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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, 19 Dec 2011 10:25:42 -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/19/t1324308400vimc18kq8dleto9.htm/, Retrieved Fri, 31 May 2024 03:53:46 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=157444, Retrieved Fri, 31 May 2024 03:53:46 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

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

-       [(Partial) Autocorrelation Function] [Paper ACF] [2011-12-19 15:25:42] [3627de22d386f4cb93d383ef7c1ade7f] [Current]

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Dataseries X:

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Histogram

Boxplots

3.7
3
2.7
2.5
2.2
2.9
3.1
3
2.8
2.5
1.9
1.9
1.8
2
2.6
2.5
2.5
1.6
1.4
0.8
1.1
1.3
1.2
1.3
1.1
1.3
1.2
1.6
1.7
1.5
0.9
1.5
1.4
1.6
1.7
1.4
1.8
1.7
1.4
1.2
1
1.7
2.4
2
2.1
2
1.8
2.7
2.3
1.9
2
2.3
2.8
2.4
2.3
2.7
2.7
2.9
3
2.2
2.3
2.8
2.8
2.8
2.2
2.6
2.8
2.5
2.4
2.3
1.9
1.7
2
2.1
1.7
1.8
1.8
1.8
1.3
1.3
1.3
1.2
1.4
2.2
2.9
3.1
3.5
3.6
4.4
4.1
5.1
5.8
5.9
5.4
5.5
4.8
3.2
2.7
2.1
1.9
0.6
0.7
-0.2
-1
-1.7
-0.7
-1
-0.9
0
0.3
0.8
0.8
1.9
2.1
2.5
2.7
2.4
2.4
2.9
3.1
3
3.4
3.7
3.5
3.5
3.3
3.1
3.4
4
3.4
3.4
3.4

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	'Gertrude Mary Cox' @ cox.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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=157444&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=157444&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=157444&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	'Gertrude Mary Cox' @ cox.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.927285	10.6537	0
2	0.840304	9.6544	0
3	0.738035	8.4794	0
4	0.61652	7.0833	0
5	0.48354	5.5555	0
6	0.345292	3.9671	5.9e-05
7	0.199867	2.2963	0.011617
8	0.041472	0.4765	0.317261
9	-0.106918	-1.2284	0.110743
10	-0.2431	-2.793	0.003
11	-0.357303	-4.1051	3.5e-05
12	-0.467717	-5.3737	0
13	-0.509525	-5.854	0
14	-0.530484	-6.0948	0
15	-0.53698	-6.1694	0
16	-0.533225	-6.1263	0
17	-0.514898	-5.9157	0
18	-0.465827	-5.3519	0
19	-0.407732	-4.6845	3e-06
20	-0.339482	-3.9004	7.6e-05
21	-0.270381	-3.1064	0.001159

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.927285 & 10.6537 & 0 \tabularnewline
2 & 0.840304 & 9.6544 & 0 \tabularnewline
3 & 0.738035 & 8.4794 & 0 \tabularnewline
4 & 0.61652 & 7.0833 & 0 \tabularnewline
5 & 0.48354 & 5.5555 & 0 \tabularnewline
6 & 0.345292 & 3.9671 & 5.9e-05 \tabularnewline
7 & 0.199867 & 2.2963 & 0.011617 \tabularnewline
8 & 0.041472 & 0.4765 & 0.317261 \tabularnewline
9 & -0.106918 & -1.2284 & 0.110743 \tabularnewline
10 & -0.2431 & -2.793 & 0.003 \tabularnewline
11 & -0.357303 & -4.1051 & 3.5e-05 \tabularnewline
12 & -0.467717 & -5.3737 & 0 \tabularnewline
13 & -0.509525 & -5.854 & 0 \tabularnewline
14 & -0.530484 & -6.0948 & 0 \tabularnewline
15 & -0.53698 & -6.1694 & 0 \tabularnewline
16 & -0.533225 & -6.1263 & 0 \tabularnewline
17 & -0.514898 & -5.9157 & 0 \tabularnewline
18 & -0.465827 & -5.3519 & 0 \tabularnewline
19 & -0.407732 & -4.6845 & 3e-06 \tabularnewline
20 & -0.339482 & -3.9004 & 7.6e-05 \tabularnewline
21 & -0.270381 & -3.1064 & 0.001159 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=157444&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]0.927285[/C][C]10.6537[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.840304[/C][C]9.6544[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.738035[/C][C]8.4794[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.61652[/C][C]7.0833[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.48354[/C][C]5.5555[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.345292[/C][C]3.9671[/C][C]5.9e-05[/C][/ROW]
[ROW][C]7[/C][C]0.199867[/C][C]2.2963[/C][C]0.011617[/C][/ROW]
[ROW][C]8[/C][C]0.041472[/C][C]0.4765[/C][C]0.317261[/C][/ROW]
[ROW][C]9[/C][C]-0.106918[/C][C]-1.2284[/C][C]0.110743[/C][/ROW]
[ROW][C]10[/C][C]-0.2431[/C][C]-2.793[/C][C]0.003[/C][/ROW]
[ROW][C]11[/C][C]-0.357303[/C][C]-4.1051[/C][C]3.5e-05[/C][/ROW]
[ROW][C]12[/C][C]-0.467717[/C][C]-5.3737[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]-0.509525[/C][C]-5.854[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]-0.530484[/C][C]-6.0948[/C][C]0[/C][/ROW]
[ROW][C]15[/C][C]-0.53698[/C][C]-6.1694[/C][C]0[/C][/ROW]
[ROW][C]16[/C][C]-0.533225[/C][C]-6.1263[/C][C]0[/C][/ROW]
[ROW][C]17[/C][C]-0.514898[/C][C]-5.9157[/C][C]0[/C][/ROW]
[ROW][C]18[/C][C]-0.465827[/C][C]-5.3519[/C][C]0[/C][/ROW]
[ROW][C]19[/C][C]-0.407732[/C][C]-4.6845[/C][C]3e-06[/C][/ROW]
[ROW][C]20[/C][C]-0.339482[/C][C]-3.9004[/C][C]7.6e-05[/C][/ROW]
[ROW][C]21[/C][C]-0.270381[/C][C]-3.1064[/C][C]0.001159[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=157444&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=157444&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	0.927285	10.6537	0
2	0.840304	9.6544	0
3	0.738035	8.4794	0
4	0.61652	7.0833	0
5	0.48354	5.5555	0
6	0.345292	3.9671	5.9e-05
7	0.199867	2.2963	0.011617
8	0.041472	0.4765	0.317261
9	-0.106918	-1.2284	0.110743
10	-0.2431	-2.793	0.003
11	-0.357303	-4.1051	3.5e-05
12	-0.467717	-5.3737	0
13	-0.509525	-5.854	0
14	-0.530484	-6.0948	0
15	-0.53698	-6.1694	0
16	-0.533225	-6.1263	0
17	-0.514898	-5.9157	0
18	-0.465827	-5.3519	0
19	-0.407732	-4.6845	3e-06
20	-0.339482	-3.9004	7.6e-05
21	-0.270381	-3.1064	0.001159

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.927285	10.6537	0
2	-0.139521	-1.603	0.055665
3	-0.149216	-1.7144	0.044405
4	-0.184981	-2.1253	0.017713
5	-0.138928	-1.5962	0.056422
6	-0.107093	-1.2304	0.110366
7	-0.139513	-1.6029	0.055675
8	-0.215338	-2.474	0.007314
9	-0.071778	-0.8247	0.205524
10	-0.064874	-0.7453	0.228693
11	0.00647	0.0743	0.47043
12	-0.16831	-1.9337	0.027643
13	0.357468	4.107	3.5e-05
14	-0.004801	-0.0552	0.478049
15	-0.028913	-0.3322	0.37014
16	-0.162767	-1.87	0.031846
17	-0.0642	-0.7376	0.231032
18	0.103824	1.1928	0.117534
19	-0.057826	-0.6644	0.253805
20	-0.136697	-1.5705	0.059344
21	-0.073249	-0.8416	0.200778

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.927285 & 10.6537 & 0 \tabularnewline
2 & -0.139521 & -1.603 & 0.055665 \tabularnewline
3 & -0.149216 & -1.7144 & 0.044405 \tabularnewline
4 & -0.184981 & -2.1253 & 0.017713 \tabularnewline
5 & -0.138928 & -1.5962 & 0.056422 \tabularnewline
6 & -0.107093 & -1.2304 & 0.110366 \tabularnewline
7 & -0.139513 & -1.6029 & 0.055675 \tabularnewline
8 & -0.215338 & -2.474 & 0.007314 \tabularnewline
9 & -0.071778 & -0.8247 & 0.205524 \tabularnewline
10 & -0.064874 & -0.7453 & 0.228693 \tabularnewline
11 & 0.00647 & 0.0743 & 0.47043 \tabularnewline
12 & -0.16831 & -1.9337 & 0.027643 \tabularnewline
13 & 0.357468 & 4.107 & 3.5e-05 \tabularnewline
14 & -0.004801 & -0.0552 & 0.478049 \tabularnewline
15 & -0.028913 & -0.3322 & 0.37014 \tabularnewline
16 & -0.162767 & -1.87 & 0.031846 \tabularnewline
17 & -0.0642 & -0.7376 & 0.231032 \tabularnewline
18 & 0.103824 & 1.1928 & 0.117534 \tabularnewline
19 & -0.057826 & -0.6644 & 0.253805 \tabularnewline
20 & -0.136697 & -1.5705 & 0.059344 \tabularnewline
21 & -0.073249 & -0.8416 & 0.200778 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=157444&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]0.927285[/C][C]10.6537[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.139521[/C][C]-1.603[/C][C]0.055665[/C][/ROW]
[ROW][C]3[/C][C]-0.149216[/C][C]-1.7144[/C][C]0.044405[/C][/ROW]
[ROW][C]4[/C][C]-0.184981[/C][C]-2.1253[/C][C]0.017713[/C][/ROW]
[ROW][C]5[/C][C]-0.138928[/C][C]-1.5962[/C][C]0.056422[/C][/ROW]
[ROW][C]6[/C][C]-0.107093[/C][C]-1.2304[/C][C]0.110366[/C][/ROW]
[ROW][C]7[/C][C]-0.139513[/C][C]-1.6029[/C][C]0.055675[/C][/ROW]
[ROW][C]8[/C][C]-0.215338[/C][C]-2.474[/C][C]0.007314[/C][/ROW]
[ROW][C]9[/C][C]-0.071778[/C][C]-0.8247[/C][C]0.205524[/C][/ROW]
[ROW][C]10[/C][C]-0.064874[/C][C]-0.7453[/C][C]0.228693[/C][/ROW]
[ROW][C]11[/C][C]0.00647[/C][C]0.0743[/C][C]0.47043[/C][/ROW]
[ROW][C]12[/C][C]-0.16831[/C][C]-1.9337[/C][C]0.027643[/C][/ROW]
[ROW][C]13[/C][C]0.357468[/C][C]4.107[/C][C]3.5e-05[/C][/ROW]
[ROW][C]14[/C][C]-0.004801[/C][C]-0.0552[/C][C]0.478049[/C][/ROW]
[ROW][C]15[/C][C]-0.028913[/C][C]-0.3322[/C][C]0.37014[/C][/ROW]
[ROW][C]16[/C][C]-0.162767[/C][C]-1.87[/C][C]0.031846[/C][/ROW]
[ROW][C]17[/C][C]-0.0642[/C][C]-0.7376[/C][C]0.231032[/C][/ROW]
[ROW][C]18[/C][C]0.103824[/C][C]1.1928[/C][C]0.117534[/C][/ROW]
[ROW][C]19[/C][C]-0.057826[/C][C]-0.6644[/C][C]0.253805[/C][/ROW]
[ROW][C]20[/C][C]-0.136697[/C][C]-1.5705[/C][C]0.059344[/C][/ROW]
[ROW][C]21[/C][C]-0.073249[/C][C]-0.8416[/C][C]0.200778[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=157444&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=157444&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	0.927285	10.6537	0
2	-0.139521	-1.603	0.055665
3	-0.149216	-1.7144	0.044405
4	-0.184981	-2.1253	0.017713
5	-0.138928	-1.5962	0.056422
6	-0.107093	-1.2304	0.110366
7	-0.139513	-1.6029	0.055675
8	-0.215338	-2.474	0.007314
9	-0.071778	-0.8247	0.205524
10	-0.064874	-0.7453	0.228693
11	0.00647	0.0743	0.47043
12	-0.16831	-1.9337	0.027643
13	0.357468	4.107	3.5e-05
14	-0.004801	-0.0552	0.478049
15	-0.028913	-0.3322	0.37014
16	-0.162767	-1.87	0.031846
17	-0.0642	-0.7376	0.231032
18	0.103824	1.1928	0.117534
19	-0.057826	-0.6644	0.253805
20	-0.136697	-1.5705	0.059344
21	-0.073249	-0.8416	0.200778

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