ProzacMarket 19puters. Using those new technologies in the early 1960s, stoc kmar-
ket researchers went to work with a vengeance exploring random
processes in these markets.
Correlation Tests
One aspect of the investigation consisted of correlation tests that
were used to determine whether specified data sequences move to-
gether to any degree. In the case of stoc kprices, price changes of a
given stoc kare recorded over a specified time period—say, a number
of days—and a subsequent period of the same length. These se-
quences (called time-series data) are then compared to determine
whether they move together to any degree—whether they show any
“correlation.”
The comparison takes the form of a correlation coefficient, a
number that reflects the degree to which the data are linearly re-
lated. In effect, the time series of data is tested for correlation by
fitting a straight line to the data and then calculating that number.
A correlation coefficient equal to zero provides evidence that the
data in the series have the property of statistical independence; cor-
relation coefficients that are close to zero (but not equal to zero)
indicate that the data are uncorrelated. A time series of data is ran-
dom if it is either independent or uncorrelated.
Consider televised lottery drawings in which winning lottery
numbers are determined by selecting numbered balls from a bin
containing numerous balls with different numbers painted on them.
The auditor retrieves a ball, records its number, and replaces that
ball. The auditor does this perhaps three times, each time retrieving,
recording, and replacing. This process has the property of statistical
independence because the number recorded after any retrieval in-
dicates nothing about the numbers recorded either previously or sub-
sequently.
Outside of a controlled context such as a lottery bin, particularly
in the context of time-series data such as stoc kprices, it is extremely
difficult to prove statistically that a series of data has the property
of statistical independence. The less restrictive property—that data
are uncorrelated—is susceptible to statistical proof and allows for
conclusions substantially similar to those which follow from the in-
dependence property.
The correlation tests of the 1960s all resulted in correlation co-
efficients that did not differ significantly from zero. This meant that