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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 computationSun, 19 Dec 2010 14:03:11 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/19/t1292767369uvm0uym36zixseu.htm/, Retrieved Sun, 05 May 2024 01:18:16 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=112397, Retrieved Sun, 05 May 2024 01:18:16 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact198
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [(Partial) Autocorrelation Function] [paperuit_ACF1] [2010-12-19 12:41:10] [7e261c986c934df955dd3ac53e9d45c6]
-   P     [(Partial) Autocorrelation Function] [paperuit_ACF1] [2010-12-19 14:03:11] [13dfa60174f50d862e8699db2153bfc5] [Current]
-   P       [(Partial) Autocorrelation Function] [ACF_uitvoerbelgie] [2010-12-22 14:29:22] [8441f95c4a5787a301bc621ebc7904ca]
-             [(Partial) Autocorrelation Function] [paperACF_uit] [2010-12-24 15:02:57] [7e261c986c934df955dd3ac53e9d45c6]
-             [(Partial) Autocorrelation Function] [Kristof Nagels] [2010-12-24 15:03:19] [8441f95c4a5787a301bc621ebc7904ca]
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Dataseries X:
15
14.4
13
13.7
13.6
15.2
12.9
14
14.1
13.2
11.3
13.3
14.4
13.3
11.6
13.2
13.1
14.6
14
14.3
13.8
13.7
11
14.4
15.6
13.7
12.6
13.2
13.3
14.3
14
13.4
13.9
13.7
10.5
14.5
15
13.5
13.5
13.2
13.8
16.2
14.7
13.9
16
14.4
12.3
15.9
15.9
15.5
15.1
14.5
15.1
17.4
16.2
15.6
17.2
14.9
13.8
17.5
16.2
17.5
16.6
16.2
16.6
19.6
15.9
18
18.3
16.3
14.9
18.2
18.4
18.5
16
17.4
17.2
19.6
17.2
18.3
19.3
18.1
16.2
18.4
20.5
19
16.5
18.7
19
19.2
20.5
19.3
20.6
20.1
16.1
20.4
19.7
15.6
14.4
13.7
14.1
15
14.2
13.6
15.4
14.8
12.5
16.2
16.1
16
15.8
15.2
15.7
18.9
17.4
17
19.8
17.7
16
19.6
19.7




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112397&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112397&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112397&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 Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk







Autocorrelation Function
Time lag kACF(k)T-STATP-value
10.6998947.69880
20.5835216.41870
30.6756247.43190
40.6479427.12740
50.5678956.24680
60.5976556.57420
70.4742445.21670
80.4871195.35830
90.4087424.49628e-06
100.2734893.00840.001598
110.3637454.00125.4e-05
120.52555.78050
130.288573.17430.000953
140.20652.27150.012442
150.261672.87840.002364
160.2765333.04190.001442
170.2611332.87250.002406
180.2944413.23880.000775
190.2367482.60420.005181
200.3023753.32610.000583

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.699894 & 7.6988 & 0 \tabularnewline
2 & 0.583521 & 6.4187 & 0 \tabularnewline
3 & 0.675624 & 7.4319 & 0 \tabularnewline
4 & 0.647942 & 7.1274 & 0 \tabularnewline
5 & 0.567895 & 6.2468 & 0 \tabularnewline
6 & 0.597655 & 6.5742 & 0 \tabularnewline
7 & 0.474244 & 5.2167 & 0 \tabularnewline
8 & 0.487119 & 5.3583 & 0 \tabularnewline
9 & 0.408742 & 4.4962 & 8e-06 \tabularnewline
10 & 0.273489 & 3.0084 & 0.001598 \tabularnewline
11 & 0.363745 & 4.0012 & 5.4e-05 \tabularnewline
12 & 0.5255 & 5.7805 & 0 \tabularnewline
13 & 0.28857 & 3.1743 & 0.000953 \tabularnewline
14 & 0.2065 & 2.2715 & 0.012442 \tabularnewline
15 & 0.26167 & 2.8784 & 0.002364 \tabularnewline
16 & 0.276533 & 3.0419 & 0.001442 \tabularnewline
17 & 0.261133 & 2.8725 & 0.002406 \tabularnewline
18 & 0.294441 & 3.2388 & 0.000775 \tabularnewline
19 & 0.236748 & 2.6042 & 0.005181 \tabularnewline
20 & 0.302375 & 3.3261 & 0.000583 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112397&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]0.699894[/C][C]7.6988[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.583521[/C][C]6.4187[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.675624[/C][C]7.4319[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.647942[/C][C]7.1274[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.567895[/C][C]6.2468[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.597655[/C][C]6.5742[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.474244[/C][C]5.2167[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.487119[/C][C]5.3583[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.408742[/C][C]4.4962[/C][C]8e-06[/C][/ROW]
[ROW][C]10[/C][C]0.273489[/C][C]3.0084[/C][C]0.001598[/C][/ROW]
[ROW][C]11[/C][C]0.363745[/C][C]4.0012[/C][C]5.4e-05[/C][/ROW]
[ROW][C]12[/C][C]0.5255[/C][C]5.7805[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.28857[/C][C]3.1743[/C][C]0.000953[/C][/ROW]
[ROW][C]14[/C][C]0.2065[/C][C]2.2715[/C][C]0.012442[/C][/ROW]
[ROW][C]15[/C][C]0.26167[/C][C]2.8784[/C][C]0.002364[/C][/ROW]
[ROW][C]16[/C][C]0.276533[/C][C]3.0419[/C][C]0.001442[/C][/ROW]
[ROW][C]17[/C][C]0.261133[/C][C]2.8725[/C][C]0.002406[/C][/ROW]
[ROW][C]18[/C][C]0.294441[/C][C]3.2388[/C][C]0.000775[/C][/ROW]
[ROW][C]19[/C][C]0.236748[/C][C]2.6042[/C][C]0.005181[/C][/ROW]
[ROW][C]20[/C][C]0.302375[/C][C]3.3261[/C][C]0.000583[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112397&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112397&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 kACF(k)T-STATP-value
10.6998947.69880
20.5835216.41870
30.6756247.43190
40.6479427.12740
50.5678956.24680
60.5976556.57420
70.4742445.21670
80.4871195.35830
90.4087424.49628e-06
100.2734893.00840.001598
110.3637454.00125.4e-05
120.52555.78050
130.288573.17430.000953
140.20652.27150.012442
150.261672.87840.002364
160.2765333.04190.001442
170.2611332.87250.002406
180.2944413.23880.000775
190.2367482.60420.005181
200.3023753.32610.000583







Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
10.6998947.69880
20.1836122.01970.02281
30.4335134.76863e-06
40.1240631.36470.087441
50.0452370.49760.309832
60.1360581.49660.068546
7-0.272941-3.00240.001628
80.1615161.77670.039068
9-0.337754-3.71530.000154
10-0.178747-1.96620.025782
110.2744963.01950.001545
120.4392344.83162e-06
13-0.205038-2.25540.012952
14-0.169785-1.86760.032116
15-0.165055-1.81560.035953
160.1372081.50930.066916
170.1394571.5340.063816
180.1168051.28490.100648
190.0469550.51650.303224
200.0682940.75120.226985

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.699894 & 7.6988 & 0 \tabularnewline
2 & 0.183612 & 2.0197 & 0.02281 \tabularnewline
3 & 0.433513 & 4.7686 & 3e-06 \tabularnewline
4 & 0.124063 & 1.3647 & 0.087441 \tabularnewline
5 & 0.045237 & 0.4976 & 0.309832 \tabularnewline
6 & 0.136058 & 1.4966 & 0.068546 \tabularnewline
7 & -0.272941 & -3.0024 & 0.001628 \tabularnewline
8 & 0.161516 & 1.7767 & 0.039068 \tabularnewline
9 & -0.337754 & -3.7153 & 0.000154 \tabularnewline
10 & -0.178747 & -1.9662 & 0.025782 \tabularnewline
11 & 0.274496 & 3.0195 & 0.001545 \tabularnewline
12 & 0.439234 & 4.8316 & 2e-06 \tabularnewline
13 & -0.205038 & -2.2554 & 0.012952 \tabularnewline
14 & -0.169785 & -1.8676 & 0.032116 \tabularnewline
15 & -0.165055 & -1.8156 & 0.035953 \tabularnewline
16 & 0.137208 & 1.5093 & 0.066916 \tabularnewline
17 & 0.139457 & 1.534 & 0.063816 \tabularnewline
18 & 0.116805 & 1.2849 & 0.100648 \tabularnewline
19 & 0.046955 & 0.5165 & 0.303224 \tabularnewline
20 & 0.068294 & 0.7512 & 0.226985 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112397&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]0.699894[/C][C]7.6988[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.183612[/C][C]2.0197[/C][C]0.02281[/C][/ROW]
[ROW][C]3[/C][C]0.433513[/C][C]4.7686[/C][C]3e-06[/C][/ROW]
[ROW][C]4[/C][C]0.124063[/C][C]1.3647[/C][C]0.087441[/C][/ROW]
[ROW][C]5[/C][C]0.045237[/C][C]0.4976[/C][C]0.309832[/C][/ROW]
[ROW][C]6[/C][C]0.136058[/C][C]1.4966[/C][C]0.068546[/C][/ROW]
[ROW][C]7[/C][C]-0.272941[/C][C]-3.0024[/C][C]0.001628[/C][/ROW]
[ROW][C]8[/C][C]0.161516[/C][C]1.7767[/C][C]0.039068[/C][/ROW]
[ROW][C]9[/C][C]-0.337754[/C][C]-3.7153[/C][C]0.000154[/C][/ROW]
[ROW][C]10[/C][C]-0.178747[/C][C]-1.9662[/C][C]0.025782[/C][/ROW]
[ROW][C]11[/C][C]0.274496[/C][C]3.0195[/C][C]0.001545[/C][/ROW]
[ROW][C]12[/C][C]0.439234[/C][C]4.8316[/C][C]2e-06[/C][/ROW]
[ROW][C]13[/C][C]-0.205038[/C][C]-2.2554[/C][C]0.012952[/C][/ROW]
[ROW][C]14[/C][C]-0.169785[/C][C]-1.8676[/C][C]0.032116[/C][/ROW]
[ROW][C]15[/C][C]-0.165055[/C][C]-1.8156[/C][C]0.035953[/C][/ROW]
[ROW][C]16[/C][C]0.137208[/C][C]1.5093[/C][C]0.066916[/C][/ROW]
[ROW][C]17[/C][C]0.139457[/C][C]1.534[/C][C]0.063816[/C][/ROW]
[ROW][C]18[/C][C]0.116805[/C][C]1.2849[/C][C]0.100648[/C][/ROW]
[ROW][C]19[/C][C]0.046955[/C][C]0.5165[/C][C]0.303224[/C][/ROW]
[ROW][C]20[/C][C]0.068294[/C][C]0.7512[/C][C]0.226985[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112397&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112397&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 kPACF(k)T-STATP-value
10.6998947.69880
20.1836122.01970.02281
30.4335134.76863e-06
40.1240631.36470.087441
50.0452370.49760.309832
60.1360581.49660.068546
7-0.272941-3.00240.001628
80.1615161.77670.039068
9-0.337754-3.71530.000154
10-0.178747-1.96620.025782
110.2744963.01950.001545
120.4392344.83162e-06
13-0.205038-2.25540.012952
14-0.169785-1.86760.032116
15-0.165055-1.81560.035953
160.1372081.50930.066916
170.1394571.5340.063816
180.1168051.28490.100648
190.0469550.51650.303224
200.0682940.75120.226985



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 (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')