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Author's title

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

Mon, 05 Dec 2011 11:14:07 -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/05/t13231016729sptfelii1hjls7.htm/, Retrieved Fri, 03 May 2024 04:35:24 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=151029, Retrieved Fri, 03 May 2024 04:35:24 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

129

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       [(Partial) Autocorrelation Function] [Identifying Integ...] [2009-11-22 12:16:10] [b98453cac15ba1066b407e146608df68]
-    D        [(Partial) Autocorrelation Function] [ACF van Y(t) (d=0...] [2009-11-26 00:58:58] [9717cb857c153ca3061376906953b329]
- R PD          [(Partial) Autocorrelation Function] [WS9 ACF] [2011-12-02 16:43:02] [abc1cbe561c2c4615f632bb3153b1275]
-   PD              [(Partial) Autocorrelation Function] [WS 9 - autocorrel...] [2011-12-05 16:14:07] [c897fb90cb9e1f725365d7e541ad7850] [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=151029&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=151029&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=151029&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	0.340803	4.1038	3.4e-05
2	0.15188	1.8289	0.034737
3	0.069428	0.836	0.20226
4	-0.043187	-0.52	0.301913
5	-0.130024	-1.5657	0.0598
6	-0.280698	-3.3801	0.000466
7	-0.147551	-1.7767	0.038853
8	-0.045664	-0.5499	0.291629
9	0.038012	0.4577	0.323919
10	0.053627	0.6458	0.25973
11	0.257345	3.0988	0.001167
12	0.81377	9.7991	0
13	0.254155	3.0604	0.001317
14	0.086393	1.0403	0.149965
15	0.011698	0.1409	0.444087
16	-0.093238	-1.1227	0.131703
17	-0.160774	-1.936	0.027408
18	-0.30311	-3.6499	0.000183
19	-0.165977	-1.9986	0.023759
20	-0.063178	-0.7608	0.224018
21	0.008648	0.1041	0.458601

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.340803 & 4.1038 & 3.4e-05 \tabularnewline
2 & 0.15188 & 1.8289 & 0.034737 \tabularnewline
3 & 0.069428 & 0.836 & 0.20226 \tabularnewline
4 & -0.043187 & -0.52 & 0.301913 \tabularnewline
5 & -0.130024 & -1.5657 & 0.0598 \tabularnewline
6 & -0.280698 & -3.3801 & 0.000466 \tabularnewline
7 & -0.147551 & -1.7767 & 0.038853 \tabularnewline
8 & -0.045664 & -0.5499 & 0.291629 \tabularnewline
9 & 0.038012 & 0.4577 & 0.323919 \tabularnewline
10 & 0.053627 & 0.6458 & 0.25973 \tabularnewline
11 & 0.257345 & 3.0988 & 0.001167 \tabularnewline
12 & 0.81377 & 9.7991 & 0 \tabularnewline
13 & 0.254155 & 3.0604 & 0.001317 \tabularnewline
14 & 0.086393 & 1.0403 & 0.149965 \tabularnewline
15 & 0.011698 & 0.1409 & 0.444087 \tabularnewline
16 & -0.093238 & -1.1227 & 0.131703 \tabularnewline
17 & -0.160774 & -1.936 & 0.027408 \tabularnewline
18 & -0.30311 & -3.6499 & 0.000183 \tabularnewline
19 & -0.165977 & -1.9986 & 0.023759 \tabularnewline
20 & -0.063178 & -0.7608 & 0.224018 \tabularnewline
21 & 0.008648 & 0.1041 & 0.458601 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=151029&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]0.340803[/C][C]4.1038[/C][C]3.4e-05[/C][/ROW]
[ROW][C]2[/C][C]0.15188[/C][C]1.8289[/C][C]0.034737[/C][/ROW]
[ROW][C]3[/C][C]0.069428[/C][C]0.836[/C][C]0.20226[/C][/ROW]
[ROW][C]4[/C][C]-0.043187[/C][C]-0.52[/C][C]0.301913[/C][/ROW]
[ROW][C]5[/C][C]-0.130024[/C][C]-1.5657[/C][C]0.0598[/C][/ROW]
[ROW][C]6[/C][C]-0.280698[/C][C]-3.3801[/C][C]0.000466[/C][/ROW]
[ROW][C]7[/C][C]-0.147551[/C][C]-1.7767[/C][C]0.038853[/C][/ROW]
[ROW][C]8[/C][C]-0.045664[/C][C]-0.5499[/C][C]0.291629[/C][/ROW]
[ROW][C]9[/C][C]0.038012[/C][C]0.4577[/C][C]0.323919[/C][/ROW]
[ROW][C]10[/C][C]0.053627[/C][C]0.6458[/C][C]0.25973[/C][/ROW]
[ROW][C]11[/C][C]0.257345[/C][C]3.0988[/C][C]0.001167[/C][/ROW]
[ROW][C]12[/C][C]0.81377[/C][C]9.7991[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.254155[/C][C]3.0604[/C][C]0.001317[/C][/ROW]
[ROW][C]14[/C][C]0.086393[/C][C]1.0403[/C][C]0.149965[/C][/ROW]
[ROW][C]15[/C][C]0.011698[/C][C]0.1409[/C][C]0.444087[/C][/ROW]
[ROW][C]16[/C][C]-0.093238[/C][C]-1.1227[/C][C]0.131703[/C][/ROW]
[ROW][C]17[/C][C]-0.160774[/C][C]-1.936[/C][C]0.027408[/C][/ROW]
[ROW][C]18[/C][C]-0.30311[/C][C]-3.6499[/C][C]0.000183[/C][/ROW]
[ROW][C]19[/C][C]-0.165977[/C][C]-1.9986[/C][C]0.023759[/C][/ROW]
[ROW][C]20[/C][C]-0.063178[/C][C]-0.7608[/C][C]0.224018[/C][/ROW]
[ROW][C]21[/C][C]0.008648[/C][C]0.1041[/C][C]0.458601[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=151029&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=151029&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	0.340803	4.1038	3.4e-05
2	0.15188	1.8289	0.034737
3	0.069428	0.836	0.20226
4	-0.043187	-0.52	0.301913
5	-0.130024	-1.5657	0.0598
6	-0.280698	-3.3801	0.000466
7	-0.147551	-1.7767	0.038853
8	-0.045664	-0.5499	0.291629
9	0.038012	0.4577	0.323919
10	0.053627	0.6458	0.25973
11	0.257345	3.0988	0.001167
12	0.81377	9.7991	0
13	0.254155	3.0604	0.001317
14	0.086393	1.0403	0.149965
15	0.011698	0.1409	0.444087
16	-0.093238	-1.1227	0.131703
17	-0.160774	-1.936	0.027408
18	-0.30311	-3.6499	0.000183
19	-0.165977	-1.9986	0.023759
20	-0.063178	-0.7608	0.224018
21	0.008648	0.1041	0.458601

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.340803	4.1038	3.4e-05
2	0.040428	0.4868	0.31356
3	0.006778	0.0816	0.467531
4	-0.08385	-1.0097	0.157164
5	-0.108858	-1.3108	0.095994
6	-0.225969	-2.721	0.003653
7	0.032406	0.3902	0.348472
8	0.04955	0.5967	0.275832
9	0.077084	0.9282	0.177421
10	-0.001956	-0.0235	0.490622
11	0.225401	2.7142	0.003725
12	0.778424	9.3735	0
13	-0.397798	-4.7901	2e-06
14	-0.264749	-3.188	0.000878
15	0.027894	0.3359	0.36872
16	0.011188	0.1347	0.446511
17	-0.066304	-0.7984	0.21297
18	0.008821	0.1062	0.45778
19	0.05363	0.6458	0.259717
20	-0.087908	-1.0586	0.145782
21	-0.00946	-0.1139	0.454734

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.340803 & 4.1038 & 3.4e-05 \tabularnewline
2 & 0.040428 & 0.4868 & 0.31356 \tabularnewline
3 & 0.006778 & 0.0816 & 0.467531 \tabularnewline
4 & -0.08385 & -1.0097 & 0.157164 \tabularnewline
5 & -0.108858 & -1.3108 & 0.095994 \tabularnewline
6 & -0.225969 & -2.721 & 0.003653 \tabularnewline
7 & 0.032406 & 0.3902 & 0.348472 \tabularnewline
8 & 0.04955 & 0.5967 & 0.275832 \tabularnewline
9 & 0.077084 & 0.9282 & 0.177421 \tabularnewline
10 & -0.001956 & -0.0235 & 0.490622 \tabularnewline
11 & 0.225401 & 2.7142 & 0.003725 \tabularnewline
12 & 0.778424 & 9.3735 & 0 \tabularnewline
13 & -0.397798 & -4.7901 & 2e-06 \tabularnewline
14 & -0.264749 & -3.188 & 0.000878 \tabularnewline
15 & 0.027894 & 0.3359 & 0.36872 \tabularnewline
16 & 0.011188 & 0.1347 & 0.446511 \tabularnewline
17 & -0.066304 & -0.7984 & 0.21297 \tabularnewline
18 & 0.008821 & 0.1062 & 0.45778 \tabularnewline
19 & 0.05363 & 0.6458 & 0.259717 \tabularnewline
20 & -0.087908 & -1.0586 & 0.145782 \tabularnewline
21 & -0.00946 & -0.1139 & 0.454734 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=151029&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]0.340803[/C][C]4.1038[/C][C]3.4e-05[/C][/ROW]
[ROW][C]2[/C][C]0.040428[/C][C]0.4868[/C][C]0.31356[/C][/ROW]
[ROW][C]3[/C][C]0.006778[/C][C]0.0816[/C][C]0.467531[/C][/ROW]
[ROW][C]4[/C][C]-0.08385[/C][C]-1.0097[/C][C]0.157164[/C][/ROW]
[ROW][C]5[/C][C]-0.108858[/C][C]-1.3108[/C][C]0.095994[/C][/ROW]
[ROW][C]6[/C][C]-0.225969[/C][C]-2.721[/C][C]0.003653[/C][/ROW]
[ROW][C]7[/C][C]0.032406[/C][C]0.3902[/C][C]0.348472[/C][/ROW]
[ROW][C]8[/C][C]0.04955[/C][C]0.5967[/C][C]0.275832[/C][/ROW]
[ROW][C]9[/C][C]0.077084[/C][C]0.9282[/C][C]0.177421[/C][/ROW]
[ROW][C]10[/C][C]-0.001956[/C][C]-0.0235[/C][C]0.490622[/C][/ROW]
[ROW][C]11[/C][C]0.225401[/C][C]2.7142[/C][C]0.003725[/C][/ROW]
[ROW][C]12[/C][C]0.778424[/C][C]9.3735[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]-0.397798[/C][C]-4.7901[/C][C]2e-06[/C][/ROW]
[ROW][C]14[/C][C]-0.264749[/C][C]-3.188[/C][C]0.000878[/C][/ROW]
[ROW][C]15[/C][C]0.027894[/C][C]0.3359[/C][C]0.36872[/C][/ROW]
[ROW][C]16[/C][C]0.011188[/C][C]0.1347[/C][C]0.446511[/C][/ROW]
[ROW][C]17[/C][C]-0.066304[/C][C]-0.7984[/C][C]0.21297[/C][/ROW]
[ROW][C]18[/C][C]0.008821[/C][C]0.1062[/C][C]0.45778[/C][/ROW]
[ROW][C]19[/C][C]0.05363[/C][C]0.6458[/C][C]0.259717[/C][/ROW]
[ROW][C]20[/C][C]-0.087908[/C][C]-1.0586[/C][C]0.145782[/C][/ROW]
[ROW][C]21[/C][C]-0.00946[/C][C]-0.1139[/C][C]0.454734[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=151029&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=151029&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	0.340803	4.1038	3.4e-05
2	0.040428	0.4868	0.31356
3	0.006778	0.0816	0.467531
4	-0.08385	-1.0097	0.157164
5	-0.108858	-1.3108	0.095994
6	-0.225969	-2.721	0.003653
7	0.032406	0.3902	0.348472
8	0.04955	0.5967	0.275832
9	0.077084	0.9282	0.177421
10	-0.001956	-0.0235	0.490622
11	0.225401	2.7142	0.003725
12	0.778424	9.3735	0
13	-0.397798	-4.7901	2e-06
14	-0.264749	-3.188	0.000878
15	0.027894	0.3359	0.36872
16	0.011188	0.1347	0.446511
17	-0.066304	-0.7984	0.21297
18	0.008821	0.1062	0.45778
19	0.05363	0.6458	0.259717
20	-0.087908	-1.0586	0.145782
21	-0.00946	-0.1139	0.454734

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 = 0.0 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 0.0 ; par3 = 0 ; 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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code