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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, 27 Nov 2009 09:22:27 -0700

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/2009/Nov/27/t125933913548yrnospaac1ssx.htm/, Retrieved Sun, 28 Apr 2024 20:49:01 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=60957, Retrieved Sun, 28 Apr 2024 20:49:01 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

144

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]
-   PD        [(Partial) Autocorrelation Function] [W8] [2009-11-25 18:19:32] [315ba876df544ad397193b5931d5f354]
-    D            [(Partial) Autocorrelation Function] [ws8 1.1] [2009-11-27 16:22:27] [95523ebdb89b97dbf680ec91e0b4bca2] [Current]
-   P               [(Partial) Autocorrelation Function] [ws8.2] [2009-11-27 16:33:59] [95cead3ebb75668735f848316249436a] 
-   P                 [(Partial) Autocorrelation Function] [ws8 model 1] [2009-11-27 17:43:46] [95cead3ebb75668735f848316249436a] 
-   P                   [(Partial) Autocorrelation Function] [workshop 8] [2009-11-28 14:47:07] [f1a50df816abcbb519e7637ff6b72fa0] 
-                       [(Partial) Autocorrelation Function] [workshop 8] [2009-11-28 14:50:29] [f1a50df816abcbb519e7637ff6b72fa0] 
-   P                   [(Partial) Autocorrelation Function] [] [2009-11-29 13:45:28] [cf890101a20378422561610e0d41fd9c] 
-   P                   [(Partial) Autocorrelation Function] [] [2009-11-29 13:48:02] [cf890101a20378422561610e0d41fd9c] 
-   P                   [(Partial) Autocorrelation Function] [] [2009-11-29 13:52:09] [cf890101a20378422561610e0d41fd9c] 
-   P                   [(Partial) Autocorrelation Function] [workshop 8] [2009-11-30 20:48:26] [309ee52d0058ff0a6f7eec15e07b2d9f] 
-   P                   [(Partial) Autocorrelation Function] [workshop 8 review] [2009-11-30 20:52:45] [309ee52d0058ff0a6f7eec15e07b2d9f] 
-   P                 [(Partial) Autocorrelation Function] [ws8 model1] [2009-11-27 17:46:01] [95cead3ebb75668735f848316249436a] 
-                     [(Partial) Autocorrelation Function] [workshop 8 review] [2009-11-30 20:36:49] [309ee52d0058ff0a6f7eec15e07b2d9f] 
-   P                 [(Partial) Autocorrelation Function] [Workshop 8: Review] [2009-12-03 15:18:52] [3cb427d596a5d2eb77fa64560dc91319] 
-   P                 [(Partial) Autocorrelation Function] [Workshop 8: Review] [2009-12-03 15:24:08] [3cb427d596a5d2eb77fa64560dc91319] 
-   P                 [(Partial) Autocorrelation Function] [Workshop 8: Review] [2009-12-03 15:27:51] [3cb427d596a5d2eb77fa64560dc91319] 
-    D                [(Partial) Autocorrelation Function] [d=D=0] [2009-12-13 14:06:46] [95cead3ebb75668735f848316249436a] 
-   PD                  [(Partial) Autocorrelation Function] [deel 2 D=d=0] [2009-12-13 17:00:23] [95cead3ebb75668735f848316249436a] 
-                       [(Partial) Autocorrelation Function] [deel1 D=d=0] [2009-12-15 19:50:39] [95cead3ebb75668735f848316249436a] 
-   PD                [(Partial) Autocorrelation Function] [D=1 d=0] [2009-12-13 14:12:45] [95cead3ebb75668735f848316249436a] 
-   PD                  [(Partial) Autocorrelation Function] [deel2 D=0, d=1] [2009-12-13 17:08:02] [95cead3ebb75668735f848316249436a] 
-   P                     [(Partial) Autocorrelation Function] [deel2 D=0 d=2] [2009-12-13 17:09:48] [95cead3ebb75668735f848316249436a] 
-   P                       [(Partial) Autocorrelation Function] [deel2 D=1, d=1] [2009-12-13 17:47:20] [95cead3ebb75668735f848316249436a] 
-   P                     [(Partial) Autocorrelation Function] [deel 2 D=1 d=2] [2009-12-13 17:13:07] [95cead3ebb75668735f848316249436a] 
-   PD                [(Partial) Autocorrelation Function] [D=d=1] [2009-12-13 14:25:43] [95cead3ebb75668735f848316249436a] 
-   PD                [(Partial) Autocorrelation Function] [D=d=1] [2009-12-13 15:09:11] [95cead3ebb75668735f848316249436a] 
-   P                   [(Partial) Autocorrelation Function] [D=2 d=1] [2009-12-13 15:52:04] [95cead3ebb75668735f848316249436a] 
-   P               [(Partial) Autocorrelation Function] [ws8.3] [2009-11-27 16:37:20] [95cead3ebb75668735f848316249436a] 
-   P               [(Partial) Autocorrelation Function] [] [2009-11-27 16:40:29] [95cead3ebb75668735f848316249436a] 

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Dataseries X:

Download CSV

Histogram

Boxplots

2.05
2.11
2.09
2.05
2.08
2.06
2.06
2.08
2.07
2.06
2.07
2.06
2.09
2.07
2.09
2.28
2.33
2.35
2.52
2.63
2.58
2.70
2.81
2.97
3.04
3.28
3.33
3.50
3.56
3.57
3.69
3.82
3.79
3.96
4.06
4.05
4.03
3.94
4.02
3.88
4.02
4.03
4.09
3.99
4.01
4.01
4.19
4.30
4.27
3.82
3.15
2.49
1.81
1.26
1.06
0.84
0.78
0.70
0.36
0.35

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' @ 72.249.127.135

\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' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=60957&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' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=60957&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=60957&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' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.936824	7.2566	0
2	0.848005	6.5686	0
3	0.748609	5.7987	0
4	0.636274	4.9286	3e-06
5	0.516723	4.0025	8.7e-05
6	0.398529	3.087	0.00153
7	0.2807	2.1743	0.016819
8	0.176793	1.3694	0.087984
9	0.091168	0.7062	0.241403
10	0.025571	0.1981	0.42183
11	-0.017439	-0.1351	0.446499
12	-0.044787	-0.3469	0.364934
13	-0.070718	-0.5478	0.292938
14	-0.102283	-0.7923	0.215658
15	-0.14086	-1.0911	0.139795
16	-0.179391	-1.3896	0.084899
17	-0.217527	-1.685	0.048596

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.936824 & 7.2566 & 0 \tabularnewline
2 & 0.848005 & 6.5686 & 0 \tabularnewline
3 & 0.748609 & 5.7987 & 0 \tabularnewline
4 & 0.636274 & 4.9286 & 3e-06 \tabularnewline
5 & 0.516723 & 4.0025 & 8.7e-05 \tabularnewline
6 & 0.398529 & 3.087 & 0.00153 \tabularnewline
7 & 0.2807 & 2.1743 & 0.016819 \tabularnewline
8 & 0.176793 & 1.3694 & 0.087984 \tabularnewline
9 & 0.091168 & 0.7062 & 0.241403 \tabularnewline
10 & 0.025571 & 0.1981 & 0.42183 \tabularnewline
11 & -0.017439 & -0.1351 & 0.446499 \tabularnewline
12 & -0.044787 & -0.3469 & 0.364934 \tabularnewline
13 & -0.070718 & -0.5478 & 0.292938 \tabularnewline
14 & -0.102283 & -0.7923 & 0.215658 \tabularnewline
15 & -0.14086 & -1.0911 & 0.139795 \tabularnewline
16 & -0.179391 & -1.3896 & 0.084899 \tabularnewline
17 & -0.217527 & -1.685 & 0.048596 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=60957&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]0.936824[/C][C]7.2566[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.848005[/C][C]6.5686[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.748609[/C][C]5.7987[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.636274[/C][C]4.9286[/C][C]3e-06[/C][/ROW]
[ROW][C]5[/C][C]0.516723[/C][C]4.0025[/C][C]8.7e-05[/C][/ROW]
[ROW][C]6[/C][C]0.398529[/C][C]3.087[/C][C]0.00153[/C][/ROW]
[ROW][C]7[/C][C]0.2807[/C][C]2.1743[/C][C]0.016819[/C][/ROW]
[ROW][C]8[/C][C]0.176793[/C][C]1.3694[/C][C]0.087984[/C][/ROW]
[ROW][C]9[/C][C]0.091168[/C][C]0.7062[/C][C]0.241403[/C][/ROW]
[ROW][C]10[/C][C]0.025571[/C][C]0.1981[/C][C]0.42183[/C][/ROW]
[ROW][C]11[/C][C]-0.017439[/C][C]-0.1351[/C][C]0.446499[/C][/ROW]
[ROW][C]12[/C][C]-0.044787[/C][C]-0.3469[/C][C]0.364934[/C][/ROW]
[ROW][C]13[/C][C]-0.070718[/C][C]-0.5478[/C][C]0.292938[/C][/ROW]
[ROW][C]14[/C][C]-0.102283[/C][C]-0.7923[/C][C]0.215658[/C][/ROW]
[ROW][C]15[/C][C]-0.14086[/C][C]-1.0911[/C][C]0.139795[/C][/ROW]
[ROW][C]16[/C][C]-0.179391[/C][C]-1.3896[/C][C]0.084899[/C][/ROW]
[ROW][C]17[/C][C]-0.217527[/C][C]-1.685[/C][C]0.048596[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=60957&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=60957&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	0.936824	7.2566	0
2	0.848005	6.5686	0
3	0.748609	5.7987	0
4	0.636274	4.9286	3e-06
5	0.516723	4.0025	8.7e-05
6	0.398529	3.087	0.00153
7	0.2807	2.1743	0.016819
8	0.176793	1.3694	0.087984
9	0.091168	0.7062	0.241403
10	0.025571	0.1981	0.42183
11	-0.017439	-0.1351	0.446499
12	-0.044787	-0.3469	0.364934
13	-0.070718	-0.5478	0.292938
14	-0.102283	-0.7923	0.215658
15	-0.14086	-1.0911	0.139795
16	-0.179391	-1.3896	0.084899
17	-0.217527	-1.685	0.048596

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.936824	7.2566	0
2	-0.242198	-1.8761	0.032757
3	-0.09841	-0.7623	0.22444
4	-0.145466	-1.1268	0.132163
5	-0.097164	-0.7526	0.227307
6	-0.045864	-0.3553	0.361819
7	-0.080316	-0.6221	0.268108
8	0.036	0.2789	0.390658
9	0.034773	0.2694	0.394291
10	0.046933	0.3635	0.358738
11	0.061739	0.4782	0.317113
12	-0.00653	-0.0506	0.479914
13	-0.107395	-0.8319	0.204387
14	-0.14495	-1.1228	0.133003
15	-0.133493	-1.034	0.152635
16	-0.04168	-0.3229	0.373964
17	-0.030064	-0.2329	0.408326

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.936824 & 7.2566 & 0 \tabularnewline
2 & -0.242198 & -1.8761 & 0.032757 \tabularnewline
3 & -0.09841 & -0.7623 & 0.22444 \tabularnewline
4 & -0.145466 & -1.1268 & 0.132163 \tabularnewline
5 & -0.097164 & -0.7526 & 0.227307 \tabularnewline
6 & -0.045864 & -0.3553 & 0.361819 \tabularnewline
7 & -0.080316 & -0.6221 & 0.268108 \tabularnewline
8 & 0.036 & 0.2789 & 0.390658 \tabularnewline
9 & 0.034773 & 0.2694 & 0.394291 \tabularnewline
10 & 0.046933 & 0.3635 & 0.358738 \tabularnewline
11 & 0.061739 & 0.4782 & 0.317113 \tabularnewline
12 & -0.00653 & -0.0506 & 0.479914 \tabularnewline
13 & -0.107395 & -0.8319 & 0.204387 \tabularnewline
14 & -0.14495 & -1.1228 & 0.133003 \tabularnewline
15 & -0.133493 & -1.034 & 0.152635 \tabularnewline
16 & -0.04168 & -0.3229 & 0.373964 \tabularnewline
17 & -0.030064 & -0.2329 & 0.408326 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=60957&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]0.936824[/C][C]7.2566[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.242198[/C][C]-1.8761[/C][C]0.032757[/C][/ROW]
[ROW][C]3[/C][C]-0.09841[/C][C]-0.7623[/C][C]0.22444[/C][/ROW]
[ROW][C]4[/C][C]-0.145466[/C][C]-1.1268[/C][C]0.132163[/C][/ROW]
[ROW][C]5[/C][C]-0.097164[/C][C]-0.7526[/C][C]0.227307[/C][/ROW]
[ROW][C]6[/C][C]-0.045864[/C][C]-0.3553[/C][C]0.361819[/C][/ROW]
[ROW][C]7[/C][C]-0.080316[/C][C]-0.6221[/C][C]0.268108[/C][/ROW]
[ROW][C]8[/C][C]0.036[/C][C]0.2789[/C][C]0.390658[/C][/ROW]
[ROW][C]9[/C][C]0.034773[/C][C]0.2694[/C][C]0.394291[/C][/ROW]
[ROW][C]10[/C][C]0.046933[/C][C]0.3635[/C][C]0.358738[/C][/ROW]
[ROW][C]11[/C][C]0.061739[/C][C]0.4782[/C][C]0.317113[/C][/ROW]
[ROW][C]12[/C][C]-0.00653[/C][C]-0.0506[/C][C]0.479914[/C][/ROW]
[ROW][C]13[/C][C]-0.107395[/C][C]-0.8319[/C][C]0.204387[/C][/ROW]
[ROW][C]14[/C][C]-0.14495[/C][C]-1.1228[/C][C]0.133003[/C][/ROW]
[ROW][C]15[/C][C]-0.133493[/C][C]-1.034[/C][C]0.152635[/C][/ROW]
[ROW][C]16[/C][C]-0.04168[/C][C]-0.3229[/C][C]0.373964[/C][/ROW]
[ROW][C]17[/C][C]-0.030064[/C][C]-0.2329[/C][C]0.408326[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=60957&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=60957&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	0.936824	7.2566	0
2	-0.242198	-1.8761	0.032757
3	-0.09841	-0.7623	0.22444
4	-0.145466	-1.1268	0.132163
5	-0.097164	-0.7526	0.227307
6	-0.045864	-0.3553	0.361819
7	-0.080316	-0.6221	0.268108
8	0.036	0.2789	0.390658
9	0.034773	0.2694	0.394291
10	0.046933	0.3635	0.358738
11	0.061739	0.4782	0.317113
12	-0.00653	-0.0506	0.479914
13	-0.107395	-0.8319	0.204387
14	-0.14495	-1.1228	0.133003
15	-0.133493	-1.034	0.152635
16	-0.04168	-0.3229	0.373964
17	-0.030064	-0.2329	0.408326

Figure 1

PNG link

Postscript link

PDF link

Figure 2

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 ;

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 (par2 == 0) {
x <- log(x)
} else {
x <- (x ^ par2 - 1) / par2
}
if (par3 > 0) x <- diff(x,lag=1,difference=par3)
if (par4 > 0) x <- diff(x,lag=par5,difference=par4)
bitmap(file='pic1.png')
racf <- acf(x, par1, main='Autocorrelation', xlab='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep=''))
dev.off()
bitmap(file='pic2.png')
rpacf <- pacf(x,par1,main='Partial Autocorrelation',xlab='lags',ylab='PACF')
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