By Campbell, Ho, Mackinley
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There are fewer nonoverlapping longhorizon returns for a given time span, so sampling errors are generally l5 Although this restriction on the fourth cross-moments of ct may seem somewhat unintuitive, it is satisfied for any process with independent increments (regardless of heterogeneity) and also for linear Gaussian ARCH processes. 41). 43), it is conceptually straightforward and may readily be formed along the lines of Newey and West (1987). An even more general (and possibly more exact) sampling theory for the variance ratios may be obtained using the results of Dufour (1981) and Dufour and Roy (1985).
Both statements have the same meaning: Using historical prices, one can predict future prices to some extent in the short run. But because the two statements are so laden with jargon, the type of response they elicit depends very much on the individual reading them. 8). Recent studies by Blume, Easley, and O'Hara (1994), Brock, Lakonishok, and LeBaron (1992), Brown and Jennings (1989), LeBaron (1996), Neftci (1991), Pau (1991), Taylor and Allen (1992),and Treynor and Ferguson (1985) signal a growing interest in technical analysis among financial academics, and so it may become a more active research area in the near future.
6). 3) were 0, the uncertainty in the sequence of e,'s would be "cancelling out" over time and would not be a very useful model of random price dynamics. , el = ql - ql-1, where qt is white noise. 3) were 00, this would be an example of long-range dependence, in which the autocorrelation function of the el's decays very slowly. An example of such a process is a fractionally differenced process (1 - L ) % ~ = ql, where ql is white noise. 5 and Lo (1991) for further discussion. Predictabilityin asset returns is a very broad and active research topic, and it is impossible to provide a complete survey of this vast literature in just a few pages.