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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Tue, 03 Jan 2012 09:18:19 -0500

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Jan/03/t1325600349fd5hya4lvyrg0le.htm/, Retrieved Fri, 03 May 2024 20:23:23 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=160949, Retrieved Fri, 03 May 2024 20:23:23 +0000

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Estimated Impact

158

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-       [(Partial) Autocorrelation Function] [] [2012-01-03 14:18:19] [b73e01d307dfd28a47e36e69f67f21fd] [Current]

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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' @ jenkins.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160949&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160949&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160949&T=0

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

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' @ jenkins.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.523084	-4.4076	1.8e-05
2	-0.059066	-0.4977	0.310117
3	0.268065	2.2588	0.013486
4	-0.133506	-1.1249	0.132201
5	0.08228	0.6933	0.245191
6	-0.010323	-0.087	0.465465
7	-0.162573	-1.3699	0.087523
8	0.15666	1.32	0.095531
9	0.094524	0.7965	0.214206
10	-0.211346	-1.7808	0.039609
11	-0.048831	-0.4115	0.34099
12	0.345442	2.9107	0.002407
13	-0.404479	-3.4082	0.00054
14	0.220073	1.8544	0.03392
15	-0.027681	-0.2332	0.40812
16	-0.160024	-1.3484	0.09091
17	0.223678	1.8847	0.031779
18	-0.120802	-1.0179	0.156092

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.523084 & -4.4076 & 1.8e-05 \tabularnewline
2 & -0.059066 & -0.4977 & 0.310117 \tabularnewline
3 & 0.268065 & 2.2588 & 0.013486 \tabularnewline
4 & -0.133506 & -1.1249 & 0.132201 \tabularnewline
5 & 0.08228 & 0.6933 & 0.245191 \tabularnewline
6 & -0.010323 & -0.087 & 0.465465 \tabularnewline
7 & -0.162573 & -1.3699 & 0.087523 \tabularnewline
8 & 0.15666 & 1.32 & 0.095531 \tabularnewline
9 & 0.094524 & 0.7965 & 0.214206 \tabularnewline
10 & -0.211346 & -1.7808 & 0.039609 \tabularnewline
11 & -0.048831 & -0.4115 & 0.34099 \tabularnewline
12 & 0.345442 & 2.9107 & 0.002407 \tabularnewline
13 & -0.404479 & -3.4082 & 0.00054 \tabularnewline
14 & 0.220073 & 1.8544 & 0.03392 \tabularnewline
15 & -0.027681 & -0.2332 & 0.40812 \tabularnewline
16 & -0.160024 & -1.3484 & 0.09091 \tabularnewline
17 & 0.223678 & 1.8847 & 0.031779 \tabularnewline
18 & -0.120802 & -1.0179 & 0.156092 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160949&T=1

[TABLE]
[ROW][C]Autocorrelation Function[/C][/ROW]
[ROW][C]Time lag k[/C][C]ACF(k)[/C][C]T-STAT[/C][C]P-value[/C][/ROW]
[ROW][C]1[/C][C]-0.523084[/C][C]-4.4076[/C][C]1.8e-05[/C][/ROW]
[ROW][C]2[/C][C]-0.059066[/C][C]-0.4977[/C][C]0.310117[/C][/ROW]
[ROW][C]3[/C][C]0.268065[/C][C]2.2588[/C][C]0.013486[/C][/ROW]
[ROW][C]4[/C][C]-0.133506[/C][C]-1.1249[/C][C]0.132201[/C][/ROW]
[ROW][C]5[/C][C]0.08228[/C][C]0.6933[/C][C]0.245191[/C][/ROW]
[ROW][C]6[/C][C]-0.010323[/C][C]-0.087[/C][C]0.465465[/C][/ROW]
[ROW][C]7[/C][C]-0.162573[/C][C]-1.3699[/C][C]0.087523[/C][/ROW]
[ROW][C]8[/C][C]0.15666[/C][C]1.32[/C][C]0.095531[/C][/ROW]
[ROW][C]9[/C][C]0.094524[/C][C]0.7965[/C][C]0.214206[/C][/ROW]
[ROW][C]10[/C][C]-0.211346[/C][C]-1.7808[/C][C]0.039609[/C][/ROW]
[ROW][C]11[/C][C]-0.048831[/C][C]-0.4115[/C][C]0.34099[/C][/ROW]
[ROW][C]12[/C][C]0.345442[/C][C]2.9107[/C][C]0.002407[/C][/ROW]
[ROW][C]13[/C][C]-0.404479[/C][C]-3.4082[/C][C]0.00054[/C][/ROW]
[ROW][C]14[/C][C]0.220073[/C][C]1.8544[/C][C]0.03392[/C][/ROW]
[ROW][C]15[/C][C]-0.027681[/C][C]-0.2332[/C][C]0.40812[/C][/ROW]
[ROW][C]16[/C][C]-0.160024[/C][C]-1.3484[/C][C]0.09091[/C][/ROW]
[ROW][C]17[/C][C]0.223678[/C][C]1.8847[/C][C]0.031779[/C][/ROW]
[ROW][C]18[/C][C]-0.120802[/C][C]-1.0179[/C][C]0.156092[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160949&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160949&T=1

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.523084	-4.4076	1.8e-05
2	-0.059066	-0.4977	0.310117
3	0.268065	2.2588	0.013486
4	-0.133506	-1.1249	0.132201
5	0.08228	0.6933	0.245191
6	-0.010323	-0.087	0.465465
7	-0.162573	-1.3699	0.087523
8	0.15666	1.32	0.095531
9	0.094524	0.7965	0.214206
10	-0.211346	-1.7808	0.039609
11	-0.048831	-0.4115	0.34099
12	0.345442	2.9107	0.002407
13	-0.404479	-3.4082	0.00054
14	0.220073	1.8544	0.03392
15	-0.027681	-0.2332	0.40812
16	-0.160024	-1.3484	0.09091
17	0.223678	1.8847	0.031779
18	-0.120802	-1.0179	0.156092

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.523084	-4.4076	1.8e-05
2	-0.458	-3.8592	0.000124
3	-0.02884	-0.243	0.40435
4	0.05412	0.456	0.324883
5	0.226802	1.9111	0.030017
6	0.174142	1.4673	0.073349
7	-0.166814	-1.4056	0.082102
8	-0.208323	-1.7554	0.041755
9	0.107334	0.9044	0.184417
10	0.12097	1.0193	0.155758
11	-0.210556	-1.7742	0.040161
12	0.153215	1.291	0.100443
13	-0.222668	-1.8762	0.032367
14	-0.014969	-0.1261	0.449994
15	0.00239	0.0201	0.491995
16	-0.041344	-0.3484	0.364297
17	-0.048112	-0.4054	0.343202
18	-0.00623	-0.0525	0.479142

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.523084 & -4.4076 & 1.8e-05 \tabularnewline
2 & -0.458 & -3.8592 & 0.000124 \tabularnewline
3 & -0.02884 & -0.243 & 0.40435 \tabularnewline
4 & 0.05412 & 0.456 & 0.324883 \tabularnewline
5 & 0.226802 & 1.9111 & 0.030017 \tabularnewline
6 & 0.174142 & 1.4673 & 0.073349 \tabularnewline
7 & -0.166814 & -1.4056 & 0.082102 \tabularnewline
8 & -0.208323 & -1.7554 & 0.041755 \tabularnewline
9 & 0.107334 & 0.9044 & 0.184417 \tabularnewline
10 & 0.12097 & 1.0193 & 0.155758 \tabularnewline
11 & -0.210556 & -1.7742 & 0.040161 \tabularnewline
12 & 0.153215 & 1.291 & 0.100443 \tabularnewline
13 & -0.222668 & -1.8762 & 0.032367 \tabularnewline
14 & -0.014969 & -0.1261 & 0.449994 \tabularnewline
15 & 0.00239 & 0.0201 & 0.491995 \tabularnewline
16 & -0.041344 & -0.3484 & 0.364297 \tabularnewline
17 & -0.048112 & -0.4054 & 0.343202 \tabularnewline
18 & -0.00623 & -0.0525 & 0.479142 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160949&T=2

[TABLE]
[ROW][C]Partial Autocorrelation Function[/C][/ROW]
[ROW][C]Time lag k[/C][C]PACF(k)[/C][C]T-STAT[/C][C]P-value[/C][/ROW]
[ROW][C]1[/C][C]-0.523084[/C][C]-4.4076[/C][C]1.8e-05[/C][/ROW]
[ROW][C]2[/C][C]-0.458[/C][C]-3.8592[/C][C]0.000124[/C][/ROW]
[ROW][C]3[/C][C]-0.02884[/C][C]-0.243[/C][C]0.40435[/C][/ROW]
[ROW][C]4[/C][C]0.05412[/C][C]0.456[/C][C]0.324883[/C][/ROW]
[ROW][C]5[/C][C]0.226802[/C][C]1.9111[/C][C]0.030017[/C][/ROW]
[ROW][C]6[/C][C]0.174142[/C][C]1.4673[/C][C]0.073349[/C][/ROW]
[ROW][C]7[/C][C]-0.166814[/C][C]-1.4056[/C][C]0.082102[/C][/ROW]
[ROW][C]8[/C][C]-0.208323[/C][C]-1.7554[/C][C]0.041755[/C][/ROW]
[ROW][C]9[/C][C]0.107334[/C][C]0.9044[/C][C]0.184417[/C][/ROW]
[ROW][C]10[/C][C]0.12097[/C][C]1.0193[/C][C]0.155758[/C][/ROW]
[ROW][C]11[/C][C]-0.210556[/C][C]-1.7742[/C][C]0.040161[/C][/ROW]
[ROW][C]12[/C][C]0.153215[/C][C]1.291[/C][C]0.100443[/C][/ROW]
[ROW][C]13[/C][C]-0.222668[/C][C]-1.8762[/C][C]0.032367[/C][/ROW]
[ROW][C]14[/C][C]-0.014969[/C][C]-0.1261[/C][C]0.449994[/C][/ROW]
[ROW][C]15[/C][C]0.00239[/C][C]0.0201[/C][C]0.491995[/C][/ROW]
[ROW][C]16[/C][C]-0.041344[/C][C]-0.3484[/C][C]0.364297[/C][/ROW]
[ROW][C]17[/C][C]-0.048112[/C][C]-0.4054[/C][C]0.343202[/C][/ROW]
[ROW][C]18[/C][C]-0.00623[/C][C]-0.0525[/C][C]0.479142[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160949&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160949&T=2

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.523084	-4.4076	1.8e-05
2	-0.458	-3.8592	0.000124
3	-0.02884	-0.243	0.40435
4	0.05412	0.456	0.324883
5	0.226802	1.9111	0.030017
6	0.174142	1.4673	0.073349
7	-0.166814	-1.4056	0.082102
8	-0.208323	-1.7554	0.041755
9	0.107334	0.9044	0.184417
10	0.12097	1.0193	0.155758
11	-0.210556	-1.7742	0.040161
12	0.153215	1.291	0.100443
13	-0.222668	-1.8762	0.032367
14	-0.014969	-0.1261	0.449994
15	0.00239	0.0201	0.491995
16	-0.041344	-0.3484	0.364297
17	-0.048112	-0.4054	0.343202
18	-0.00623	-0.0525	0.479142

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

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

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ; par8 = ;

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 (par8 != '') par8 <- as.numeric(par8)
ox <- x
if (par8 == '') {
if (par2 == 0) {
x <- log(x)
} else {
x <- (x ^ par2 - 1) / par2
}
} else {
x <- log(x,base=par8)
}
if (par3 > 0) x <- diff(x,lag=1,difference=par3)
if (par4 > 0) x <- diff(x,lag=par5,difference=par4)
bitmap(file='picts.png')
op <- par(mfrow=c(2,1))
plot(ox,type='l',main='Original Time Series',xlab='time',ylab='value')
if (par8=='') {
mytitle <- paste('Working Time Series (lambda=',par2,', d=',par3,', D=',par4,')',sep='')
mysub <- paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')
} else {
mytitle <- paste('Working Time Series (base=',par8,', d=',par3,', D=',par4,')',sep='')
mysub <- paste('(base=',par8,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')
}
plot(x,type='l', main=mytitle,xlab='time',ylab='value')
par(op)
dev.off()
bitmap(file='pic1.png')
racf <- acf(x, par1, main='Autocorrelation', xlab='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=mysub)
dev.off()
bitmap(file='pic2.png')
rpacf <- pacf(x,par1,main='Partial Autocorrelation',xlab='lags',ylab='PACF',sub=mysub)
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('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('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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Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code