Hello,
I am attending a course in Computational Statistics at ETH and in one of the
assignments I am asked to prove that a time series is not autocorrelated using
the R function "acf".
I tried out the acf function with the given data, according to what I found
here: http://landshape.org/enm/options-for-acf-in-r/ this test data does not
look IID but rather shows some trends so how can I then prove that it is not
autocorrelated? maybe the trends are ok?
I have bought several titles on R but none really explains autocorrelation or
how to interpret the acf function ... the integrated help is also a bit dry.
These are the books I have on R:
- Introductory Statistics with R (Springer)
- A handbook of Statistical Analyses using R (CRC)
- R in a Nutshell (Oreilly)
- Statistical Computing with R (CRC)
Thanks in advance,
Best regards,
Giovanni
#
========================================================================================#
Computational Statistics
# Series 4
# Author: Giovanni Azua
# Date: 16 April 2010
#
========================================================================================rm(list=ls())
# clear workspace
#
========================================================================================#
EXERCISE 1.(c)
#
========================================================================================
# load dataset from web
#bmwlr <- scan("http://stat.ethz.ch/Teaching/Datasets/bmw.dat")
# load dataset from file
bmwlr <- scan("/Users/bravegag/code/compstats/bmw.dat")
par(mfrow=c(1,2)) # visualize two plots
acf(bmwlr, lag.max = 10)
acf(bmwlr^2, lag.max = 10)
[[alternative HTML version deleted]]
Giovanni Azua <bravegag <at> gmail.com> writes:> > Hello, > > I am attending a course in Computational Statistics at > ETH and in one of the assignments I am asked to prove > that a time series is not autocorrelated using the R function "acf". > > I tried out the acf function with the given data, > according to what I found here: > http://landshape.org/enm/options-for-acf-in-r/ > this test data does not look IID but rather shows > some trends so how can I then prove that it is not > autocorrelated? maybe the trends are ok? > > I have bought several titles on R but none really explains > autocorrelation or how to interpret the acf > function ... the integrated help is also a bit dry.Hmmm. The acf() shows what looks to be fairly mild autocorrelation at lag 1 (rho=0.09228), which is strongly significant according to the Durbin-Watson test ...> aa <- acf(bmwlr) > aa$acf[2] ## 0.09228> library(car) > durbinWatsonTest(lm(bmwlr~1))lag Autocorrelation D-W Statistic p-value 1 0.09228737 1.815334 0.002 Alternative hypothesis: rho != 0 However, I don't know where you're getting the idea of a trend from: the plot looks noisy (although there is one big excursion in the middle) ? Are you confusing "trend" with "autocorrelation"? I would suggest general time-series books -- Chatfield has several at various levels.
Hello Denis,
(1) I appreciate your feedback, however, I feel I have all the right to ask a
specific question related R namely what's the interpretation of the acf
function plot. I gave away the information that it is a homework because many
times people before helping ask what's the context for the question at hand.
If I don't understand something I will for sure ask. I don't have
anything to hide so I don't care if there are professors subscribed to this
list. My ultimate goal is to learn and it doesn't really matter whether it
is studying a book, asking an assistant or asking in a forum.
(2) After looking in many references and not finding any clue ... I Googled for
information and found that I should be "looking for cyclic patterns"
i.e. oscillations? There are none in this dataset so I presume there would not
be any autocorrelation, oder?
(3) This is something very unfortunate ... the course Lectures are great, the
course script is very comprehensive, however, the assignments many times include
questions that are a bit off topic like in this case of Time Series and includes
no actual reference ... so it is no surprise that even after diligently
attending all lectures and doing all exercises I get stuck. Please recommend
what's the best book in this topic of Time Series analysis maybe with R. I
will buy it.
(4) Yes they mentioned something like this in the assignment "Dependency
can be verified by showing that under the model, Cov(X_t^2,X_{t-h}^2) \neq 0, h
> 0 (complicated). Plot and interpret the autocorrelation functions of X_t
and X_t^2 for the BMW-dataset."
http://stat.ethz.ch/teaching/lectures/FS_2010/CompStat/series4.pdf
Thank you.
Best regards,
Giovanni
On Apr 17, 2010, at 7:25 PM, Dennis Murphy wrote:
> Hi:
>
> (1) If you read the posting guide (as you were asked to do before posting),
you would find out
> rather quickly that this is not a forum to help you with homework.
Moreover, several of your
> professors may subscribe to this list and notice your request.
> (2) What 'trend' is in this data set? It has excessive variation at
certain points of the series,
> but what trend?
> (3) None of your cited references is likely to have much that describes
what autocorrelation means.
> (The only exception might be HSAUR, but it focuses more on the
programming than the concepts.)
> I'd consult an actual time series text to learn the concepts you
need to make sense of the plots.
> (4) You can't 'prove' that the series in question is (or is
not) autocorrelated with R or any other
> software; however, it can be used to provide empirical support for
one hypothesis or the other.
> Proof is a mathematical construct involving deductive logic, whereas
statistical inference uses
> inductive logic. They represent different approaches to problem
solving.
>
> HTH,
> Dennis
[[alternative HTML version deleted]]