Five stock price sequences are examined quantitatively for structure as predicated by: 1) a random walk model; 2) a continuously differentiable price process; 3) a dynamic model consisting of transients of a discrete process. The first and third models also make predictions in agreement with trading lore. The data are examined by the method of coincident events. Positive evidence is found for both the random walk and discrete transient model, and slightly against the continuous price process. The theoretical predictions seems better confirmed by data at price minima than price maxima. The data are in partial disagreement with the predictions of both the random walk and discrete transient model that large volume and large second differences of price should tend to occur at the same time. Some confirmation is found for items of trading lore not predicted by theory. The non-random properties of stock prices are primarily found in short interval data (daily and weekly) and in individual stock prices as opposed to an average.