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1 Discussion Paper Series A No
2 autocorrelataion cross-autocorrelataion Lo/MacKinlay [1988, 1990] (A)
3 Lo/MacKinlay [1988] mean-reversion Fama/French [1988] Poterba/Summers [1988] Kim/Nelson/Startz [1991] Richardson/Stock [1989] Lo/MacKinlay [1988, 1990, 1999] cross-autocorrelation 1988 Lo/MacKinlay [1988] Center for Research in Securities Prices CRSP NYSE-AMEX variance ratio test (1) CRSP (2) (3) ; (4) 1990 Lo/MacKinlay [1990] (2)-(4) CRSP Lo/MacKinlay [1988, 1990] Lo/MacKinlay CRSP Dow-Jones S&P500 1
4 CRSP Dow-Jones S&P TOPIX CRSP Dow-Jones S&P500 Lo/MacKinlay [1988] 1 Chang/McQueen/Pinger [1999] PACAP Lo/MacKinlay (1988, 1990) PACAP 6 CRSP 3 Lo/MacKinlay [1988, 1990] Badrinath/Kale/Noe [1995], Boudoh/Richardson/Whitelaw [1994], Brennan/Jegadeesh/Saminathan [1993], Conrad/Kaul/Nimalendran [1991], Jegadeesh/Titman [1995], Mech [1995] 2
5 2 TOPIX TOPIX QUICK Lo/MacKinlay [1988, 1990] ARCH [ 1 ] Ljung-Box Q TOPIX Q 3
6 [ 2 ] CRSP CRSP TOPIX 8.8% 5% TOPIX 10% Q 5 2 4
7 truncated nonsynchronous trading 3.2 cross-autocorrelations 3 4 Υ(k) Υ(0) 3 Υ(1) R 4t 1 R 1t 14.0% R 1t 1 R 4t 0.2% 4 Υ(k) Υ (k) k [ 3 ] 5
8 R 3t 3 R 2t, R 2t 3 R 3t Υ(3) Υ (3) [ 5 ] TOPIX r t = α + β 1 y t 1 + β 2 r t 1 u t 1 + ɛ t (1) if r t 0 u t =1 otherwise u t =0 β TOPIX 2 truncated AR(1) (1) 6 (A) AR(1) TOPIX 6
9 [ 6 ] (B) β 2 β 2 5% 5% β TOPIX β
10 Lo and MacKinlay [1990c] contrarian Lo and MacKinlay [1990] Campbell, Lo, and MacKinlay [1997, 3 ] nonsynchronous trading / / / [1998] 10 8
11 / / / [1998] Badrinath, S. G., J. R. Kale, and T. H. Noe [1995], Of Shepherds, Sheep, and the Cross-autocorrelations in Equity Returns, Review of Financial Studies 8, pp Boudoukh, J., M. P. Richardson, and R. F. Whitelaw [1994], A Tale of Three Schools: Insights on Autocorrelations of Short-Horizon Stock Returns Review of Financial Studies 7, pp Brennan, M. J., N. Jegadeesh, and B. Swaminathan [1993], Investment Analysis and the Adjustment of Stock Prices to Common Information, Review of Financial Studies 6, pp Campbell, J. Y., A. W. Lo, and A. C. MacKinlay [1997], The Econometrics of Financial Markets, Princeton University Press. Chang, E. C., G. R. McQueen, and J. M. Pinegar [1999], Cross- Autocorrelation in Asian Stock Markets, Pacific-Basin Finance Journal 7, pp Fama, E. F. and K. R. French [1988], Permanent and Temporary Components of Stock Prices, Journal of Political Economy 96, pp Jegadeesh, N. and S. Titman [1995], Overreaction, Delayed Reaction, and Contrarian Profits, Review of Financial Studies 8, pp Kim, M., C. R. Nelson, and R. Startz [1991], Mean Reversion in Stock Prices? A Reappraisal of the Empirical Evidence, Review of Economic Studies 58, pp Lo, A. W. and A. C. MacKinlay [1988], Stock Market Prices Do Not Follow Random Walks: Evidence From a Simple Specification Test, Review of Financial Studies 1, pp and [1990], When are Contrarian Profits Due to Stock Marekt Overreaction? Review of Financial Studies 3, pp
12 and, A Non-random Walk Down Wall Street, Princeton: Princeton University Press, Mech, T. S. [1993], Portfolio Return Autocorrelation, Journal of Financial Economics 34, pp Poterba, J. M. and L. H. Summers [1988] Mean Reversion in Stock Prices, Journal of Financial Economics 22, pp Richardson, M. and J. H. Stock [1989], Drawing Inferences from Statistics Based on Multiyear Asset Returns, Journal of Financial Economics 25, pp
13 [0.04] [0.00] [0.00] [0.00] [0.79] [0.00] TOPIX N/A [0.35] [0.00] [0.64] [0.00]
14 2 ρ i = i Q i = i Ljung-Box Q ( ) 1% ( ) 5% ( ) 10% 3 4 (A) ρ 1 ρ 2 ρ 3 ρ 4 Q5 Q TOPIX
15 2 (B) ρ 1 ρ 2 ρ 3 ρ 4 Q5 Q TOPIX (C) ρ 1 ρ 2 ρ 3 ρ 4 Q5 Q TOPIX
16 3 Cross-autocorrelation matrices R 1t = 2 R 2t = 1 R 3t = 1 R 4t = 1 Lo/MacKinlay [1988, 1990] Υ(0) = R 1t R 2t R 3t R 4t Υ(1) = R 1t 1 R 2t 1 R 3t 1 R 4t Υ(2) = R 1t 2 R 2t 2 R 3t 2 R 4t Υ(3) = R 1t 3 R 2t 3 R 3t 3 R 4t
17 Υ(4) = R 1t 4 R 2t 4 R 3t 4 R 4t
18 Υ(1) Υ (1) = R 1t 1 R 2t 1 R 3t 1 R 4t Υ(2) Υ (2) = R 1t 2 R 2t 2 R 3t 2 R 4t Υ(3) Υ (3) = R 1t 3 R 2t 3 R 3t 3 R 4t Υ(4) Υ (4) = R 1t 4 R 2t 4 R 3t 4 R 4t
19 5 (A) Υ(1) Υ (1) = R 1t 1 R 2t 1 R 3t 1 R 4t Υ(2) Υ (2) = R 1t 2 R 2t 2 R 3t 2 R 4t Υ(3) Υ (3) = R 1t 3 R 2t 3 R 3t 3 R 4t Υ(4) Υ (4) = R 1t 4 R 2t 4 R 3t 4 R 4t
20 5 (B) Υ(1) Υ (1) = R 1t 1 R 2t 1 R 3t 1 R 4t Υ(2) Υ (2) = R 1t 2 R 2t 2 R 3t 2 R 4t Υ(3) Υ (3) = R 1t 3 R 2t 3 R 3t 3 R 4t Υ(4) Υ (4) = R 1t 4 R 2t 4 R 3t 4 R 4t
21 6 TOPIX r t = α + β 1 r t 1 + β 2 u t 1 r t 1 if r t 0 u t =1 otherwise u t =0 r t TOPIX (A) β 2 =0 TOPIX β [S.E.] [0.046] [0.067] [0.059] R 2 0.1(%) β [S.E.] [0.046] [0.066] [0.059] R 2 0.0(%) (B) TOPIX β [S.E.] [0.069] [0.090] [0.103] β [S.E.] [0.134 ] [0.178] [0.181 ] R 2 0.7(%)
22 6 TOPIX (B) β [S.E.] [0.067] [0.086] [0.101] β [S.E.] [0.137 ] [0.184] [0.188 ] R 2 0.7(%) S.E. =White Heteroskedasticity-Consistent ( ) 5% ( ) 10% 20
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