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Inducing Stationarity in Time Series-Q2

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

Title produced by software: (Partial) Autocorrelation Function

Date of computation: Mon, 10 Dec 2007 13:52:25 -0700

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2007/Dec/10/t1197319135c8zxfvzt5yz8omx.htm/, Retrieved Mon, 10 Dec 2007 21:38:57 +0100

User-defined keywords:

s0650550 s0650062

Dataseries X:

» Textbox « » Textfile « » CSV «

2.25 1.85 1.75 1.75 1.55 1.5 1.5 1.1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1.21 1.25 1.25 1.45 1.5 1.5 1.64 1.75 1.93 2 2.17 2.25 2.39 2.5 2.5 2.65 2.75 2.75 2.9 3 3 3 3

Text written by user:

Output produced by software:

Summary of compuational transaction Raw Input view raw input (R code) Raw Output view raw output of R engine Computing time 2 seconds R Server 'Gwilym Jenkins' @ 72.249.127.135 Autocorrelation Function Time lag k ACF(k) T-STAT P-value 0 1 6.7823 0 1 -0.379777 -2.5758 0.99336 2 -0.264145 -1.7915 0.960105 3 0.442638 3.0021 0.002162 4 -0.230665 -1.5644 0.937717 5 -0.121337 -0.8229 0.792608 6 0.104511 0.7088 0.241003 7 0.04413 0.2993 0.383028 8 0.110883 0.752 0.227928 9 -0.160072 -1.0857 0.858358 10 0.120276 0.8158 0.209423 11 0.025876 0.1755 0.430729 12 -0.14689 -0.9963 0.837832 13 0.124094 0.8416 0.20217 14 -0.075305 -0.5107 0.694013 15 0.007514 0.051 0.479788 16 0.012906 0.0875 0.465314 17 -0.145204 -0.9848 0.835067 18 0.256188 1.7376 0.044491 19 -0.119233 -0.8087 0.788568 20 -0.189188 -1.2831 0.897064 21 0.325983 2.2109 0.016026 22 -0.19236 -1.3046 0.900749 23 -0.191336 -1.2977 0.89957 24 0.236312 1.6027 0.057918 25 -0.087849 -0.5958 0.722892 26 -0.037835 -0.2566 0.600687 27 0.010151 0.0688 0.472705 28 0.092317 0.6261 0.267163 29 -0.031588 -0.2142 0.584346 30 -0.18144 -1.2306 0.887633 31 0.147085 0.9976 0.161852 32 -0.013272 -0.09 0.535667 33 -0.164366 -1.1148 0.864633 34 0.178456 1.2103 0.116164 35 -0.010824 -0.0734 0.529103 36 -0.048388 -0.3282 0.627868 37 0.107965 0.7323 0.233864 38 -0.140833 -0.9552 0.82776 39 0.08033 0.5448 0.294254 40 -0.016246 -0.1102 0.543629 41 -0.072657 -0.4928 0.687745 42 0.074379 0.5045 0.308171 43 0.022019 0.1493 0.440969 44 -0.037881 -0.2569 0.600807 45 0.034676 0.2352 0.407554 46 NA NA NA 47 NA NA NA 48 NA NA NA 49 NA NA NA 50 NA NA NA 51 NA NA NA 52 NA NA NA 53 NA NA NA 54 NA NA NA 55 NA NA NA 56 NA NA NA 57 NA NA NA 58 NA NA NA 59 NA NA NA Partial Autocorrelation Function Time lag k PACF(k) T-STAT P-value 0 -0.379777 -2.5758 0.99336 1 -0.477203 -3.2365 0.998877 2 0.171314 1.1619 0.125633 3 -0.084383 -0.5723 0.715051 4 -0.067678 -0.459 0.675807 5 -0.232976 -1.5801 0.939534 6 0.049271 0.3342 0.369885 7 0.293133 1.9881 0.026384 8 0.047481 0.322 0.374444 9 0.098191 0.666 0.25438 10 -0.058822 -0.3989 0.654112 11 0.080168 0.5437 0.294628 12 0.111224 0.7544 0.22724 13 -0.071674 -0.4861 0.685404 14 -0.042323 -0.2871 0.612319 15 -0.177962 -1.207 0.883198 16 -0.200129 -1.3573 0.909352 17 0.128773 0.8734 0.193496 18 -0.000361 -0.0024 0.500971 19 -0.191648 -1.2998 0.899931 20 -0.044706 -0.3032 0.618451 21 -0.028542 -0.1936 0.576321 22 -0.08628 -0.5852 0.719356 23 -0.081374 -0.5519 0.708157 24 -0.119757 -0.8122 0.789578 25 -0.020279 -0.1375 0.554398 26 -0.0602 -0.4083 0.657525 27 0.112709 0.7644 0.224257 28 0.006889 0.0467 0.481467 29 -0.081287 -0.5513 0.707957 30 -0.069479 -0.4712 0.680149 31 -0.00617 -0.0418 0.516599 32 -0.007338 -0.0498 0.519738 33 -0.013714 -0.093 0.53685 34 0.002797 0.019 0.492474 35 -0.017963 -0.1218 0.548218 36 0.154081 1.045 0.150735 37 -0.011617 -0.0788 0.531228 38 -0.036511 -0.2476 0.597239 39 -0.092178 -0.6252 0.732529 40 0.082758 0.5613 0.288661 41 -0.100998 -0.685 0.75161 42 -0.004744 -0.0322 0.512766 43 -0.09281 -0.6295 0.733921 44 -0.048752 -0.3307 0.628795 45 NA NA NA 46 NA NA NA 47 NA NA NA 48 NA NA NA 49 NA NA NA 50 NA NA NA 51 NA NA NA 52 NA NA NA 53 NA NA NA 54 NA NA NA 55 NA NA NA 56 NA NA NA 57 NA NA NA 58 NA NA NA 59 NA NA NA

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/10/t1197319135c8zxfvzt5yz8omx/1q27z1197319943.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/10/t1197319135c8zxfvzt5yz8omx/1q27z1197319943.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/10/t1197319135c8zxfvzt5yz8omx/2zofz1197319943.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2007/Dec/10/t1197319135c8zxfvzt5yz8omx/2zofz1197319943.ps (open in new window)

Parameters:

par1 = 60 ; par2 = 1 ; par3 = 2 ; par4 = 1 ; par5 = 12 ;

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 (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='lags',ylab='ACF') 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 1:par1) { 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(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-1,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(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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