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Author

*The author of this computation has been verified*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Tue, 06 Dec 2011 14:46:33 -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/2011/Dec/06/t1323200816dv58017i88nw592.htm/, Retrieved Sun, 28 Apr 2024 22:23:17 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=151838, Retrieved Sun, 28 Apr 2024 22:23:17 +0000

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No (this computation is public)

User-defined keywords

Estimated Impact

125

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-     [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-12 13:32:37] [76963dc1903f0f612b6153510a3818cf]
- R  D  [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-17 12:14:40] [76963dc1903f0f612b6153510a3818cf]
-         [Univariate Explorative Data Analysis] [Run Sequence Plot...] [2008-12-22 18:19:51] [1ce0d16c8f4225c977b42c8fa93bc163]
- RMP       [Univariate Data Series] [Identifying Integ...] [2009-11-22 12:08:06] [b98453cac15ba1066b407e146608df68]
- RMP         [(Partial) Autocorrelation Function] [Births] [2010-11-29 09:36:27] [b98453cac15ba1066b407e146608df68]
F R PD          [(Partial) Autocorrelation Function] [autocorrelatiefun...] [2010-12-02 19:51:36] [97ad38b1c3b35a5feca8b85f7bc7b3ff]
F                 [(Partial) Autocorrelation Function] [Autocorrelatiefun...] [2010-12-02 19:55:48] [97ad38b1c3b35a5feca8b85f7bc7b3ff]
- R P               [(Partial) Autocorrelation Function] [] [2011-12-04 12:45:52] [9401a40688cf36283be626153bc5a38b]
- R                     [(Partial) Autocorrelation Function] [WS9.3] [2011-12-06 19:46:33] [7c363341293f6644b8647ab9153ed4f7] [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	3 seconds
R Server	'George Udny Yule' @ yule.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 & 3 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=151838&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=151838&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=151838&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	3 seconds
R Server	'George Udny Yule' @ yule.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.067835	-0.5254	0.300604
2	0.159939	1.2389	0.110106
3	0.247549	1.9175	0.029969
4	-0.096469	-0.7472	0.228917
5	0.127406	0.9869	0.163831
6	-0.112407	-0.8707	0.193694
7	-0.202835	-1.5712	0.060703
8	-0.030078	-0.233	0.408283
9	-0.176185	-1.3647	0.088718
10	-0.194355	-1.5055	0.068726
11	-0.037405	-0.2897	0.386506
12	-0.465521	-3.6059	0.000317
13	0.018937	0.1467	0.441936
14	0.023464	0.1818	0.428194
15	-0.033775	-0.2616	0.397255
16	0.030577	0.2368	0.40679
17	0.067425	0.5223	0.301703
18	0.239767	1.8572	0.034094

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.067835 & -0.5254 & 0.300604 \tabularnewline
2 & 0.159939 & 1.2389 & 0.110106 \tabularnewline
3 & 0.247549 & 1.9175 & 0.029969 \tabularnewline
4 & -0.096469 & -0.7472 & 0.228917 \tabularnewline
5 & 0.127406 & 0.9869 & 0.163831 \tabularnewline
6 & -0.112407 & -0.8707 & 0.193694 \tabularnewline
7 & -0.202835 & -1.5712 & 0.060703 \tabularnewline
8 & -0.030078 & -0.233 & 0.408283 \tabularnewline
9 & -0.176185 & -1.3647 & 0.088718 \tabularnewline
10 & -0.194355 & -1.5055 & 0.068726 \tabularnewline
11 & -0.037405 & -0.2897 & 0.386506 \tabularnewline
12 & -0.465521 & -3.6059 & 0.000317 \tabularnewline
13 & 0.018937 & 0.1467 & 0.441936 \tabularnewline
14 & 0.023464 & 0.1818 & 0.428194 \tabularnewline
15 & -0.033775 & -0.2616 & 0.397255 \tabularnewline
16 & 0.030577 & 0.2368 & 0.40679 \tabularnewline
17 & 0.067425 & 0.5223 & 0.301703 \tabularnewline
18 & 0.239767 & 1.8572 & 0.034094 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=151838&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]-0.067835[/C][C]-0.5254[/C][C]0.300604[/C][/ROW]
[ROW][C]2[/C][C]0.159939[/C][C]1.2389[/C][C]0.110106[/C][/ROW]
[ROW][C]3[/C][C]0.247549[/C][C]1.9175[/C][C]0.029969[/C][/ROW]
[ROW][C]4[/C][C]-0.096469[/C][C]-0.7472[/C][C]0.228917[/C][/ROW]
[ROW][C]5[/C][C]0.127406[/C][C]0.9869[/C][C]0.163831[/C][/ROW]
[ROW][C]6[/C][C]-0.112407[/C][C]-0.8707[/C][C]0.193694[/C][/ROW]
[ROW][C]7[/C][C]-0.202835[/C][C]-1.5712[/C][C]0.060703[/C][/ROW]
[ROW][C]8[/C][C]-0.030078[/C][C]-0.233[/C][C]0.408283[/C][/ROW]
[ROW][C]9[/C][C]-0.176185[/C][C]-1.3647[/C][C]0.088718[/C][/ROW]
[ROW][C]10[/C][C]-0.194355[/C][C]-1.5055[/C][C]0.068726[/C][/ROW]
[ROW][C]11[/C][C]-0.037405[/C][C]-0.2897[/C][C]0.386506[/C][/ROW]
[ROW][C]12[/C][C]-0.465521[/C][C]-3.6059[/C][C]0.000317[/C][/ROW]
[ROW][C]13[/C][C]0.018937[/C][C]0.1467[/C][C]0.441936[/C][/ROW]
[ROW][C]14[/C][C]0.023464[/C][C]0.1818[/C][C]0.428194[/C][/ROW]
[ROW][C]15[/C][C]-0.033775[/C][C]-0.2616[/C][C]0.397255[/C][/ROW]
[ROW][C]16[/C][C]0.030577[/C][C]0.2368[/C][C]0.40679[/C][/ROW]
[ROW][C]17[/C][C]0.067425[/C][C]0.5223[/C][C]0.301703[/C][/ROW]
[ROW][C]18[/C][C]0.239767[/C][C]1.8572[/C][C]0.034094[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=151838&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=151838&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	-0.067835	-0.5254	0.300604
2	0.159939	1.2389	0.110106
3	0.247549	1.9175	0.029969
4	-0.096469	-0.7472	0.228917
5	0.127406	0.9869	0.163831
6	-0.112407	-0.8707	0.193694
7	-0.202835	-1.5712	0.060703
8	-0.030078	-0.233	0.408283
9	-0.176185	-1.3647	0.088718
10	-0.194355	-1.5055	0.068726
11	-0.037405	-0.2897	0.386506
12	-0.465521	-3.6059	0.000317
13	0.018937	0.1467	0.441936
14	0.023464	0.1818	0.428194
15	-0.033775	-0.2616	0.397255
16	0.030577	0.2368	0.40679
17	0.067425	0.5223	0.301703
18	0.239767	1.8572	0.034094

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.067835	-0.5254	0.300604
2	0.156056	1.2088	0.11574
3	0.27523	2.1319	0.018559
4	-0.089655	-0.6945	0.245035
5	0.028202	0.2184	0.41391
6	-0.151136	-1.1707	0.123175
7	-0.231032	-1.7896	0.039285
8	-0.085424	-0.6617	0.255351
9	-0.047364	-0.3669	0.357501
10	-0.132525	-1.0265	0.15438
11	-0.006664	-0.0516	0.479501
12	-0.428202	-3.3168	0.000775
13	-0.072993	-0.5654	0.286954
14	0.124777	0.9665	0.168832
15	0.240599	1.8637	0.033632
16	-0.112397	-0.8706	0.193714
17	-0.022202	-0.172	0.432017
18	0.125179	0.9696	0.168062

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.067835 & -0.5254 & 0.300604 \tabularnewline
2 & 0.156056 & 1.2088 & 0.11574 \tabularnewline
3 & 0.27523 & 2.1319 & 0.018559 \tabularnewline
4 & -0.089655 & -0.6945 & 0.245035 \tabularnewline
5 & 0.028202 & 0.2184 & 0.41391 \tabularnewline
6 & -0.151136 & -1.1707 & 0.123175 \tabularnewline
7 & -0.231032 & -1.7896 & 0.039285 \tabularnewline
8 & -0.085424 & -0.6617 & 0.255351 \tabularnewline
9 & -0.047364 & -0.3669 & 0.357501 \tabularnewline
10 & -0.132525 & -1.0265 & 0.15438 \tabularnewline
11 & -0.006664 & -0.0516 & 0.479501 \tabularnewline
12 & -0.428202 & -3.3168 & 0.000775 \tabularnewline
13 & -0.072993 & -0.5654 & 0.286954 \tabularnewline
14 & 0.124777 & 0.9665 & 0.168832 \tabularnewline
15 & 0.240599 & 1.8637 & 0.033632 \tabularnewline
16 & -0.112397 & -0.8706 & 0.193714 \tabularnewline
17 & -0.022202 & -0.172 & 0.432017 \tabularnewline
18 & 0.125179 & 0.9696 & 0.168062 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=151838&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]-0.067835[/C][C]-0.5254[/C][C]0.300604[/C][/ROW]
[ROW][C]2[/C][C]0.156056[/C][C]1.2088[/C][C]0.11574[/C][/ROW]
[ROW][C]3[/C][C]0.27523[/C][C]2.1319[/C][C]0.018559[/C][/ROW]
[ROW][C]4[/C][C]-0.089655[/C][C]-0.6945[/C][C]0.245035[/C][/ROW]
[ROW][C]5[/C][C]0.028202[/C][C]0.2184[/C][C]0.41391[/C][/ROW]
[ROW][C]6[/C][C]-0.151136[/C][C]-1.1707[/C][C]0.123175[/C][/ROW]
[ROW][C]7[/C][C]-0.231032[/C][C]-1.7896[/C][C]0.039285[/C][/ROW]
[ROW][C]8[/C][C]-0.085424[/C][C]-0.6617[/C][C]0.255351[/C][/ROW]
[ROW][C]9[/C][C]-0.047364[/C][C]-0.3669[/C][C]0.357501[/C][/ROW]
[ROW][C]10[/C][C]-0.132525[/C][C]-1.0265[/C][C]0.15438[/C][/ROW]
[ROW][C]11[/C][C]-0.006664[/C][C]-0.0516[/C][C]0.479501[/C][/ROW]
[ROW][C]12[/C][C]-0.428202[/C][C]-3.3168[/C][C]0.000775[/C][/ROW]
[ROW][C]13[/C][C]-0.072993[/C][C]-0.5654[/C][C]0.286954[/C][/ROW]
[ROW][C]14[/C][C]0.124777[/C][C]0.9665[/C][C]0.168832[/C][/ROW]
[ROW][C]15[/C][C]0.240599[/C][C]1.8637[/C][C]0.033632[/C][/ROW]
[ROW][C]16[/C][C]-0.112397[/C][C]-0.8706[/C][C]0.193714[/C][/ROW]
[ROW][C]17[/C][C]-0.022202[/C][C]-0.172[/C][C]0.432017[/C][/ROW]
[ROW][C]18[/C][C]0.125179[/C][C]0.9696[/C][C]0.168062[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=151838&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=151838&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	-0.067835	-0.5254	0.300604
2	0.156056	1.2088	0.11574
3	0.27523	2.1319	0.018559
4	-0.089655	-0.6945	0.245035
5	0.028202	0.2184	0.41391
6	-0.151136	-1.1707	0.123175
7	-0.231032	-1.7896	0.039285
8	-0.085424	-0.6617	0.255351
9	-0.047364	-0.3669	0.357501
10	-0.132525	-1.0265	0.15438
11	-0.006664	-0.0516	0.479501
12	-0.428202	-3.3168	0.000775
13	-0.072993	-0.5654	0.286954
14	0.124777	0.9665	0.168832
15	0.240599	1.8637	0.033632
16	-0.112397	-0.8706	0.193714
17	-0.022202	-0.172	0.432017
18	0.125179	0.9696	0.168062

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 = 0 ; par4 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ; par8 = 2 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ; par8 = 2 ;

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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code