Urgent Help needed regarding r1 Autocorrelation

#1
I'm searching from past 2 hours on the internet and I'm unable to find a solved example of calculating r1 first coefficient of correlation from the successive observations on timeline.

Sixteen successive observations on a stationary time series are as follows: 1.6, 0.8, 1.2, 0.5, 0.9, 1.1, 1.1, 0.6, 1.5, 0.8, 0.9, 1.2, 0.5, 1.3, 0.8, 1.2 Calculate r1???

I'm not asking to solve this question I have searched the formula

but how to apply? . I've quoted a sample question. Please give the link of any solved example alike this, it will make me understand how this formula is applied to solve? I understand Y(bar) is the mean of this data. What are Yt and Yt-1 what they stand for, If Yt is simple 1.6, Yt-1=0.6? Please clearly explain. I've searched alot and read about making pair etc but didn't found a solved example to make me understand. English is not my native language Thanks in advance.
 
Last edited:

CB

Super Moderator
#2
What are Yt and Yt-1 what they stand for, If Yt is simple 1.6, Yt-1=0.6? Please clearly explain.
Yt-1 is just the observation before Yt. So it is missing for Y1 = 1.6. But if we take the second value of 0.8, then Yt-1 is 1.6.

To calculate the lag 1 autocorrelation all you need to do is correlate the observations with the lagged set of observations (using a single lag).

I.e. correlate the observed series:
0.8, 1.2, 0.5, 0.9, 1.1, 1.1, 0.6, 1.5, 0.8, 0.9, 1.2, 0.5, 1.3, 0.8, 1.2
With the lagged series:
1.6, 0.8, 1.2, 0.5, 0.9, 1.1, 1.1, 0.6, 1.5, 0.8, 0.9, 1.2, 0.5, 1.3, 0.8