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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

Fri, 24 Dec 2010 13:44:06 +0000

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/2010/Dec/24/t1293198107aoclltdq5tpikdu.htm/, Retrieved Tue, 30 Apr 2024 06:04:23 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=114951, Retrieved Tue, 30 Apr 2024 06:04:23 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

115

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

-     [Univariate Data Series] [] [2008-12-08 19:22:39] [d2d412c7f4d35ffbf5ee5ee89db327d4]
- RMP   [ARIMA Forecasting] [] [2010-12-14 14:23:29] [abe7df3fc544bbb0ed435b4e9982bc91]
- RMPD      [(Partial) Autocorrelation Function] [] [2010-12-24 13:44:06] [29eeba0e6ce2cd83aa315a4a7ff8c4aa] [Current]

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Dataseries X:

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Histogram

Boxplots

6.4
7.7
9.2
8.6
7.4
8.6
6.2
6
6.6
5.1
4.7
5
3.6
1.9
-0.1
-5.7
-5.6
-6.4
-7.7
-8
-11.9
-15.4
-15.5
-13.4
-10.9
-10.8
-7.3
-6.5
-5.1
-5.3
-6.8
-8.4
-8.4
-9.7
-8.8
-9.6
-11.5
-11
-14.9
-16.2
-14.4
-17.3
-15.7
-12.6
-9.4
-8.1
-5.4
-4.6
-4.9
-4
-3.1
-1.3
0
-0.4
3
0.4
1.2
0.6
-1.3
-3.2
-1.8
-3.6
-4.2
-6.9
-8
-7.5
-8.2
-7.6
-3.7
-1.7
-0.7
0.2
0.6
2.2
3.3
5.3
5.5
6.3
7.7
6.5
5.5
6.9
5.7
6.9
6.1
4.8
3.7
5.8
6.8
8.5
7.2
5
4.7
2.3
2.4
0.1
1.9
1.7
2
-1.9
0.5
-1.3
-3.3
-2.8
-8
-13.9
-21.9
-28.8
-27.6
-31.4
-31.8
-29.4
-27.6
-23.6
-22.8
-18.2
-17.8
-14.2
-8.8
-7.9
-7
-7
-3.6
-2.4
-4.9
-7.7
-6.5
-5.1
-3.4
-2.8
0.8

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	'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=114951&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=114951&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114951&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	'George Udny Yule' @ 72.249.76.132

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.348905	3.9781	5.7e-05
2	0.340908	3.887	8.1e-05
3	0.260048	2.965	0.001801
4	0.085721	0.9774	0.165102
5	0.093752	1.0689	0.14354
6	-0.018079	-0.2061	0.418504
7	-0.065412	-0.7458	0.228563
8	-0.038715	-0.4414	0.32982
9	-0.139513	-1.5907	0.057054
10	-0.124079	-1.4147	0.079771
11	-0.144273	-1.645	0.051196
12	-0.167587	-1.9108	0.029117
13	-0.189294	-2.1583	0.016371
14	-0.051903	-0.5918	0.277512
15	-0.006471	-0.0738	0.470648
16	-0.067196	-0.7661	0.222489
17	0.006913	0.0788	0.468649
18	-0.015063	-0.1717	0.431953
19	0.027231	0.3105	0.378346
20	-0.004223	-0.0482	0.480834
21	0.016066	0.1832	0.427472

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.348905 & 3.9781 & 5.7e-05 \tabularnewline
2 & 0.340908 & 3.887 & 8.1e-05 \tabularnewline
3 & 0.260048 & 2.965 & 0.001801 \tabularnewline
4 & 0.085721 & 0.9774 & 0.165102 \tabularnewline
5 & 0.093752 & 1.0689 & 0.14354 \tabularnewline
6 & -0.018079 & -0.2061 & 0.418504 \tabularnewline
7 & -0.065412 & -0.7458 & 0.228563 \tabularnewline
8 & -0.038715 & -0.4414 & 0.32982 \tabularnewline
9 & -0.139513 & -1.5907 & 0.057054 \tabularnewline
10 & -0.124079 & -1.4147 & 0.079771 \tabularnewline
11 & -0.144273 & -1.645 & 0.051196 \tabularnewline
12 & -0.167587 & -1.9108 & 0.029117 \tabularnewline
13 & -0.189294 & -2.1583 & 0.016371 \tabularnewline
14 & -0.051903 & -0.5918 & 0.277512 \tabularnewline
15 & -0.006471 & -0.0738 & 0.470648 \tabularnewline
16 & -0.067196 & -0.7661 & 0.222489 \tabularnewline
17 & 0.006913 & 0.0788 & 0.468649 \tabularnewline
18 & -0.015063 & -0.1717 & 0.431953 \tabularnewline
19 & 0.027231 & 0.3105 & 0.378346 \tabularnewline
20 & -0.004223 & -0.0482 & 0.480834 \tabularnewline
21 & 0.016066 & 0.1832 & 0.427472 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=114951&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]0.348905[/C][C]3.9781[/C][C]5.7e-05[/C][/ROW]
[ROW][C]2[/C][C]0.340908[/C][C]3.887[/C][C]8.1e-05[/C][/ROW]
[ROW][C]3[/C][C]0.260048[/C][C]2.965[/C][C]0.001801[/C][/ROW]
[ROW][C]4[/C][C]0.085721[/C][C]0.9774[/C][C]0.165102[/C][/ROW]
[ROW][C]5[/C][C]0.093752[/C][C]1.0689[/C][C]0.14354[/C][/ROW]
[ROW][C]6[/C][C]-0.018079[/C][C]-0.2061[/C][C]0.418504[/C][/ROW]
[ROW][C]7[/C][C]-0.065412[/C][C]-0.7458[/C][C]0.228563[/C][/ROW]
[ROW][C]8[/C][C]-0.038715[/C][C]-0.4414[/C][C]0.32982[/C][/ROW]
[ROW][C]9[/C][C]-0.139513[/C][C]-1.5907[/C][C]0.057054[/C][/ROW]
[ROW][C]10[/C][C]-0.124079[/C][C]-1.4147[/C][C]0.079771[/C][/ROW]
[ROW][C]11[/C][C]-0.144273[/C][C]-1.645[/C][C]0.051196[/C][/ROW]
[ROW][C]12[/C][C]-0.167587[/C][C]-1.9108[/C][C]0.029117[/C][/ROW]
[ROW][C]13[/C][C]-0.189294[/C][C]-2.1583[/C][C]0.016371[/C][/ROW]
[ROW][C]14[/C][C]-0.051903[/C][C]-0.5918[/C][C]0.277512[/C][/ROW]
[ROW][C]15[/C][C]-0.006471[/C][C]-0.0738[/C][C]0.470648[/C][/ROW]
[ROW][C]16[/C][C]-0.067196[/C][C]-0.7661[/C][C]0.222489[/C][/ROW]
[ROW][C]17[/C][C]0.006913[/C][C]0.0788[/C][C]0.468649[/C][/ROW]
[ROW][C]18[/C][C]-0.015063[/C][C]-0.1717[/C][C]0.431953[/C][/ROW]
[ROW][C]19[/C][C]0.027231[/C][C]0.3105[/C][C]0.378346[/C][/ROW]
[ROW][C]20[/C][C]-0.004223[/C][C]-0.0482[/C][C]0.480834[/C][/ROW]
[ROW][C]21[/C][C]0.016066[/C][C]0.1832[/C][C]0.427472[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=114951&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114951&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	0.348905	3.9781	5.7e-05
2	0.340908	3.887	8.1e-05
3	0.260048	2.965	0.001801
4	0.085721	0.9774	0.165102
5	0.093752	1.0689	0.14354
6	-0.018079	-0.2061	0.418504
7	-0.065412	-0.7458	0.228563
8	-0.038715	-0.4414	0.32982
9	-0.139513	-1.5907	0.057054
10	-0.124079	-1.4147	0.079771
11	-0.144273	-1.645	0.051196
12	-0.167587	-1.9108	0.029117
13	-0.189294	-2.1583	0.016371
14	-0.051903	-0.5918	0.277512
15	-0.006471	-0.0738	0.470648
16	-0.067196	-0.7661	0.222489
17	0.006913	0.0788	0.468649
18	-0.015063	-0.1717	0.431953
19	0.027231	0.3105	0.378346
20	-0.004223	-0.0482	0.480834
21	0.016066	0.1832	0.427472

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.348905	3.9781	5.7e-05
2	0.249553	2.8453	0.002578
3	0.101651	1.159	0.124291
4	-0.107035	-1.2204	0.112264
5	0.003019	0.0344	0.486297
6	-0.073914	-0.8428	0.200458
7	-0.066258	-0.7555	0.225671
8	0.011701	0.1334	0.447037
9	-0.090809	-1.0354	0.151207
10	-0.050816	-0.5794	0.281663
11	-0.051312	-0.585	0.279765
12	-0.052777	-0.6017	0.274196
13	-0.098105	-1.1186	0.132694
14	0.118011	1.3455	0.090398
15	0.095719	1.0914	0.138566
16	-0.095914	-1.0936	0.138078
17	-0.011135	-0.127	0.449583
18	-0.016367	-0.1866	0.426129
19	0.023999	0.2736	0.392403
20	-0.054008	-0.6158	0.269556
21	0.025868	0.2949	0.384254

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.348905 & 3.9781 & 5.7e-05 \tabularnewline
2 & 0.249553 & 2.8453 & 0.002578 \tabularnewline
3 & 0.101651 & 1.159 & 0.124291 \tabularnewline
4 & -0.107035 & -1.2204 & 0.112264 \tabularnewline
5 & 0.003019 & 0.0344 & 0.486297 \tabularnewline
6 & -0.073914 & -0.8428 & 0.200458 \tabularnewline
7 & -0.066258 & -0.7555 & 0.225671 \tabularnewline
8 & 0.011701 & 0.1334 & 0.447037 \tabularnewline
9 & -0.090809 & -1.0354 & 0.151207 \tabularnewline
10 & -0.050816 & -0.5794 & 0.281663 \tabularnewline
11 & -0.051312 & -0.585 & 0.279765 \tabularnewline
12 & -0.052777 & -0.6017 & 0.274196 \tabularnewline
13 & -0.098105 & -1.1186 & 0.132694 \tabularnewline
14 & 0.118011 & 1.3455 & 0.090398 \tabularnewline
15 & 0.095719 & 1.0914 & 0.138566 \tabularnewline
16 & -0.095914 & -1.0936 & 0.138078 \tabularnewline
17 & -0.011135 & -0.127 & 0.449583 \tabularnewline
18 & -0.016367 & -0.1866 & 0.426129 \tabularnewline
19 & 0.023999 & 0.2736 & 0.392403 \tabularnewline
20 & -0.054008 & -0.6158 & 0.269556 \tabularnewline
21 & 0.025868 & 0.2949 & 0.384254 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=114951&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]0.348905[/C][C]3.9781[/C][C]5.7e-05[/C][/ROW]
[ROW][C]2[/C][C]0.249553[/C][C]2.8453[/C][C]0.002578[/C][/ROW]
[ROW][C]3[/C][C]0.101651[/C][C]1.159[/C][C]0.124291[/C][/ROW]
[ROW][C]4[/C][C]-0.107035[/C][C]-1.2204[/C][C]0.112264[/C][/ROW]
[ROW][C]5[/C][C]0.003019[/C][C]0.0344[/C][C]0.486297[/C][/ROW]
[ROW][C]6[/C][C]-0.073914[/C][C]-0.8428[/C][C]0.200458[/C][/ROW]
[ROW][C]7[/C][C]-0.066258[/C][C]-0.7555[/C][C]0.225671[/C][/ROW]
[ROW][C]8[/C][C]0.011701[/C][C]0.1334[/C][C]0.447037[/C][/ROW]
[ROW][C]9[/C][C]-0.090809[/C][C]-1.0354[/C][C]0.151207[/C][/ROW]
[ROW][C]10[/C][C]-0.050816[/C][C]-0.5794[/C][C]0.281663[/C][/ROW]
[ROW][C]11[/C][C]-0.051312[/C][C]-0.585[/C][C]0.279765[/C][/ROW]
[ROW][C]12[/C][C]-0.052777[/C][C]-0.6017[/C][C]0.274196[/C][/ROW]
[ROW][C]13[/C][C]-0.098105[/C][C]-1.1186[/C][C]0.132694[/C][/ROW]
[ROW][C]14[/C][C]0.118011[/C][C]1.3455[/C][C]0.090398[/C][/ROW]
[ROW][C]15[/C][C]0.095719[/C][C]1.0914[/C][C]0.138566[/C][/ROW]
[ROW][C]16[/C][C]-0.095914[/C][C]-1.0936[/C][C]0.138078[/C][/ROW]
[ROW][C]17[/C][C]-0.011135[/C][C]-0.127[/C][C]0.449583[/C][/ROW]
[ROW][C]18[/C][C]-0.016367[/C][C]-0.1866[/C][C]0.426129[/C][/ROW]
[ROW][C]19[/C][C]0.023999[/C][C]0.2736[/C][C]0.392403[/C][/ROW]
[ROW][C]20[/C][C]-0.054008[/C][C]-0.6158[/C][C]0.269556[/C][/ROW]
[ROW][C]21[/C][C]0.025868[/C][C]0.2949[/C][C]0.384254[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=114951&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114951&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	0.348905	3.9781	5.7e-05
2	0.249553	2.8453	0.002578
3	0.101651	1.159	0.124291
4	-0.107035	-1.2204	0.112264
5	0.003019	0.0344	0.486297
6	-0.073914	-0.8428	0.200458
7	-0.066258	-0.7555	0.225671
8	0.011701	0.1334	0.447037
9	-0.090809	-1.0354	0.151207
10	-0.050816	-0.5794	0.281663
11	-0.051312	-0.585	0.279765
12	-0.052777	-0.6017	0.274196
13	-0.098105	-1.1186	0.132694
14	0.118011	1.3455	0.090398
15	0.095719	1.0914	0.138566
16	-0.095914	-1.0936	0.138078
17	-0.011135	-0.127	0.449583
18	-0.016367	-0.1866	0.426129
19	0.023999	0.2736	0.392403
20	-0.054008	-0.6158	0.269556
21	0.025868	0.2949	0.384254

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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code