Question

From the following observations of annual EPS for a company, what is the first-order autocorrelation?

Time	EPS
1	3.05
2	3.29
3	4.12
4	4.37
5	5.39
6	5.6

Note that using the CORREL() spreadsheet function will not produce the correct result. Though for a large sample it'll be really close, for a small sample such as this one the difference can be significant. This is because for the autocorrelation you use the variance of the full sample in the denominator, as well as use the full sample to find the mean for use in covariance. In contrast, the CORREL function will treat the two subsets of the time series as separate data, and calculate separate mean and standard deviation for each.

Answer 1

The first order autocorrelation formula between and is given below:

.... (I)

Considering values from the above table

  

  

Substituting the above in (I),

The first order autocorrelation for the annual EPS for a company is 0.9166