Microeconimics Analysis

(a) Figure 1 is an indicator of downward trend. The scatter plot clearly shows that when time is moving forward, dividend tends to decline. Also, from the SAS output (figure 2), we can use the statistics to test the null hypothesis that it does not have a downward trend. Thus the alternative hypothesis is that there is a downward trend, in other words, the coefficient related to time is less than 0. This is a directional test, thus we need to use the two-step test. First, the related p-value, when divided in half, is less than 0.05. Second, the coefficient estimate of the trend component is -0.65445, thus the sign of the coefficient is consistence with the alternative hypothesis. In conclusion, it is reasonable to conclude that there is a downward trend.

(b) The trend model is: DIV t=109.08894-0.65445t+εt .The intercept estimate is 109.08894 and the slope estimate is -0.65445.According to figure 2, we can see the p-values associated with both coefficients are less than 0.05, thus we can be reasonably certain that the two model parameters are both statistically significant. As to the shareholders’ claim, the null hypothesis is that the slope coefficient is equal to zero in the population. The alternative hypothesis is that the slope coefficient is less than zero in the population. Since the estimate of the slope is less than zero and p value, when divided by two, is less than 0.05. We can reject null hypothesis and accept alternative. Therefore, we are reasonably sure that dividend of Coca Cola Company is declining and the claim of the shareholders is supported.

(c) The null hypothesis is the series is white noise.

Symbolically: Ho: ρ1=ρ2=ρ3=……=0; Ha: NOT (ρ1= ρ2= … = 0)

Figure 3 SAS output of ACF for up to 24 lags

We could use portmanteau test to test the null hypothesis and use the statistics from the SAS output above. The p-value associated with lag24 is less than 0.05, thus we could reject the null hypothesis and be reasonably sure that in the first 24 lags, at least one autocorrelation is different from zero in the population. In other word, we are reasonably sure that the residue is not