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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_autocorrelation.wasp
Title produced by software(Partial) Autocorrelation Function
Date of computationTue, 18 Dec 2007 06:14:27 -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/2007/Dec/18/t1197982634wr0f1e44de5h9b5.htm/, Retrieved Sat, 25 Apr 2026 15:25:40 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=4501, Retrieved Sat, 25 Apr 2026 15:25:40 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact423

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] [tijdreeks4] [2007-12-18 13:14:27] [157a0cf3c12a7482b4e6935b4c49d48f] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
3,5300
3,4900
3,5100
3,5300
3,5400
3,5600
3,5800
3,6100
3,5600
3,5600
3,6100
3,6100
3,6200
3,6300
3,6500
3,7200
3,7200
3,7300
3,7300
3,7200
3,7200
3,7000
3,7100
3,7200
3,7200
3,7300
3,7300
3,7300
3,7500
3,7400
3,8300
3,9400
3,9500
3,9700
3,9900
3,9900
4,0000
4,0000
4,0000
3,9900
3,9600
3,9800
4,0300
4,0800
4,0700
4,0700
4,0500
4,0500
4,0500
4,0600
4,0700
4,0900
4,0900
4,1100
4,1700
4,1800
4,1600
4,1600
4,1700
4,1700
4,1900
4,2000
4,1900
4,1800
4,1200
4,1200
4,1300
4,1500
4,1200
4,1100
4,1000
4,1000

Tables (Output of Computation)





Summary of compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\begin{tabular}{lllllllll}
\hline
Summary of compuational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 4 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4501&T=0

[TABLE]
[ROW][C]Summary of compuational 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]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=4501&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4501&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 compuational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001






Autocorrelation Function
Time lag kACF(k)T-STATP-value
018.48530
10.9685668.21860
20.9285177.87870
30.8895067.54770
40.8507447.21880
50.8109196.88090
60.7725896.55560
70.7363456.24810
80.7020625.95720
90.6573345.57770
100.6131145.20241e-06
110.573664.86773e-06
120.5320674.51471.2e-05
130.4887684.14734.5e-05
140.4445653.77230.000165
150.4053843.43980.000486
160.3725643.16130.001149
170.3363322.85390.002818

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 8.4853 & 0 \tabularnewline
1 & 0.968566 & 8.2186 & 0 \tabularnewline
2 & 0.928517 & 7.8787 & 0 \tabularnewline
3 & 0.889506 & 7.5477 & 0 \tabularnewline
4 & 0.850744 & 7.2188 & 0 \tabularnewline
5 & 0.810919 & 6.8809 & 0 \tabularnewline
6 & 0.772589 & 6.5556 & 0 \tabularnewline
7 & 0.736345 & 6.2481 & 0 \tabularnewline
8 & 0.702062 & 5.9572 & 0 \tabularnewline
9 & 0.657334 & 5.5777 & 0 \tabularnewline
10 & 0.613114 & 5.2024 & 1e-06 \tabularnewline
11 & 0.57366 & 4.8677 & 3e-06 \tabularnewline
12 & 0.532067 & 4.5147 & 1.2e-05 \tabularnewline
13 & 0.488768 & 4.1473 & 4.5e-05 \tabularnewline
14 & 0.444565 & 3.7723 & 0.000165 \tabularnewline
15 & 0.405384 & 3.4398 & 0.000486 \tabularnewline
16 & 0.372564 & 3.1613 & 0.001149 \tabularnewline
17 & 0.336332 & 2.8539 & 0.002818 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4501&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]0[/C][C]1[/C][C]8.4853[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.968566[/C][C]8.2186[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.928517[/C][C]7.8787[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.889506[/C][C]7.5477[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.850744[/C][C]7.2188[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.810919[/C][C]6.8809[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.772589[/C][C]6.5556[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.736345[/C][C]6.2481[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.702062[/C][C]5.9572[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.657334[/C][C]5.5777[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]0.613114[/C][C]5.2024[/C][C]1e-06[/C][/ROW]
[ROW][C]11[/C][C]0.57366[/C][C]4.8677[/C][C]3e-06[/C][/ROW]
[ROW][C]12[/C][C]0.532067[/C][C]4.5147[/C][C]1.2e-05[/C][/ROW]
[ROW][C]13[/C][C]0.488768[/C][C]4.1473[/C][C]4.5e-05[/C][/ROW]
[ROW][C]14[/C][C]0.444565[/C][C]3.7723[/C][C]0.000165[/C][/ROW]
[ROW][C]15[/C][C]0.405384[/C][C]3.4398[/C][C]0.000486[/C][/ROW]
[ROW][C]16[/C][C]0.372564[/C][C]3.1613[/C][C]0.001149[/C][/ROW]
[ROW][C]17[/C][C]0.336332[/C][C]2.8539[/C][C]0.002818[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=4501&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4501&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
018.48530
10.9685668.21860
20.9285177.87870
30.8895067.54770
40.8507447.21880
50.8109196.88090
60.7725896.55560
70.7363456.24810
80.7020625.95720
90.6573345.57770
100.6131145.20241e-06
110.573664.86773e-06
120.5320674.51471.2e-05
130.4887684.14734.5e-05
140.4445653.77230.000165
150.4053843.43980.000486
160.3725643.16130.001149
170.3363322.85390.002818






Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
00.9685668.21860
1-0.155177-1.31670.903945
20.0152340.12930.448753
3-0.023849-0.20240.579899
4-0.038075-0.32310.626213
50.0076720.06510.474136
60.0045530.03860.484645
70.0045330.03850.484711
8-0.199569-1.69340.952649
90.0326510.27710.391267
100.0354760.3010.382131
11-0.082673-0.70150.757376
12-0.031008-0.26310.603393
13-0.048817-0.41420.660031
140.0526790.4470.328109
150.0487570.41370.340156
16-0.074416-0.63140.735123
17-0.012747-0.10820.542915

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.968566 & 8.2186 & 0 \tabularnewline
1 & -0.155177 & -1.3167 & 0.903945 \tabularnewline
2 & 0.015234 & 0.1293 & 0.448753 \tabularnewline
3 & -0.023849 & -0.2024 & 0.579899 \tabularnewline
4 & -0.038075 & -0.3231 & 0.626213 \tabularnewline
5 & 0.007672 & 0.0651 & 0.474136 \tabularnewline
6 & 0.004553 & 0.0386 & 0.484645 \tabularnewline
7 & 0.004533 & 0.0385 & 0.484711 \tabularnewline
8 & -0.199569 & -1.6934 & 0.952649 \tabularnewline
9 & 0.032651 & 0.2771 & 0.391267 \tabularnewline
10 & 0.035476 & 0.301 & 0.382131 \tabularnewline
11 & -0.082673 & -0.7015 & 0.757376 \tabularnewline
12 & -0.031008 & -0.2631 & 0.603393 \tabularnewline
13 & -0.048817 & -0.4142 & 0.660031 \tabularnewline
14 & 0.052679 & 0.447 & 0.328109 \tabularnewline
15 & 0.048757 & 0.4137 & 0.340156 \tabularnewline
16 & -0.074416 & -0.6314 & 0.735123 \tabularnewline
17 & -0.012747 & -0.1082 & 0.542915 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4501&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]0[/C][C]0.968566[/C][C]8.2186[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]-0.155177[/C][C]-1.3167[/C][C]0.903945[/C][/ROW]
[ROW][C]2[/C][C]0.015234[/C][C]0.1293[/C][C]0.448753[/C][/ROW]
[ROW][C]3[/C][C]-0.023849[/C][C]-0.2024[/C][C]0.579899[/C][/ROW]
[ROW][C]4[/C][C]-0.038075[/C][C]-0.3231[/C][C]0.626213[/C][/ROW]
[ROW][C]5[/C][C]0.007672[/C][C]0.0651[/C][C]0.474136[/C][/ROW]
[ROW][C]6[/C][C]0.004553[/C][C]0.0386[/C][C]0.484645[/C][/ROW]
[ROW][C]7[/C][C]0.004533[/C][C]0.0385[/C][C]0.484711[/C][/ROW]
[ROW][C]8[/C][C]-0.199569[/C][C]-1.6934[/C][C]0.952649[/C][/ROW]
[ROW][C]9[/C][C]0.032651[/C][C]0.2771[/C][C]0.391267[/C][/ROW]
[ROW][C]10[/C][C]0.035476[/C][C]0.301[/C][C]0.382131[/C][/ROW]
[ROW][C]11[/C][C]-0.082673[/C][C]-0.7015[/C][C]0.757376[/C][/ROW]
[ROW][C]12[/C][C]-0.031008[/C][C]-0.2631[/C][C]0.603393[/C][/ROW]
[ROW][C]13[/C][C]-0.048817[/C][C]-0.4142[/C][C]0.660031[/C][/ROW]
[ROW][C]14[/C][C]0.052679[/C][C]0.447[/C][C]0.328109[/C][/ROW]
[ROW][C]15[/C][C]0.048757[/C][C]0.4137[/C][C]0.340156[/C][/ROW]
[ROW][C]16[/C][C]-0.074416[/C][C]-0.6314[/C][C]0.735123[/C][/ROW]
[ROW][C]17[/C][C]-0.012747[/C][C]-0.1082[/C][C]0.542915[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=4501&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4501&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
00.9685668.21860
1-0.155177-1.31670.903945
20.0152340.12930.448753
3-0.023849-0.20240.579899
4-0.038075-0.32310.626213
50.0076720.06510.474136
60.0045530.03860.484645
70.0045330.03850.484711
8-0.199569-1.69340.952649
90.0326510.27710.391267
100.0354760.3010.382131
11-0.082673-0.70150.757376
12-0.031008-0.26310.603393
13-0.048817-0.41420.660031
140.0526790.4470.328109
150.0487570.41370.340156
16-0.074416-0.63140.735123
17-0.012747-0.10820.542915


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 1:par1) {
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(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-1,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(mytstat,lengthx),6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')