Hi Vincy, Take a look on the material bellow, maybe they can help you:
http://www.statoek.wiso.uni-goettingen.de/veranstaltungen/zeitreihen/sommer03/ts_r_intro.pdf http://www.maths.bris.ac.uk/~mazlc/TSA/r-ts.pdf http://www.stat.pitt.edu/stoffer/tsa2/R_time_series_quick_fix.htm On Thu, Aug 25, 2011 at 7:18 AM, Vincy Pyne <vincy_p...@yahoo.ca> wrote: > Dear R list > > As suggested by Prof Brian Ripley, I have tried to read acf literature. The > main problem is I am not the statistician and hence have some problem in > understanding the concepts immediately. I came across one literature ( > http://www.stat.nus.edu.sg/~staxyc/REG32.pdf) on auto-correlation giving > the methodology. As per that literature, the auto-correlation is arrived at > as per following. > > y = > c(15.91,9.80,17.16,16.68,15.53,22.66,31.01,8.62,45.82,10.97,45.46,28.69,36.75,37.75, > 41.18,42.67,46.05, 43.70,53.08,47.56) > > t = c(1:20) # defining time variable. > > Fitting y = a + bt + e, I get the estimates of a and b as a = 9.12 and b = > 2.07. So using these estimates I obtain > > y_fit = > c(11.19,13.26,15.33,17.40,19.47,21.54,23.61,25.68,27.75,29.82,31.89,33.96, > 36.03,38.10, 40.17,42.24,44.31,46.38,48.45,50.52) # these are fitted > values. > > > e_t = (y - y_fit) # dif between the observed y and fitted value of > corresponding y > > > e_t > [1] 4.72 -3.46 1.83 -0.72 -3.94 1.12 7.40 > [8] -17.06 18.07 -18.85 13.57 -5.27 0.72 -0.35 > [15] > 1.01 0.43 1.74 -2.68 4.63 -2.96 > > # We define > > e_t1 = > c(-3.46,1.83,-0.72,-3.94,1.12,7.40,-17.06,18.07,-18.85,13.57,-5.27,0.72,-0.35,1.01, > 0.43,1.74,-2.68,4.63,-2.96) # 1 st element of e_t deleted > > e_t2 = > c(4.72,-3.46,1.83,-0.72,-3.94,1.12,7.40,-17.06,18.07,-18.85,13.57,-5.27,0.72,-0.35, > 1.01, 0.43,1.74,-2.68,4.63) # Original series with last element deleted > > > cor(e_t1, e_t2) > > > cor(e_t1, e_t2) > [1] -0.8732316 > > > However, if I use > > acf(y, 1) > > Autocorrelations of series y, by lag > > 0 1 > 1.000 0.343 > > I am simply not able to figure out how acf is used? > > Thanking you in advance. > > Regards > > Vincy > > --- On Wed, 8/24/11, Prof Brian Ripley <rip...@stats.ox.ac.uk> wrote: > > From: Prof Brian Ripley <rip...@stats.ox.ac.uk> > Subject: Re: [R] Autocorrelation using library(tseries) > To: "Vincy Pyne" <vincy_p...@yahoo.ca> > Cc: r-help@r-project.org > Received: > Wednesday, August 24, 2011, 9:08 AM > > Your understanding is wrong. For a start, there is no function acf() in > package tseries: it is in stats. > > And the autocorrelation at lag one is not the correlation omitting the > first and last values: it uses the mean and variance estimated from the > whole series and divisor n. > > Have you looked at the reference given on ?acf ? As the help says > > (This contains the exact definitions used.) > > Neither the R help pages nor R-help are intended as tutorials in > statistics. > > On Wed, 24 Aug 2011, Vincy Pyne wrote: > > > 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. > > But that is not the definitive reference, and no, it doesn't (and what it > does give is not the conventional definition in the time series literature). > > > 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 > > > > > > > > [[alternative HTML version deleted]] > > > > > > -- Brian D. Ripley, rip...@stats.ox.ac.uk > Professor of Applied Statistics, http://www.stats.ox.ac.uk/~ripley/ > University of Oxford, > Tel: +44 1865 272861 (self) > 1 South Parks Road, +44 1865 272866 (PA) > Oxford OX1 3TG, UK Fax: +44 1865 272595 > > [[alternative HTML version deleted]] > > > ______________________________________________ > R-help@r-project.org mailing list > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide > http://www.R-project.org/posting-guide.html > and provide commented, minimal, self-contained, reproducible code. > > -- Atenciosamente, Raphael Saldanha saldanha.plan...@gmail.com [[alternative HTML version deleted]]
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