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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_autocorrelation.wasp
Title produced by software(Partial) Autocorrelation Function
Date of computationSat, 17 Dec 2011 10:48:24 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Dec/17/t13241369207ou5tl2mm4asm6d.htm/, Retrieved Wed, 11 Feb 2026 03:56:43 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=156409, Retrieved Wed, 11 Feb 2026 03:56:43 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact375

Tree of Dependent Computations

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       [Univariate Data Series] [Identifying Integ...] [2009-11-22 12:08:06] [b98453cac15ba1066b407e146608df68]
- RMP         [(Partial) Autocorrelation Function] [Births] [2010-11-29 09:36:27] [b98453cac15ba1066b407e146608df68]
- R PD          [(Partial) Autocorrelation Function] [] [2011-12-02 10:47:46] [54b1f171ce7a12209ffa11b565e1dcf5]
-    D            [(Partial) Autocorrelation Function] [Paper: ACF] [2011-12-17 09:27:09] [54b1f171ce7a12209ffa11b565e1dcf5]
-   P               [(Partial) Autocorrelation Function] [Paper: ACF 2] [2011-12-17 10:12:03] [54b1f171ce7a12209ffa11b565e1dcf5]
-   PD                [(Partial) Autocorrelation Function] [Paper: ACF 2] [2011-12-17 15:47:22] [54b1f171ce7a12209ffa11b565e1dcf5]
-   P                     [(Partial) Autocorrelation Function] [Paper: ACF] [2011-12-17 15:48:24] [70041e5e9044b1d424b6896a10522877] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
37
30
47
35
30
43
82
40
47
19
52
136
80
42
54
66
81
63
137
72
107
58
36
52
79
77
54
84
48
96
83
66
61
53
30
74
69
59
42
65
70
100
63
105
82
81
75
102
121
98
76
77
63
37
35
23
40
29
37
51
20
28
13
22
25
13
16
13
16
17
9
17
25
14
8
7
10
7
10
3

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.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 & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=156409&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=156409&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=156409&T=0

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net






Autocorrelation Function
Time lag kACF(k)T-STATP-value
10.657735.88290
20.5793045.18151e-06
30.4889044.37291.8e-05
40.506734.53231e-05
50.4915024.39611.7e-05
60.4431783.96398e-05
70.4006313.58340.000291
80.3379353.02260.001683
90.3232242.8910.002471
100.2080891.86120.033194
110.1821211.62890.053629
120.2348922.10090.019397
130.1624851.45330.075025
140.1019050.91150.182393
150.0369550.33050.370929
160.038590.34520.365441
170.0075310.06740.473233
180.0374430.33490.369288
190.0199220.17820.429514

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.65773 & 5.8829 & 0 \tabularnewline
2 & 0.579304 & 5.1815 & 1e-06 \tabularnewline
3 & 0.488904 & 4.3729 & 1.8e-05 \tabularnewline
4 & 0.50673 & 4.5323 & 1e-05 \tabularnewline
5 & 0.491502 & 4.3961 & 1.7e-05 \tabularnewline
6 & 0.443178 & 3.9639 & 8e-05 \tabularnewline
7 & 0.400631 & 3.5834 & 0.000291 \tabularnewline
8 & 0.337935 & 3.0226 & 0.001683 \tabularnewline
9 & 0.323224 & 2.891 & 0.002471 \tabularnewline
10 & 0.208089 & 1.8612 & 0.033194 \tabularnewline
11 & 0.182121 & 1.6289 & 0.053629 \tabularnewline
12 & 0.234892 & 2.1009 & 0.019397 \tabularnewline
13 & 0.162485 & 1.4533 & 0.075025 \tabularnewline
14 & 0.101905 & 0.9115 & 0.182393 \tabularnewline
15 & 0.036955 & 0.3305 & 0.370929 \tabularnewline
16 & 0.03859 & 0.3452 & 0.365441 \tabularnewline
17 & 0.007531 & 0.0674 & 0.473233 \tabularnewline
18 & 0.037443 & 0.3349 & 0.369288 \tabularnewline
19 & 0.019922 & 0.1782 & 0.429514 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=156409&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]0.65773[/C][C]5.8829[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.579304[/C][C]5.1815[/C][C]1e-06[/C][/ROW]
[ROW][C]3[/C][C]0.488904[/C][C]4.3729[/C][C]1.8e-05[/C][/ROW]
[ROW][C]4[/C][C]0.50673[/C][C]4.5323[/C][C]1e-05[/C][/ROW]
[ROW][C]5[/C][C]0.491502[/C][C]4.3961[/C][C]1.7e-05[/C][/ROW]
[ROW][C]6[/C][C]0.443178[/C][C]3.9639[/C][C]8e-05[/C][/ROW]
[ROW][C]7[/C][C]0.400631[/C][C]3.5834[/C][C]0.000291[/C][/ROW]
[ROW][C]8[/C][C]0.337935[/C][C]3.0226[/C][C]0.001683[/C][/ROW]
[ROW][C]9[/C][C]0.323224[/C][C]2.891[/C][C]0.002471[/C][/ROW]
[ROW][C]10[/C][C]0.208089[/C][C]1.8612[/C][C]0.033194[/C][/ROW]
[ROW][C]11[/C][C]0.182121[/C][C]1.6289[/C][C]0.053629[/C][/ROW]
[ROW][C]12[/C][C]0.234892[/C][C]2.1009[/C][C]0.019397[/C][/ROW]
[ROW][C]13[/C][C]0.162485[/C][C]1.4533[/C][C]0.075025[/C][/ROW]
[ROW][C]14[/C][C]0.101905[/C][C]0.9115[/C][C]0.182393[/C][/ROW]
[ROW][C]15[/C][C]0.036955[/C][C]0.3305[/C][C]0.370929[/C][/ROW]
[ROW][C]16[/C][C]0.03859[/C][C]0.3452[/C][C]0.365441[/C][/ROW]
[ROW][C]17[/C][C]0.007531[/C][C]0.0674[/C][C]0.473233[/C][/ROW]
[ROW][C]18[/C][C]0.037443[/C][C]0.3349[/C][C]0.369288[/C][/ROW]
[ROW][C]19[/C][C]0.019922[/C][C]0.1782[/C][C]0.429514[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=156409&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=156409&T=1

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Autocorrelation Function
Time lag kACF(k)T-STATP-value
10.657735.88290
20.5793045.18151e-06
30.4889044.37291.8e-05
40.506734.53231e-05
50.4915024.39611.7e-05
60.4431783.96398e-05
70.4006313.58340.000291
80.3379353.02260.001683
90.3232242.8910.002471
100.2080891.86120.033194
110.1821211.62890.053629
120.2348922.10090.019397
130.1624851.45330.075025
140.1019050.91150.182393
150.0369550.33050.370929
160.038590.34520.365441
170.0075310.06740.473233
180.0374430.33490.369288
190.0199220.17820.429514






Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
10.657735.88290
20.2585442.31250.011661
30.0686320.61390.270525
40.1925161.72190.044475
50.1128021.00890.158025
60.0017080.01530.493925
70.0082050.07340.470839
8-0.051643-0.46190.322699
90.0085670.07660.469557
10-0.178249-1.59430.057405
11-0.039062-0.34940.363861
120.1732741.54980.062567
13-0.114663-1.02560.154092
14-0.09203-0.82310.206438
15-0.022858-0.20440.419262
160.0130140.11640.453813
17-0.048731-0.43590.332056
180.0775350.69350.245004
190.0570250.510.305711

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.65773 & 5.8829 & 0 \tabularnewline
2 & 0.258544 & 2.3125 & 0.011661 \tabularnewline
3 & 0.068632 & 0.6139 & 0.270525 \tabularnewline
4 & 0.192516 & 1.7219 & 0.044475 \tabularnewline
5 & 0.112802 & 1.0089 & 0.158025 \tabularnewline
6 & 0.001708 & 0.0153 & 0.493925 \tabularnewline
7 & 0.008205 & 0.0734 & 0.470839 \tabularnewline
8 & -0.051643 & -0.4619 & 0.322699 \tabularnewline
9 & 0.008567 & 0.0766 & 0.469557 \tabularnewline
10 & -0.178249 & -1.5943 & 0.057405 \tabularnewline
11 & -0.039062 & -0.3494 & 0.363861 \tabularnewline
12 & 0.173274 & 1.5498 & 0.062567 \tabularnewline
13 & -0.114663 & -1.0256 & 0.154092 \tabularnewline
14 & -0.09203 & -0.8231 & 0.206438 \tabularnewline
15 & -0.022858 & -0.2044 & 0.419262 \tabularnewline
16 & 0.013014 & 0.1164 & 0.453813 \tabularnewline
17 & -0.048731 & -0.4359 & 0.332056 \tabularnewline
18 & 0.077535 & 0.6935 & 0.245004 \tabularnewline
19 & 0.057025 & 0.51 & 0.305711 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=156409&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]0.65773[/C][C]5.8829[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.258544[/C][C]2.3125[/C][C]0.011661[/C][/ROW]
[ROW][C]3[/C][C]0.068632[/C][C]0.6139[/C][C]0.270525[/C][/ROW]
[ROW][C]4[/C][C]0.192516[/C][C]1.7219[/C][C]0.044475[/C][/ROW]
[ROW][C]5[/C][C]0.112802[/C][C]1.0089[/C][C]0.158025[/C][/ROW]
[ROW][C]6[/C][C]0.001708[/C][C]0.0153[/C][C]0.493925[/C][/ROW]
[ROW][C]7[/C][C]0.008205[/C][C]0.0734[/C][C]0.470839[/C][/ROW]
[ROW][C]8[/C][C]-0.051643[/C][C]-0.4619[/C][C]0.322699[/C][/ROW]
[ROW][C]9[/C][C]0.008567[/C][C]0.0766[/C][C]0.469557[/C][/ROW]
[ROW][C]10[/C][C]-0.178249[/C][C]-1.5943[/C][C]0.057405[/C][/ROW]
[ROW][C]11[/C][C]-0.039062[/C][C]-0.3494[/C][C]0.363861[/C][/ROW]
[ROW][C]12[/C][C]0.173274[/C][C]1.5498[/C][C]0.062567[/C][/ROW]
[ROW][C]13[/C][C]-0.114663[/C][C]-1.0256[/C][C]0.154092[/C][/ROW]
[ROW][C]14[/C][C]-0.09203[/C][C]-0.8231[/C][C]0.206438[/C][/ROW]
[ROW][C]15[/C][C]-0.022858[/C][C]-0.2044[/C][C]0.419262[/C][/ROW]
[ROW][C]16[/C][C]0.013014[/C][C]0.1164[/C][C]0.453813[/C][/ROW]
[ROW][C]17[/C][C]-0.048731[/C][C]-0.4359[/C][C]0.332056[/C][/ROW]
[ROW][C]18[/C][C]0.077535[/C][C]0.6935[/C][C]0.245004[/C][/ROW]
[ROW][C]19[/C][C]0.057025[/C][C]0.51[/C][C]0.305711[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=156409&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=156409&T=2

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
10.657735.88290
20.2585442.31250.011661
30.0686320.61390.270525
40.1925161.72190.044475
50.1128021.00890.158025
60.0017080.01530.493925
70.0082050.07340.470839
8-0.051643-0.46190.322699
90.0085670.07660.469557
10-0.178249-1.59430.057405
11-0.039062-0.34940.363861
120.1732741.54980.062567
13-0.114663-1.02560.154092
14-0.09203-0.82310.206438
15-0.022858-0.20440.419262
160.0130140.11640.453813
17-0.048731-0.43590.332056
180.0775350.69350.245004
190.0570250.510.305711


Figures (Output of Computation)

Input Parameters & R Code

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 (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')