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Author's title

Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Tue, 16 Aug 2011 16:11:55 -0400

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/Aug/16/t13135255505xs8ve1h9prf06x.htm/, Retrieved Mon, 13 May 2024 23:55:23 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=123906, Retrieved Mon, 13 May 2024 23:55:23 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

mattias debbaut

Estimated Impact

164

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

-       [(Partial) Autocorrelation Function] [tijdreeks B - aut...] [2011-08-16 20:11:55] [d41d8cd98f00b204e9800998ecf8427e] [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	2 seconds
R Server	'AstonUniversity' @ aston.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 & 2 seconds \tabularnewline
R Server & 'AstonUniversity' @ aston.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123906&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'AstonUniversity' @ aston.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123906&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123906&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	2 seconds
R Server	'AstonUniversity' @ aston.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.405358	-4.2126	2.6e-05
2	-0.041274	-0.4289	0.334415
3	0.37679	3.9157	7.9e-05
4	-0.279674	-2.9065	0.002218
5	-0.215225	-2.2367	0.013681
6	0.254714	2.6471	0.004667
7	-0.212501	-2.2084	0.014666
8	-0.220791	-2.2945	0.011847
9	0.324776	3.3752	0.000513
10	-0.034898	-0.3627	0.358781
11	-0.343344	-3.5681	0.000269
12	0.830492	8.6307	0
13	-0.399276	-4.1494	3.3e-05
14	-0.015546	-0.1616	0.435976
15	0.352144	3.6596	0.000196
16	-0.31446	-3.268	0.000726
17	-0.14497	-1.5066	0.067419
18	0.205942	2.1402	0.017294
19	-0.198609	-2.064	0.020707
20	-0.132993	-1.3821	0.084896

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.405358 & -4.2126 & 2.6e-05 \tabularnewline
2 & -0.041274 & -0.4289 & 0.334415 \tabularnewline
3 & 0.37679 & 3.9157 & 7.9e-05 \tabularnewline
4 & -0.279674 & -2.9065 & 0.002218 \tabularnewline
5 & -0.215225 & -2.2367 & 0.013681 \tabularnewline
6 & 0.254714 & 2.6471 & 0.004667 \tabularnewline
7 & -0.212501 & -2.2084 & 0.014666 \tabularnewline
8 & -0.220791 & -2.2945 & 0.011847 \tabularnewline
9 & 0.324776 & 3.3752 & 0.000513 \tabularnewline
10 & -0.034898 & -0.3627 & 0.358781 \tabularnewline
11 & -0.343344 & -3.5681 & 0.000269 \tabularnewline
12 & 0.830492 & 8.6307 & 0 \tabularnewline
13 & -0.399276 & -4.1494 & 3.3e-05 \tabularnewline
14 & -0.015546 & -0.1616 & 0.435976 \tabularnewline
15 & 0.352144 & 3.6596 & 0.000196 \tabularnewline
16 & -0.31446 & -3.268 & 0.000726 \tabularnewline
17 & -0.14497 & -1.5066 & 0.067419 \tabularnewline
18 & 0.205942 & 2.1402 & 0.017294 \tabularnewline
19 & -0.198609 & -2.064 & 0.020707 \tabularnewline
20 & -0.132993 & -1.3821 & 0.084896 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123906&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]-0.405358[/C][C]-4.2126[/C][C]2.6e-05[/C][/ROW]
[ROW][C]2[/C][C]-0.041274[/C][C]-0.4289[/C][C]0.334415[/C][/ROW]
[ROW][C]3[/C][C]0.37679[/C][C]3.9157[/C][C]7.9e-05[/C][/ROW]
[ROW][C]4[/C][C]-0.279674[/C][C]-2.9065[/C][C]0.002218[/C][/ROW]
[ROW][C]5[/C][C]-0.215225[/C][C]-2.2367[/C][C]0.013681[/C][/ROW]
[ROW][C]6[/C][C]0.254714[/C][C]2.6471[/C][C]0.004667[/C][/ROW]
[ROW][C]7[/C][C]-0.212501[/C][C]-2.2084[/C][C]0.014666[/C][/ROW]
[ROW][C]8[/C][C]-0.220791[/C][C]-2.2945[/C][C]0.011847[/C][/ROW]
[ROW][C]9[/C][C]0.324776[/C][C]3.3752[/C][C]0.000513[/C][/ROW]
[ROW][C]10[/C][C]-0.034898[/C][C]-0.3627[/C][C]0.358781[/C][/ROW]
[ROW][C]11[/C][C]-0.343344[/C][C]-3.5681[/C][C]0.000269[/C][/ROW]
[ROW][C]12[/C][C]0.830492[/C][C]8.6307[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]-0.399276[/C][C]-4.1494[/C][C]3.3e-05[/C][/ROW]
[ROW][C]14[/C][C]-0.015546[/C][C]-0.1616[/C][C]0.435976[/C][/ROW]
[ROW][C]15[/C][C]0.352144[/C][C]3.6596[/C][C]0.000196[/C][/ROW]
[ROW][C]16[/C][C]-0.31446[/C][C]-3.268[/C][C]0.000726[/C][/ROW]
[ROW][C]17[/C][C]-0.14497[/C][C]-1.5066[/C][C]0.067419[/C][/ROW]
[ROW][C]18[/C][C]0.205942[/C][C]2.1402[/C][C]0.017294[/C][/ROW]
[ROW][C]19[/C][C]-0.198609[/C][C]-2.064[/C][C]0.020707[/C][/ROW]
[ROW][C]20[/C][C]-0.132993[/C][C]-1.3821[/C][C]0.084896[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123906&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123906&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	-0.405358	-4.2126	2.6e-05
2	-0.041274	-0.4289	0.334415
3	0.37679	3.9157	7.9e-05
4	-0.279674	-2.9065	0.002218
5	-0.215225	-2.2367	0.013681
6	0.254714	2.6471	0.004667
7	-0.212501	-2.2084	0.014666
8	-0.220791	-2.2945	0.011847
9	0.324776	3.3752	0.000513
10	-0.034898	-0.3627	0.358781
11	-0.343344	-3.5681	0.000269
12	0.830492	8.6307	0
13	-0.399276	-4.1494	3.3e-05
14	-0.015546	-0.1616	0.435976
15	0.352144	3.6596	0.000196
16	-0.31446	-3.268	0.000726
17	-0.14497	-1.5066	0.067419
18	0.205942	2.1402	0.017294
19	-0.198609	-2.064	0.020707
20	-0.132993	-1.3821	0.084896

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.405358	-4.2126	2.6e-05
2	-0.246013	-2.5566	0.005979
3	0.326351	3.3915	0.000486
4	0.013291	0.1381	0.445202
5	-0.407736	-4.2373	2.4e-05
6	-0.180864	-1.8796	0.031429
7	-0.030911	-0.3212	0.374325
8	-0.235766	-2.4502	0.007943
9	-0.063048	-0.6552	0.256862
10	0.198792	2.0659	0.020615
11	-0.320728	-3.3331	0.000588
12	0.6687	6.9493	0
13	0.033964	0.353	0.3624
14	0.084584	0.879	0.190669
15	-0.085996	-0.8937	0.186736
16	-0.050161	-0.5213	0.301617
17	0.110056	1.1437	0.12763
18	-0.105444	-1.0958	0.1378
19	0.035112	0.3649	0.357954
20	0.087747	0.9119	0.181929

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.405358 & -4.2126 & 2.6e-05 \tabularnewline
2 & -0.246013 & -2.5566 & 0.005979 \tabularnewline
3 & 0.326351 & 3.3915 & 0.000486 \tabularnewline
4 & 0.013291 & 0.1381 & 0.445202 \tabularnewline
5 & -0.407736 & -4.2373 & 2.4e-05 \tabularnewline
6 & -0.180864 & -1.8796 & 0.031429 \tabularnewline
7 & -0.030911 & -0.3212 & 0.374325 \tabularnewline
8 & -0.235766 & -2.4502 & 0.007943 \tabularnewline
9 & -0.063048 & -0.6552 & 0.256862 \tabularnewline
10 & 0.198792 & 2.0659 & 0.020615 \tabularnewline
11 & -0.320728 & -3.3331 & 0.000588 \tabularnewline
12 & 0.6687 & 6.9493 & 0 \tabularnewline
13 & 0.033964 & 0.353 & 0.3624 \tabularnewline
14 & 0.084584 & 0.879 & 0.190669 \tabularnewline
15 & -0.085996 & -0.8937 & 0.186736 \tabularnewline
16 & -0.050161 & -0.5213 & 0.301617 \tabularnewline
17 & 0.110056 & 1.1437 & 0.12763 \tabularnewline
18 & -0.105444 & -1.0958 & 0.1378 \tabularnewline
19 & 0.035112 & 0.3649 & 0.357954 \tabularnewline
20 & 0.087747 & 0.9119 & 0.181929 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123906&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]-0.405358[/C][C]-4.2126[/C][C]2.6e-05[/C][/ROW]
[ROW][C]2[/C][C]-0.246013[/C][C]-2.5566[/C][C]0.005979[/C][/ROW]
[ROW][C]3[/C][C]0.326351[/C][C]3.3915[/C][C]0.000486[/C][/ROW]
[ROW][C]4[/C][C]0.013291[/C][C]0.1381[/C][C]0.445202[/C][/ROW]
[ROW][C]5[/C][C]-0.407736[/C][C]-4.2373[/C][C]2.4e-05[/C][/ROW]
[ROW][C]6[/C][C]-0.180864[/C][C]-1.8796[/C][C]0.031429[/C][/ROW]
[ROW][C]7[/C][C]-0.030911[/C][C]-0.3212[/C][C]0.374325[/C][/ROW]
[ROW][C]8[/C][C]-0.235766[/C][C]-2.4502[/C][C]0.007943[/C][/ROW]
[ROW][C]9[/C][C]-0.063048[/C][C]-0.6552[/C][C]0.256862[/C][/ROW]
[ROW][C]10[/C][C]0.198792[/C][C]2.0659[/C][C]0.020615[/C][/ROW]
[ROW][C]11[/C][C]-0.320728[/C][C]-3.3331[/C][C]0.000588[/C][/ROW]
[ROW][C]12[/C][C]0.6687[/C][C]6.9493[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.033964[/C][C]0.353[/C][C]0.3624[/C][/ROW]
[ROW][C]14[/C][C]0.084584[/C][C]0.879[/C][C]0.190669[/C][/ROW]
[ROW][C]15[/C][C]-0.085996[/C][C]-0.8937[/C][C]0.186736[/C][/ROW]
[ROW][C]16[/C][C]-0.050161[/C][C]-0.5213[/C][C]0.301617[/C][/ROW]
[ROW][C]17[/C][C]0.110056[/C][C]1.1437[/C][C]0.12763[/C][/ROW]
[ROW][C]18[/C][C]-0.105444[/C][C]-1.0958[/C][C]0.1378[/C][/ROW]
[ROW][C]19[/C][C]0.035112[/C][C]0.3649[/C][C]0.357954[/C][/ROW]
[ROW][C]20[/C][C]0.087747[/C][C]0.9119[/C][C]0.181929[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123906&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123906&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	-0.405358	-4.2126	2.6e-05
2	-0.246013	-2.5566	0.005979
3	0.326351	3.3915	0.000486
4	0.013291	0.1381	0.445202
5	-0.407736	-4.2373	2.4e-05
6	-0.180864	-1.8796	0.031429
7	-0.030911	-0.3212	0.374325
8	-0.235766	-2.4502	0.007943
9	-0.063048	-0.6552	0.256862
10	0.198792	2.0659	0.020615
11	-0.320728	-3.3331	0.000588
12	0.6687	6.9493	0
13	0.033964	0.353	0.3624
14	0.084584	0.879	0.190669
15	-0.085996	-0.8937	0.186736
16	-0.050161	-0.5213	0.301617
17	0.110056	1.1437	0.12763
18	-0.105444	-1.0958	0.1378
19	0.035112	0.3649	0.357954
20	0.087747	0.9119	0.181929

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 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; 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