*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: Fri, 27 Nov 2009 05:06:01 -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/Nov/27/t1259323738zfemqgfoqfgrkox.htm/, Retrieved Fri, 27 Nov 2009 13:09:01 +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/Nov/27/t1259323738zfemqgfoqfgrkox.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 «

1.4 1.2 1 1.7 2.4 2 2.1 2 1.8 2.7 2.3 1.9 2 2.3 2.8 2.4 2.3 2.7 2.7 2.9 3 2.2 2.3 2.8 2.8 2.8 2.2 2.6 2.8 2.5 2.4 2.3 1.9 1.7 2 2.1 1.7 1.8 1.8 1.8 1.3 1.3 1.3 1.2 1.4 2.2 2.9 3.1 3.5 3.6 4.4 4.1 5.1 5.8 5.9 5.4 5.5 4.8 3.2 2.7 2.1 1.9 0.6 0.7 -0.2 -1 -1.7 -0.7 -1

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 0.898914 7.4669 0 2 0.781736 6.4936 0 3 0.62357 5.1798 1e-06 4 0.462613 3.8428 0.000134 5 0.289744 2.4068 0.009387 6 0.129928 1.0793 0.142114 7 -0.03955 -0.3285 0.371753 8 -0.18764 -1.5587 0.061826 9 -0.329312 -2.7355 0.003956 10 -0.430032 -3.5721 0.000325 11 -0.511026 -4.2449 3.3e-05 12 -0.564007 -4.685 7e-06 13 -0.545723 -4.5331 1.2e-05 14 -0.500065 -4.1539 4.6e-05 15 -0.429683 -3.5692 0.000328 16 -0.364071 -3.0242 0.00175 17 -0.293325 -2.4365 0.008707 18 -0.228028 -1.8941 0.031199 19 -0.150897 -1.2534 0.107137 20 -0.091293 -0.7583 0.225417 21 -0.020922 -0.1738 0.431269 22 0.034755 0.2887 0.38684 23 0.075951 0.6309 0.265097 24 0.110339 0.9165 0.181288 25 0.130191 1.0815 0.141631 26 0.131987 1.0964 0.138366 27 0.125698 1.0441 0.150035 28 0.128886 1.0706 0.144039 29 0.128254 1.0654 0.145215 30 0.129944 1.0794 0.142085 31 0.124607 1.0351 0.152127 32 0.12356 1.0264 0.154151 33 0.11098 0.9219 0.179905 34 0.094718 0.7868 0.217051 35 0.077741 0.6458 0.260286 36 0.062307 0.5176 0.30321 37 0.036821 0.3059 0.380317 38 0.021282 0.1768 0.430099 39 0.010286 0.0854 0.46608 40 -0.002034 -0.0169 0.493285 41 -0.014467 -0.1202 0.452347 42 -0.03019 -0.2508 0.401367 43 -0.051247 -0.4257 0.33583 44 -0.065946 -0.5478 0.292803 45 -0.086052 -0.7148 0.238572 46 -0.094522 -0.7852 0.217525 47 -0.103222 -0.8574 0.197088 48 -0.120148 -0.998 0.160878 49 -0.112441 -0.934 0.176779 50 -0.105494 -0.8763 0.191954 51 -0.106003 -0.8805 0.190815 52 -0.101369 -0.842 0.201338 53 -0.093495 -0.7766 0.220016 54 -0.077918 -0.6472 0.259814 55 -0.050876 -0.4226 0.336949 56 -0.029787 -0.2474 0.402656 57 -0.007569 -0.0629 0.475023 58 0.009982 0.0829 0.467079 59 0.024917 0.207 0.41832 60 0.051389 0.4269 0.335402 Partial Autocorrelation Function Time lag k PACF(k) T-STAT P-value 1 0.898914 7.4669 0 2 -0.137067 -1.1386 0.129411 3 -0.277418 -2.3044 0.012107 4 -0.093085 -0.7732 0.221015 5 -0.142066 -1.1801 0.121009 6 -0.05939 -0.4933 0.311673 7 -0.190439 -1.5819 0.059122 8 -0.07507 -0.6236 0.267481 9 -0.133222 -1.1066 0.136149 10 0.001245 0.0103 0.49589 11 -0.080394 -0.6678 0.253244 12 -0.103283 -0.8579 0.196949 13 0.240273 1.9959 0.024949 14 -0.012814 -0.1064 0.457772 15 -0.039776 -0.3304 0.371048 16 -0.157992 -1.3124 0.09687 17 -0.067674 -0.5621 0.28792 18 -0.051822 -0.4305 0.3341 19 -0.013536 -0.1124 0.455402 20 -0.108989 -0.9053 0.184221 21 0.001297 0.0108 0.495718 22 0.039749 0.3302 0.371134 23 -0.109467 -0.9093 0.183178 24 0.015808 0.1313 0.447956 25 -0.002431 -0.0202 0.491973 26 -0.036389 -0.3023 0.381678 27 -0.038728 -0.3217 0.374326 28 0.042707 0.3547 0.36193 29 -0.039984 -0.3321 0.370399 30 -0.006328 -0.0526 0.479116 31 0.012314 0.1023 0.459413 32 -0.02704 -0.2246 0.411471 33 0.007608 0.0632 0.474897 34 -0.053649 -0.4456 0.328626 35 -0.01547 -0.1285 0.449063 36 0.000468 0.0039 0.498453 37 -0.054821 -0.4554 0.325133 38 0.003755 0.0312 0.487605 39 0.043185 0.3587 0.360449 40 0.009478 0.0787 0.468737 41 -0.011636 -0.0967 0.46164 42 -0.008953 -0.0744 0.470465 43 -0.083675 -0.6951 0.244678 44 0.028133 0.2337 0.407959 45 -0.069851 -0.5802 0.281825 46 -0.012053 -0.1001 0.460269 47 -0.032585 -0.2707 0.393725 48 -0.089557 -0.7439 0.229728 49 0.109959 0.9134 0.182111 50 -0.026973 -0.2241 0.411688 51 -0.083135 -0.6906 0.246076 52 -0.014504 -0.1205 0.452228 53 0.013415 0.1114 0.455799 54 -0.018556 -0.1541 0.438976 55 0.00274 0.0228 0.490955 56 -0.045935 -0.3816 0.35198 57 -0.07663 -0.6365 0.263266 58 0.04293 0.3566 0.361239 59 -0.04659 -0.387 0.349971 60 0.022263 0.1849 0.426913

Charts produced by software:

http://www.freestatistics.org/blog/date/2009/Nov/27/t1259323738zfemqgfoqfgrkox/1l1kn1259323560.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/27/t1259323738zfemqgfoqfgrkox/1l1kn1259323560.ps (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/27/t1259323738zfemqgfoqfgrkox/2fff91259323560.png (open in new window) http://www.freestatistics.org/blog/date/2009/Nov/27/t1259323738zfemqgfoqfgrkox/2fff91259323560.ps (open in new window)

Parameters (Session):

par1 = 60 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = 60 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; 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')

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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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