Dear R list

I am trying to understand the auto-correlation concept. Auto-correlation is the self-correlation of random variable X with a certain time lag of say t.

The article "http://www.mit.tut.fi/MIT-3010/luentokalvot/lk10-11/MDA_lecture16_11.pdf" (Page no. 9 and 10) gives the methodology as under. 

Suppose you have a time series observations as say

X = c(44,41,46,49,49,50,40,44,49,41) 

# For autocorrelation with time lag of 1 we define 

A = c(41,46,49,49,50,40,44,49,41)  # first element of X not considered
B = c(44,41,46,49,49,50,40,44,49) # Last element of X not considered

> cor(A,B)
[1] -0.02581234

However, if I try the acf command using library tseries I get

acf(X, 1)

Autocorrelations of series ‘X’, by
 lag

     0      1 
 1.000 -0.019 

So by usual correlation command (where same random variable X is converted into two series with a time lag of 1), I obtain auto-correlation as -0.02581234 and by acf command I get auto-correlation = -0.019 (for time lag of 1).

I am not able to figure out where I am going wrong or is it my understanding of auto-correlation procedure is wrong?

Will be grateful if someone guides .

Vincy



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