:00 No. 1 3.285 1.445 0.784 1.120 1.367 0.643 1.109 0.818 1.315 1.224 No. 2 4.390 2.137 1.854 1.378 1.719 1.189 1.059 1.054 0.847 1.290 No. 3 5.607 1.868 1.887 1.438 1.762 1.669 1.367 1.216 0.930 1.068 No. 4 5.499 2.209 1.892 2.127 2.124 1.409 1.038 1.260 1.306 1.254 No. 5 5.044 2.491 1.672 1.710 1.662 1.441 1.119 0.981 0.789 1.388 No. 6 5.545 2.223 1.778 1.708 1.624 1.283 0.818 0.958 0.900 1.505 900 9:00-9:29 2 6 30 23
7a Lag 10 min 5 min 1min 0 0.004148 ( 2.724) 0.011969 ( 9.200) 0.026337 (17.871) 1-0.267 (-1.051) 0.060 ( 1.134) -0.281 (-7.081) 2-0.002 (-0.337) -0.078 (-1.397) 0.039 ( 1.077) 3-0.012 (-1.825) 0.064 ( 1.328) 0.043 ( 1.264) 4-0.002 (-0.356) -0.022 (-0.584) 0.027 ( 0.871) 5 0.002 ( 0.221) -0.011 (-0.753) -0.037 (-1.301) 6 0.007 ( 0.936) 0.013 ( 0.590) -0.007 (-0.276) 7 0.040 ( 1.408) 8-0.050 (-1.844) 9-0.003 (-0.095) 10 0.054 ( 1.853) 11-0.033 (-1.128) 12-0.010 (-0.343) 13-0.009 (-0.303) 14 0.032 ( 1.000) 15-0.024 (-0.799) heteroskedasticity and autocorrelation consistent 24
7b Lag 10 min 5 min 1min 0 0.002819 ( 7.274) 0.024132 ( 7.801) 0.033688 (20.705) 1-0.077 (-0.893) -0.303 (-3.662) -0.294 (-8.358) 2-0.007 (-0.682) -0.031 (-0.816) 0.089 ( 2.724) 3-0.006 (-0.491) 0.059 ( 1.334) -0.091 (-3.147) 4 0.005 ( 0.384) -0.058 (-1.200) -0.013 (-0.475) 5 0.003 ( 0.248) -0.017 (-0.230) -0.039 (-1.401) 6 0.005 ( 0.313) 0.130 ( 1.487) -0.010 (-0.349) 7-0.002 (-0.082) 8-0.031 (-1.230) 9-0.007 (-0.258) 10 0.029 ( 1.070) 11-0.003 (-0.106) 12-0.022 (-0.765) 13-0.020 (-0.774) 14 0.052 ( 1.936) 15 0.006 ( 0.217) heteroskedasticity and autocorrelation consistent 25
7c Lag 10 min 5 min 1min 0 0.000137 ( 9.911) 0.000260 ( 9.731) 0.000601 (18.457) 1 0.083 ( 1.664) 0.115 ( 1.994) -0.106 (-2.467) 2-0.017 (-0.533) 0.027 ( 1.150) -0.050 (-2.483) 3-0.018 (-0.509) -0.012 (-0.606) -0.007 (-0.417) 4-0.003 (-0.087) 0.001 ( 0.110) 0.008 ( 0.487) 5 0.001 ( 0.063) -0.006 (-0.505) 0.015 ( 1.009) 6-0.006 (-0.154) 0.001 ( 0.047) -0.007 (-0.598) 7-0.012 (-0.989) 8-0.013 (-1.053) 9-0.026 (-2.193) 10 0.001 ( 0.090) 11 0.001 ( 0.052) 12 0.014 ( 1.513) 13-0.006 (-0.713) 14-0.004 (-0.490) 15 0.003 ( 0.430) heteroskedasticity and autocorrelation consistent 26
8a Lag 10 min 5 min 1min -15 0.002 ( 0.216) -14-0.005 (-0.353) -13-0.010 (-0.721) -12 0.014 ( 1.160) -11-0.012 (-1.038) -10 0.008 ( 0.886) -9 0.014 ( 1.201) -8 0.010 ( 1.019) -7-0.003 (-0.292) -6 0.016 ( 1.001) -0.012 (-0.913) 0.037 ( 2.654) -5 0.002 ( 0.175) 0.002 ( 0.146) 0.044 ( 2.898) -4-0.004 (-0.246) 0.014 ( 1.082) 0.033 ( 2.297) -3-0.032 (-1.453) 0.008 ( 0.715) 0.014 ( 0.900) -2 0.040 ( 1.546) -0.003 (-0.168) 0.081 ( 5.293) -1-0.023 (-0.517) 0.231 ( 6.839) 0.003 ( 0.255) 0 0.349 ( 4.317) 0.537 ( 7.770) 0.014 ( 0.945) 1 0.120 ( 2.192) 0.102 ( 4.939) -0.015 (-0.876) 2-0.037 (-0.893) 0.021 ( 1.761) -0.008 (-0.417) 3-0.000 (-0.039) -0.005 (-0.541) -0.006 (-0.306) 4-0.007 (-0.642) -0.013 (-0.982) -0.022 (-1.383) 5-0.012 (-0.865) 0.008 ( 0.696) -0.031 (-1.661) 6 0.006 ( 0.446) 0.006 ( 1.107) 0.014 ( 0.998) 7 0.007 ( 0.422) 8-0.037 (-1.733) 9-0.020 (-1.044) 10 0.015 ( 0.985) 11 0.038 ( 1.951) 12-0.042 (-1.652) 13 0.123 ( 1.878) 14-0.244 (-1.905) 15 0.048 ( 0.310) heteroskedasticity and autocorrelation consistent 27
8b Lag 10 min 5 min 1min -15-0.036 (-1.535) -14-0.001 (-0.047) -13 0.024 ( 1.268) -12 0.006 ( 0.330) -11 0.030 ( 1.482) -10-0.001 (-0.032) -9-0.032 (-1.589) -8 0.006 ( 0.267) -7-0.015 (-0.742) -6 0.007 ( 0.771) 0.015 ( 0.421) -0.029 (-1.411) -5 0.001 ( 0.055) -0.076 (-1.680) -0.003 (-0.144) -4 0.001 ( 0.151) 0.050 ( 1.592) -0.071 (-3.614) -3-0.017 (-1.972) 0.034 ( 1.046) 0.009 ( 0.558) -2-0.002 (-0.309) -0.067 (-1.539) -0.056 (-3.211) -1 0.039 ( 2.850) -0.075 (-2.205) -0.015 (-0.907) 0-0.316 (-4.074) -0.378 (-8.007) -0.060 (-3.641) 1 0.148 ( 1.044) -0.006 (-0.502) 0.032 ( 2.009) 2-0.329 (-1.540) -0.002 (-0.126) -0.009 (-0.635) 3 0.189 ( 1.045) -0.019 (-0.886) -0.024 (-1.503) 4 0.002 ( 0.276) -0.009 (-0.446) 0.022 ( 1.259) 5-0.007 (-0.648) -0.001 (-0.053) -0.030 (-1.678) 6 0.027 ( 2.139) 0.013 ( 0.597) 0.014 ( 0.922) 7 0.004 ( 0.254) 8 0.031 ( 1.706) 9-0.023 (-1.224) 10 0.007 ( 0.402) 11 0.022 ( 1.192) 12-0.015 (-0.946) 13-0.014 (-0.940) 14 0.015 ( 0.911) 15-0.021 (-1.012) heteroskedasticity and autocorrelation consistent 28
8c Lag 10 min 5 min 1min -15 0.004 ( 0.591) -14 0.007 ( 0.975) -13 0.001 ( 0.084) -12-0.009 (-1.057) -11 0.007 ( 0.914) -10 0.003 ( 0.434) -9-0.019 (-2.175) -8 0.030 ( 2.696) -7-0.013 (-0.977) -6-0.004 (-0.250) 0.021 ( 1.527) 0.002 ( 0.172) -5 0.009 ( 0.399) 0.023 ( 1.196) -0.005 (-0.417) -4-0.046 (-2.035) -0.048 (-1.974) -0.000 (-0.019) -3 0.028 ( 0.880) 0.031 ( 1.379) -0.004 (-0.377) -2-0.011 (-0.286) -0.036 (-1.699) -0.033 (-2.630) -1-0.024 (-0.628) -0.122 (-4.590) 0.008 ( 0.665) 0-0.190 (-3.569) -0.297 (-6.523) -0.007 (-0.468) 1 0.065 ( 4.397) -0.082 (-4.084) -0.003 (-0.222) 2 0.013 ( 1.005) 0.010 ( 0.509) 0.004 ( 0.214) 3 0.011 ( 0.623) -0.010 (-0.632) 0.028 ( 1.667) 4-0.004 (-0.259) 0.005 ( 1.392) 0.016 ( 1.013) 5-0.018 (-1.004) 0.002 ( 0.327) 0.022 ( 1.487) 6 0.040 ( 0.800) 0.014 ( 1.404) 0.019 ( 1.509) 7-0.000 (-0.039) 8 0.029 ( 2.935) 9 0.008 ( 0.728) 10-0.009 (-0.527) 11-0.010 (-0.474) 12-0.039 (-1.252) 13 0.059 ( 1.203) 14 0.119 ( 1.832) 15-0.108 (-1.059) heteroskedasticity and autocorrelation consistent 29