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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 computationWed, 10 Dec 2008 10:34:21 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Dec/10/t12289308920d6p124j9vfn6hl.htm/, Retrieved Tue, 10 Feb 2026 14:13:47 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=32046, Retrieved Tue, 10 Feb 2026 14:13:47 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact405

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [(Partial) Autocorrelation Function] [] [2008-12-10 17:34:21] [1fa440a634ec541bd583650ead0404df] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
100
100
100
100,1
100
100
99,8
100
99,9
99,2
98,7
98,7
98,9
99,2
99,8
100,5
100,1
100,5
98,4
98,6
99
99,1
98,9
98,5
96,9
96,8
97
97
96,9
97,1
97,2
97,9
98,9
99,2
99,5
99,3
99,9
100
100,3
100,5
100,7
100,9
100,8
100,9
101
100,3
100,1
99,8
99,9
99,9
100,2
99,7
100,4
100,9
101,3
101,4
101,3
100,9
100,9
100,9
101,1
101,1
101,3
101,8
102,9
103,2
103,3
104,5
105
104,9
104,9
105,4
106
105,7
105,9
106,2
106,4
106,9
107,3
107,9
109,2
110,2
110,2
110,5
110,6
110,8
111,3
111,1
111,2
111,2
111,1
111,5
112,1
111,4

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'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=32046&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=32046&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=32046&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'Gwilym Jenkins' @ 72.249.127.135






Autocorrelation Function
Time lag kACF(k)T-STATP-value
10.9685449.39040
20.9300969.01760
30.8924188.65230
40.8556148.29550
50.816747.91860
60.7764477.52790
70.7333937.11050
80.6897666.68750
90.6479066.28170
100.6055565.87110
110.5626715.45530
120.5202175.04371e-06
130.4758724.61376e-06
140.4365834.23282.7e-05
150.4033933.9118.7e-05
160.3729963.61630.000241
170.342983.32530.00063
180.3141983.04630.001504
190.2827852.74170.003659

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.968544 & 9.3904 & 0 \tabularnewline
2 & 0.930096 & 9.0176 & 0 \tabularnewline
3 & 0.892418 & 8.6523 & 0 \tabularnewline
4 & 0.855614 & 8.2955 & 0 \tabularnewline
5 & 0.81674 & 7.9186 & 0 \tabularnewline
6 & 0.776447 & 7.5279 & 0 \tabularnewline
7 & 0.733393 & 7.1105 & 0 \tabularnewline
8 & 0.689766 & 6.6875 & 0 \tabularnewline
9 & 0.647906 & 6.2817 & 0 \tabularnewline
10 & 0.605556 & 5.8711 & 0 \tabularnewline
11 & 0.562671 & 5.4553 & 0 \tabularnewline
12 & 0.520217 & 5.0437 & 1e-06 \tabularnewline
13 & 0.475872 & 4.6137 & 6e-06 \tabularnewline
14 & 0.436583 & 4.2328 & 2.7e-05 \tabularnewline
15 & 0.403393 & 3.911 & 8.7e-05 \tabularnewline
16 & 0.372996 & 3.6163 & 0.000241 \tabularnewline
17 & 0.34298 & 3.3253 & 0.00063 \tabularnewline
18 & 0.314198 & 3.0463 & 0.001504 \tabularnewline
19 & 0.282785 & 2.7417 & 0.003659 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=32046&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]0.968544[/C][C]9.3904[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.930096[/C][C]9.0176[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.892418[/C][C]8.6523[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.855614[/C][C]8.2955[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.81674[/C][C]7.9186[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.776447[/C][C]7.5279[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.733393[/C][C]7.1105[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.689766[/C][C]6.6875[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.647906[/C][C]6.2817[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]0.605556[/C][C]5.8711[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]0.562671[/C][C]5.4553[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.520217[/C][C]5.0437[/C][C]1e-06[/C][/ROW]
[ROW][C]13[/C][C]0.475872[/C][C]4.6137[/C][C]6e-06[/C][/ROW]
[ROW][C]14[/C][C]0.436583[/C][C]4.2328[/C][C]2.7e-05[/C][/ROW]
[ROW][C]15[/C][C]0.403393[/C][C]3.911[/C][C]8.7e-05[/C][/ROW]
[ROW][C]16[/C][C]0.372996[/C][C]3.6163[/C][C]0.000241[/C][/ROW]
[ROW][C]17[/C][C]0.34298[/C][C]3.3253[/C][C]0.00063[/C][/ROW]
[ROW][C]18[/C][C]0.314198[/C][C]3.0463[/C][C]0.001504[/C][/ROW]
[ROW][C]19[/C][C]0.282785[/C][C]2.7417[/C][C]0.003659[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=32046&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=32046&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
10.9685449.39040
20.9300969.01760
30.8924188.65230
40.8556148.29550
50.816747.91860
60.7764477.52790
70.7333937.11050
80.6897666.68750
90.6479066.28170
100.6055565.87110
110.5626715.45530
120.5202175.04371e-06
130.4758724.61376e-06
140.4365834.23282.7e-05
150.4033933.9118.7e-05
160.3729963.61630.000241
170.342983.32530.00063
180.3141983.04630.001504
190.2827852.74170.003659






Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
10.9685449.39040
2-0.128871-1.24950.107301
30.0049950.04840.480739
4-0.009699-0.0940.462641
5-0.056249-0.54540.2934
6-0.036553-0.35440.361919
7-0.06509-0.63110.264762
8-0.026644-0.25830.398363
90.0034490.03340.486697
10-0.040378-0.39150.348164
11-0.028946-0.28060.389803
12-0.016863-0.16350.43524
13-0.061907-0.60020.274905
140.0617410.59860.275438
150.052950.51340.304448
160.0052550.05090.479737
17-0.014603-0.14160.443857
18-0.005754-0.05580.477814
19-0.07559-0.73290.232731

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.968544 & 9.3904 & 0 \tabularnewline
2 & -0.128871 & -1.2495 & 0.107301 \tabularnewline
3 & 0.004995 & 0.0484 & 0.480739 \tabularnewline
4 & -0.009699 & -0.094 & 0.462641 \tabularnewline
5 & -0.056249 & -0.5454 & 0.2934 \tabularnewline
6 & -0.036553 & -0.3544 & 0.361919 \tabularnewline
7 & -0.06509 & -0.6311 & 0.264762 \tabularnewline
8 & -0.026644 & -0.2583 & 0.398363 \tabularnewline
9 & 0.003449 & 0.0334 & 0.486697 \tabularnewline
10 & -0.040378 & -0.3915 & 0.348164 \tabularnewline
11 & -0.028946 & -0.2806 & 0.389803 \tabularnewline
12 & -0.016863 & -0.1635 & 0.43524 \tabularnewline
13 & -0.061907 & -0.6002 & 0.274905 \tabularnewline
14 & 0.061741 & 0.5986 & 0.275438 \tabularnewline
15 & 0.05295 & 0.5134 & 0.304448 \tabularnewline
16 & 0.005255 & 0.0509 & 0.479737 \tabularnewline
17 & -0.014603 & -0.1416 & 0.443857 \tabularnewline
18 & -0.005754 & -0.0558 & 0.477814 \tabularnewline
19 & -0.07559 & -0.7329 & 0.232731 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=32046&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]0.968544[/C][C]9.3904[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.128871[/C][C]-1.2495[/C][C]0.107301[/C][/ROW]
[ROW][C]3[/C][C]0.004995[/C][C]0.0484[/C][C]0.480739[/C][/ROW]
[ROW][C]4[/C][C]-0.009699[/C][C]-0.094[/C][C]0.462641[/C][/ROW]
[ROW][C]5[/C][C]-0.056249[/C][C]-0.5454[/C][C]0.2934[/C][/ROW]
[ROW][C]6[/C][C]-0.036553[/C][C]-0.3544[/C][C]0.361919[/C][/ROW]
[ROW][C]7[/C][C]-0.06509[/C][C]-0.6311[/C][C]0.264762[/C][/ROW]
[ROW][C]8[/C][C]-0.026644[/C][C]-0.2583[/C][C]0.398363[/C][/ROW]
[ROW][C]9[/C][C]0.003449[/C][C]0.0334[/C][C]0.486697[/C][/ROW]
[ROW][C]10[/C][C]-0.040378[/C][C]-0.3915[/C][C]0.348164[/C][/ROW]
[ROW][C]11[/C][C]-0.028946[/C][C]-0.2806[/C][C]0.389803[/C][/ROW]
[ROW][C]12[/C][C]-0.016863[/C][C]-0.1635[/C][C]0.43524[/C][/ROW]
[ROW][C]13[/C][C]-0.061907[/C][C]-0.6002[/C][C]0.274905[/C][/ROW]
[ROW][C]14[/C][C]0.061741[/C][C]0.5986[/C][C]0.275438[/C][/ROW]
[ROW][C]15[/C][C]0.05295[/C][C]0.5134[/C][C]0.304448[/C][/ROW]
[ROW][C]16[/C][C]0.005255[/C][C]0.0509[/C][C]0.479737[/C][/ROW]
[ROW][C]17[/C][C]-0.014603[/C][C]-0.1416[/C][C]0.443857[/C][/ROW]
[ROW][C]18[/C][C]-0.005754[/C][C]-0.0558[/C][C]0.477814[/C][/ROW]
[ROW][C]19[/C][C]-0.07559[/C][C]-0.7329[/C][C]0.232731[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=32046&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=32046&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
10.9685449.39040
2-0.128871-1.24950.107301
30.0049950.04840.480739
4-0.009699-0.0940.462641
5-0.056249-0.54540.2934
6-0.036553-0.35440.361919
7-0.06509-0.63110.264762
8-0.026644-0.25830.398363
90.0034490.03340.486697
10-0.040378-0.39150.348164
11-0.028946-0.28060.389803
12-0.016863-0.16350.43524
13-0.061907-0.60020.274905
140.0617410.59860.275438
150.052950.51340.304448
160.0052550.05090.479737
17-0.014603-0.14160.443857
18-0.005754-0.05580.477814
19-0.07559-0.73290.232731


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ;
Parameters (R input):
par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ;
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 (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='lags',ylab='ACF')
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')