Paper: AutoCorrelation Function d=D=0

*The author of this computation has been verified*

R Software Module: /rwasp_autocorrelation.wasp (opens new window with default values)

Title produced by software: (Partial) Autocorrelation Function

Date of computation: Mon, 14 Dec 2009 02:12:40 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2009/Dec/14/t12607820528plac9q3qmzrzt8.htm/, Retrieved Mon, 14 Dec 2009 10:14:14 +0100

BibTeX entries for LaTeX users:

@Manual{KEY, author = {{YOUR NAME}}, publisher = {Office for Research Development and Education}, title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2009/Dec/14/t12607820528plac9q3qmzrzt8.htm/}, year = {2009}, } @Manual{R, title = {R: A Language and Environment for Statistical Computing}, author = {{R Development Core Team}}, organization = {R Foundation for Statistical Computing}, address = {Vienna, Austria}, year = {2009}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, }

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

423 427 441 449 452 462 455 461 461 463 462 456 455 456 472 472 471 465 459 465 468 467 463 460 462 461 476 476 471 453 443 442 444 438 427 424 416 406 431 434 418 412 404 409 412 406 398 397 385 390 413 413 401 397 397 409 419 424 428 430

Output produced by software:

Summary of computational transaction Raw Input view raw input (R code) Raw Output view raw output of R engine Computing time 1 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Autocorrelation Function Time lag k ACF(k) T-STAT P-value 1 0.945338 7.3226 0 2 0.870555 6.7433 0 3 0.819839 6.3504 0 4 0.789012 6.1117 0 5 0.770654 5.9695 0 6 0.733202 5.6794 0 7 0.659606 5.1093 2e-06 8 0.573016 4.4386 2e-05 9 0.504201 3.9055 0.000121 10 0.460625 3.568 0.000357 11 0.436596 3.3819 0.000636 12 0.387657 3.0028 0.001948 13 0.282802 2.1906 0.016189 14 0.179245 1.3884 0.08507 15 0.105537 0.8175 0.208442 16 0.055918 0.4331 0.333234 17 0.020102 0.1557 0.438391 18 -0.03262 -0.2527 0.400694 19 -0.105021 -0.8135 0.209577 20 -0.185765 -1.4389 0.077684 21 -0.240125 -1.86 0.033894 22 -0.272188 -2.1084 0.019592 23 -0.296834 -2.2993 0.012493 24 -0.330595 -2.5608 0.006489 25 -0.387777 -3.0037 0.001943 26 -0.44256 -3.4281 0.000552 27 -0.464409 -3.5973 0.000326 28 -0.458644 -3.5526 0.000375 29 -0.438967 -3.4002 0.000601 30 -0.427925 -3.3147 0.00078 31 -0.427286 -3.3097 0.000792 32 -0.428072 -3.3158 0.000777 33 -0.407572 -3.157 0.001247 34 -0.380073 -2.944 0.002301 35 -0.354323 -2.7446 0.00399 36 -0.331756 -2.5698 0.006339 Partial Autocorrelation Function Time lag k PACF(k) T-STAT P-value 1 0.945338 7.3226 0 2 -0.217311 -1.6833 0.048759 3 0.231577 1.7938 0.038943 4 0.068491 0.5305 0.298853 5 0.107223 0.8305 0.204761 6 -0.198352 -1.5364 0.064845 7 -0.255828 -1.9816 0.026054 8 -0.125948 -0.9756 0.166593 9 0.023338 0.1808 0.428576 10 0.052158 0.404 0.343821 11 0.132511 1.0264 0.154405 12 -0.217195 -1.6824 0.048846 13 -0.413437 -3.2025 0.001091 14 0.063935 0.4952 0.31112 15 0.013199 0.1022 0.459454 16 0.000133 0.001 0.499591 17 0.021283 0.1649 0.434804 18 -0.037427 -0.2899 0.386442 19 0.070445 0.5457 0.293659 20 -0.169246 -1.311 0.097431 21 0.073737 0.5712 0.28501 22 -0.159844 -1.2381 0.110242 23 -0.052513 -0.4068 0.342816 24 0.128032 0.9917 0.162656 25 0.003909 0.0303 0.487972 26 -0.091504 -0.7088 0.240602 27 0.110088 0.8527 0.198599 28 0.052632 0.4077 0.342477 29 0.123257 0.9547 0.17177 30 -0.002336 -0.0181 0.492811 31 0.0912 0.7064 0.241328 32 -0.004487 -0.0348 0.486194 33 -0.02131 -0.1651 0.434723 34 -0.142634 -1.1048 0.13682 35 -0.056315 -0.4362 0.332123 36 -0.058484 -0.453 0.326085

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Dec/14/t12607820528plac9q3qmzrzt8/1ofut1260781959.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/14/t12607820528plac9q3qmzrzt8/1ofut1260781959.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/14/t12607820528plac9q3qmzrzt8/27cxy1260781959.png (open in new window) http://www.freestatistics.org/blog/date/2009/Dec/14/t12607820528plac9q3qmzrzt8/27cxy1260781959.ps (open in new window)

Parameters (Session):

par1 = 12 ;

Parameters (R input):

par1 = 36 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = MA ; par7 = 0.95 ;

R code (references can be found in the software module):

if (par1 == 'Default') { par1 = 10*log10(length(x)) } else { par1 <- as.numeric(par1) } par2 <- as.numeric(par2) par3 <- as.numeric(par3) par4 <- as.numeric(par4) par5 <- as.numeric(par5) if (par6 == 'White Noise') par6 <- 'white' else par6 <- 'ma' par7 <- as.numeric(par7) if (par2 == 0) { x <- log(x) } else { x <- (x ^ par2 - 1) / par2 } if (par3 > 0) x <- diff(x,lag=1,difference=par3) if (par4 > 0) x <- diff(x,lag=par5,difference=par4) bitmap(file='pic1.png') racf <- acf(x, par1, main='Autocorrelation', xlab='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')) dev.off() bitmap(file='pic2.png') rpacf <- pacf(x,par1,main='Partial Autocorrelation',xlab='lags',ylab='PACF') dev.off() (myacf <- c(racf$acf)) (mypacf <- c(rpacf$acf)) lengthx <- length(x) sqrtn <- sqrt(lengthx) load(file='createtable') a<-table.start() a<-table.row.start(a) a<-table.element(a,'Autocorrelation Function',4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Time lag k',header=TRUE) a<-table.element(a,hyperlink('http://www.xycoon.com/basics.htm','ACF(k)','click here for more information about the Autocorrelation Function'),header=TRUE) a<-table.element(a,'T-STAT',header=TRUE) a<-table.element(a,'P-value',header=TRUE) a<-table.row.end(a) for (i in 2:(par1+1)) { a<-table.row.start(a) a<-table.element(a,i-1,header=TRUE) a<-table.element(a,round(myacf[i],6)) mytstat <- myacf[i]*sqrtn a<-table.element(a,round(mytstat,4)) a<-table.element(a,round(1-pt(abs(mytstat),lengthx),6)) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a,'Partial Autocorrelation Function',4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Time lag k',header=TRUE) a<-table.element(a,hyperlink('http://www.xycoon.com/basics.htm','PACF(k)','click here for more information about the Partial Autocorrelation Function'),header=TRUE) a<-table.element(a,'T-STAT',header=TRUE) a<-table.element(a,'P-value',header=TRUE) a<-table.row.end(a) for (i in 1:par1) { a<-table.row.start(a) a<-table.element(a,i,header=TRUE) a<-table.element(a,round(mypacf[i],6)) mytstat <- mypacf[i]*sqrtn a<-table.element(a,round(mytstat,4)) a<-table.element(a,round(1-pt(abs(mytstat),lengthx),6)) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable1.tab')

Copyright

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa

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