Price to Earning Historical TimeSeries

Auto-Correlation and Partial Auto-Correlation Graphs

Conclusion

As it can be seen in the auto-correlation and partial auto-correlation graphs, the price to earning ratio in historical U.S. stocks is a process that is neither autoregressive nor moving average. A moving average process of degree q, has an auto-correlation function with the first q + 1 coefficients significant. An autoregressive process has a partial autocorrelation function with the first p + 1 coefficients significant. Having these facts in mind, we observe these functions for our process. As it can be seen in the auto-correlation diagram, the first 11 and the 20th auto-correlation coefficients are significant and 1st, 5th and 7th partial auto-correlation coefficients are significant. Thus, the auto-correlation diagram does not demonstrate a moving average behavior and the partial auto-correlation diagram is not similar to that of an auto-regressive process. Therefore, the diagram for the