REGRESSION RESULTS FOR EQUATION (1) WITH INSIGNIFICANT VARIABLES DELETED 1960-74

1-month 3-month 6-month 9-month 12-month

-0.092 -0.257 -0.386 -0.492 -0.158

Intercept (-1.03) (-2.05) (-2.2) (-2.33) (-0.62)

3.108 3.930

TOLSR (2.01) (2.12)

0,002 0.005 0.007 0.008 0.010

CONFIDENCE (1.79) (3.54) (3.59) (3.8) (4.05)

-0.003

S & P 500 P/E (-3.57)

-0.095 -0.226 -0.274 -0.379 -0.642

SPEC SHT SALES (-.167) (-2.75) (-2.09) (-2.49) (-4.43)

-0.441 -0.534 SECONDARY/NYSE V (-2.3) (-2.11)

0.775 2.506 3.882 5.058 5.881

MF CASH/ASSETS (2.62) (6.02) (5.4) (5.61) (6.18)

-0.012 -0.041 -0.067 -0.085 -0.108

BILLRATE (-2.64) (-6.7) (-7.27) (-7.59) (-8.71)

-2.786 -4.556 -6.770 -7.288 -8.597

% CHG. CPI (-1.69) (-1.96) (-2.19) (-1.94) (-2.02)

R2 0.082 0.351 0.455 0.467 0.493

Durbin-Watson Stat 2.404 0.940 9.779 0.537 0.453

DF 172 171 167 165 162

not work at all. The bill rate has highly significant coefficients while the inflation rates coefficients tend to have significant but lower t ratios. The failure of the money growth variable is consistent with some other research, indicating that any lag between change in monetary policy and stock market reaction is very short. In fact, the market appears to anticipate changes in monetary policy.1

Comparing the results for the different adjustment periods, we see that

R for the one-month period is rather low but rises from .082 to .351 in the three-month period with a further rise to .455 in the six-month period. There are slight further rises in the nine- and twelve-month periods. Apparently market indicators are of modest value in predicting one-month price changes but of significantly greater value for longer periods.

For all periods except the one-month the Durbin Watson is well below 2, indicating a serious degree of autocorrelation in the errors terms. This is not unexpected. If the indicators miss in one three-month period, it is to be anticipated that they would miss in the same direction in three month beginning with the next month. The same would be true for other adjustment periods. Since we have no way to predict the direction of error, it would be meaningless to apply one of the autoregression techniques.

A question that arises here involves a comparison of the forecasting power of the indicators jointly with their use alone. This question can be approached by reference to the simple correlation coefficients between the independent variables and the dependent variables. Table 3 presents these correlation coefficients.

By squaring these correlation coefficients, we obtain the R which would obtain in a one-variable regression. Since the highest correlation is .41, the

-2 -2

largest R would be less than .17 compared with a considerably higher R for

the corresponding multiple regression. Clearly the joint usage of the market indicators improves the fit for the 1960-74 period. This is not surprising given their diversity, and it might not be surprising if joint usage of mood variables offered,little additional explanatory power. There should, however, be considerable nonoverlapping information in the other types of indicators. If they work individually, they should work better in a joint framework.

A second question that Table 3 addresses is the time pattern of the relationship. Are there different lag structures for the different variables? It appears that there are. In general the strength of the relationship tends to

Refer to sources in footnote 10.

Variable

1-month 3-month 6-month 9-month

12-month

rise with the adjustment period. There are monotonically increasing correlation coefficients for TOLSR, floor trader short sales confidence index, and specialist short sales. The bill rate and inflation rate correlations reach their highest value at nine months while declining slightly in the 12-month period. The secondary distribution correlation reaches a peak in the 3-month period declining thereafter. This suggests that corporate officials may have rather short time horizon in the timing of their distribution decisions. The other variables do not appear to have a consistent pattern of correlation coefficients. The PE ratio has the incorrect sign for each adjustment period while the mutual fund cash position has an incorrect but insignificant sign in the longer adjustment periods.

IV. Further Tests

While the above stated results are interesting, they are far from conclusive. They suggest that some of the indicators have forecasting potential although one can not be sure that the relations found will continue to hold in the future. Since their degree of stability in the past may be an indication of future stability, it is useful to split the sample into two separate time periods. In this way we can compare the coefficients for the two sets of regressions. First the data for 1960-74 and then 1968-74 are used in fitting the equations used in Table 2. These results appear in Tables 4 and 5.

CORRELATIONS BETWEEN INDICATORS AND SUBSEOUENT CHANGE IN INDEX