coefficients and R/S range statisticsactually may be. The random walk is rejected under both the i.i.d. andthe stratified variance procedures for the LSE at the 99% confidencelevel, using the autoregression coefficient test. The hypothesis that theNYSE autoregression coefficient vector is different from zero cannotbe rejected, however. The rejection level of 84% under the i.i.d. sam-pling scheme is similar to rejection levels found by previous research-ers using NYSE data over later periods. The joint tests on autoregres-sion coefficients performed on the deviations from rolling 20-yearmeans fail to reject the null at traditional confidence levels. Thus, whilethe results are suggestive of mean reversion in both markets, they arenot conclusive when autoregression tests are used.
The joint tests on the more general R/S statistics yield slightlystronger results, however. While the joint tests performed on the R/Sstatistics derived from the raw LSE series and the raw NYSE seriesare inconclusive, the joint tests performed on the demeaned LSE andNYSE capital appreciation series are both significant at the 95% level.They indicate the likelihood that deviations from the lagged 20-yearmean are not temporally independent. Table 5 and table 7 suggest thereasons for the joint departure from the null. In both tables, the R/Sstatistics are unusually low over 2—4-year horizons and unusually highover the 8-year horizon, regardless of whether the i.i.d. or the stratifiedvariance bootstrap is used. Thus, the joint rejection does not resultfrom a consistent deviation in one direction but from what appears tobe reversion over the short horizons and persistence over the longhorizons—even after the 20-year moving average has been removed.
V. Conclusion
The same tests used in previous research to demonstrate the lack oflong-term memory in NYSE stock market prices during the variousperiods from 1872 to 1987 suggest that long-term memory may exist inLSE stock prices over the period of 1700-1989 and in deviations from20-year means in both markets. This conclusion is based on auto-regression tests as well as on R/S range tests and is robust to tech-niques designed to preserve the particular temporal pattern of stockmarket variance. These results may be interpreted as evidence ofevolving dividend policies and/or changing expected financial returnsthat result from the changing composition of the index through thecenturies of U.S. and U.K. capital market history. Substituting devia-tions from the lagged 20-year mean appears to eliminate the evolution-ary effects from the LSE series, indicating that the long-term persistentpatterns appear to mask a tendency for reversion toward the mean inthe LSE and possibly in the NYSE. This behavior is consistent withmodels of stock returns proposed by Poterba and Summers (1988) andPatterns of Stock Market Prices 269
empirically examined by Fama and French (1988). It could be causedby rational time variation in expected returns, as postulated by Conradand Kaul (1988) and explored by Jacquier and Nanda (1989) or byspeculative bubbles of the sort discussed by DeBont and Thaler (1985)and Flood, Hodrick, and Kaplan (1987). Although consistent with allmodels that hypothesize long-term reversion in asset prices, the testsunder discussion in this article, as currently formulated, cannot distin-guish among them. Whether the serial dependence in long-term capitalappreciation returns may be used to obtain arbitrage profits is anothermatter entirely. Rhea (1932) and his predecessor, Joseph Henry Dow,apparently thought so. A test of market efficiency based on the tempo-ral patterns identified in this article would require a trading test and ameasure of the total investor return rather than the capital appreciationcomponent alone, and, in all likelihood, an investor horizon greaterthan a single lifespan.
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