Correlations: serial and auto
by Clifford J. Sherry, Ph.D.
Suppose you are testing a pricing pattern to see what relationship it has to future price movement. Or,
you are testing an indicator's correlations with price movement. In each case, you need a definitive test to
tell you if there exists a statistically significant relationship.
Again, much of the early work testing the various forms of the efficient market hypothesis utilized either
serial or auto correlation techniques. (See for example, P. Cottner's Random Character of Stock Market
Prices, M.I.T. Press, Cambridge, 1964). Unfortunately, correlation techniques may not provide an
adequate test of this hypothesis and using these techniques may lead to false conclusions.
If you are to test whether or not relationships exist, it is important for you to understand how
correlograms are constructed and what they mean. As an example, the techniques described here will
reliably show meaningful correlations, if they exist. I will use a series of artificial "prices" to minimize
problems of interpretation.
Beginning with Figure 1, we will construct the "lag-1" serial correlogram by examining sequential pairs
of prices. That is, we will compare the action of today's price with that of yesterday's— the price with a