ANALYSIS OF VARIANCE TESTS FOR LOCAL TRENDS IN THE STANDARD AND POOR'S INDEX.

In this paper, we present evidence that local trends do exist in the Standard and Poor's Index. We begin by assuming that the logarithm of the price at time t[sub 1], say log P(t[sub 1]), has an expected value which is a linear function of time. That is, E log P(t[sub 1]) = at[sub 1] + b where a and b are arbitrary but fixed constants. Then we use the techniques of the analysis of variance to test whether any constants in the expression above satisfy the data. The tests show that these data are not explained by such an expected value. We conclude that the mean is different (certainly more complicated than at[sub 1] + b) over different intervals of time. The changes in expected value over these intervals are referred to as local trends. Finally, by repetition of the tests for different interval sizes, we find that the tests are significant for interval sizes up to approximately one year but not longer. Thus the evidence suggests that the local trends, when they occur, do not last longer than this period of time. [ABSTRACT FROM AUTHOR]