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These sorts of statements can be made only by taking the pattern at face value. Of course, the stock market is not this simple. Historical patterns may be visibly compelling and easy to apply, but they suffer from four important limitations.

The first limitation is that historical patterns can only represent the past. Though the past can be known and expressed with precision, future results can never be known. No matter how helpful a given pattern is at understanding the past, the possibility that the future structure of the pattern could be substantially different always exists.

Second, a historical pattern only represents general tendencies of the data. Although any given type of year is expressed as a single number, it actually represents a wide range of results. For example, look at the summary below and take note of the number of times that each year type of the four-year pattern fell within a certain range of annual return. The point is that the distribution of annual returns is so wide as to make the one average return figure almost meaningless as a guide to specific expectations.

The third limitation to be aware of is that any set of data will produce a pattern. That there is a pattern does not indicate it is meaningful. Patterns can emerge from the data of even totally unrelated phenomena. For example, combining the yearly change in the Arctic bobcat population with the annual change in the price of gold will still produce one distinct and well-formed pattern. A pattern of this kind, obviously, would be meaningless, but simply looking at the pattern itself would not tell us that. Making inferences about the future with historical patterns always requires going beyond the pattern's visible character alone.

The fourth, and final, limitation in using historical patterns is that the interpretation of the pattern is a function of its presentation, not a function of the data. By careful but honest manipulation, the same data can suggest different conclusions. For example, Figure 3 is the eight-year pattern presented a little differently. The eight types of years are still in the same order, but the bars have been shifted forward so that bar 6 now appears as bar 1.

Looking at Figure 3, our mind's eye might favor a different conclusion than those previously. Rather than seeing two four-year patterns, one might now see two abnormally strong years dominating six quite average years. Which of the two interpretations of the pattern is more valid? Clearly, basing our conclusion on presentation alone may be insufficient and misleading.

With these concerns in mind, can we take either the four- and eight-year Presidential election patterns seriously? We turn now to a search to justify the patterns based either on the market's environment or on a statistical study of the relationships of the pattern's data.