R help - Nov 2011 - acf?

I started to check what I thought I knew with autocovariance and it doesn’t
jive with the the calculations given by ‘R’. I was wondering if there is
some scaling or something that I am not aware of.

 

Take the example

 

Ø  d <- 1:10

Ø  (a <- acf(d, type="covariance", demean=FALSE, plot=FALSE))

 

Autocovariances of series ‘d’, by lag

 

   0    1    2    3    4    5    6    7    8    9 

38.5 33.0 27.6 22.4 17.5 13.0  9.0  5.6  2.9  1.0

 

But when I calculate it manually (for lag of 1) like:

 

Ø  y1 <- d – mean(d)

Ø  dl <- c(d[-1], d[1])

Ø  y2 <- dl – mean(d)

Ø  mean(y1*y2)

[1] 3.75

 

What am I missing to get this basic concept? Isn’t it E[(Yt – ut)(Ys – us)]?

 

Thank you.

 

Kevin


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On Sat, Nov 5, 2011 at 12:26 AM, Kevin Burton <rkevinburton at
charter.net> wrote:
> I started to check what I thought I knew with autocovariance and it doesn?t
> jive with the the calculations given by ?R?. I was wondering if there is
> some scaling or something that I am not aware of.
>
>
>
> Take the example
>
>
>
> ? ?d <- 1:10
>
> ? ?(a <- acf(d, type="covariance", demean=FALSE, plot=FALSE))
>
>
>
> Autocovariances of series ?d?, by lag
>
>
>
> ? 0 ? ?1 ? ?2 ? ?3 ? ?4 ? ?5 ? ?6 ? ?7 ? ?8 ? ?9
>
> 38.5 33.0 27.6 22.4 17.5 13.0 ?9.0 ?5.6 ?2.9 ?1.0
>
>
>
> But when I calculate it manually (for lag of 1) like:
>
>
>
> ? ?y1 <- d ? mean(d)
>
> ? ?dl <- c(d[-1], d[1])
>
> ? ?y2 <- dl ? mean(d)
>
> ? ?mean(y1*y2)
>
> [1] 3.75
>
>
>
> What am I missing to get this basic concept? Isn?t it E[(Yt ? ut)(Ys ?
us)]?
>
Try this:
> d <- 1:10
> dm <- d - mean(d)
> sum(dm[-1] * dm[-10]) / 10
[1] 5.775
> acf(d, type = "cov", plot = FALSE)[1]
Autocovariances of series ?d?, by lag

   1
5.78
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