This report contains the results of a research study on the income trends of Yahoo, Inc. over the last nine years (between 2006 and 2014). Data was obtained from the Yahoo Finance website (finance.yahoo.com) and analyzed through scatter diagram, eyeballing and regression to determine trend, cyclicality, seasonality, and auto-regression.
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The data was obtained from the Yahoo Finance website (finance.yahoo.com) and analyzed through scatter diagram, eyeballing and regression to determine trend, cyclicality, seasonality, and auto-regression.
|Table 1 |
Yahoo Returns between 2006 and 2014
|Date||YAHOO (YHOO)||Date||YAHOO (YHOO)|
The data was summarized to represent the income as average income per quarter.
|Table 2 |
Yahoo Returns for the Different Quarters between 2006 and 2014
Figure 1 below is a scatter diagram highlighting the trend, seasonability and cyclicality of Yahoo income.
The scatter diagram illustrates three different trends over the nine-year period (between January 3, 2006 and May 1, 2007. Yahoo income experienced a downward trend between the first quarter of 2006 and last quarter of 2008. Between the fourth quarter of 2008 and third quarter of 2012, Yahoo’s income were relatively constant but exhibited moderate variations of a sinusoidal pattern. In other words, the income grew moderately between the last quarter of 2008 and last quarter of 2009 then declined toward the third quarter of 2010. The returns then again grew and declined between the third quarter of 2010 and third quarter of 2011. However, the income experienced an upward trend between the third quarter of 2012 towards the last quarter of 2013 before starting a declining trend.
Seasonality and Cyclicality
The scatter diagram illustrates non-existence of seasonality and cyclicality. The Yahoo returns experienced a downward returns for all the quarters from 2006 to 2008. The returns also exhbited an upward trend from the third quarter through the last quarter of 2013. The returns of the fourth quarter of 2008 increased while the returns of the fourth quarter of 2009 decreased. Additionally, the returns of the third quarters of 2007, 2010, and 2011 decreased while the returns of the third quarter of 2012 increased. Cyclicality would describe Yahoo stock when the income fluctuates generally according to changes in the seasons’ cycle (Mills, 1990).
Hypothesis Testing and Auto-Regression
Null hypothesis (H0): The highest-order parameter is not significant (βp = 0).
Alternate hypothesis (H1): The highest-order parameter is significant (βp ≠ 0).
Based on an alpha level of significance of 0.05, the decision rule is to reject the null hypothesis if the p-value is less than 0.05 but fail to reject the null hypothesis when the p-value is greater than 0.05.
|Adjusted R Square||0.850895833|
The r-square value of approximately 0.8554 implies that the data was a good fit for the regression model. In other words, about 85.54% of the variations in the dependent variable (Yt) which represents returns are accounted for by the data (or the changes in the x-variable (in this case, Yt-1).
Analysis of Variance (ANOVA)
The results of the analysis of variance (significance F or P-value = 5.4924 * 10-15) leads to the rejection of the null hypothesis (βp = 0) because the p-value < 0.005. As a result, the alternate hypothesis (βp ≠ 0) is favored. This mean the regression model is significant.
Regression Analysis Results
|Coefficients||Standard Error||t Stat||P-value||Lower 95%||Upper 95%|
|X Variable 1||0.939182555||0.068257397||13.75942523||5.49241E-15||0.800146787||1.078218|
The following is the estimated linear regression model: Yt = 1.3985 + 0.9392 X ± 1.6433, where: yt= returns and x = yt-1.
The x variable is significant (the p-value of 5.49241*10-15 is less than the alpha level of 0.05). The constant or intercept appears to be non-significant (P> 0.05).
The following are the y values (or returns) estimated using the regression equation:
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- In-sample: Yt = 1.3985 + (0.9392 * 16.4) ± 1.6433 = 16.80138 ± 1.6433
- Out-sample: Yt = 1.3985 + (0.9392 * 45) ± 1.6433 = 43.6625 ± 1.6433
Mills, T. C. (1990). Time series techniques for economists. New York: Cambridge University Press. Web.