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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 12:41:10 +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/t1292762342739ad8wh3brfbdd.htm/, Retrieved Sun, 05 May 2024 02:15:51 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=112326, Retrieved Sun, 05 May 2024 02:15:51 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact141
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] [13dfa60174f50d862e8699db2153bfc5] [Current]
-   P     [(Partial) Autocorrelation Function] [paperuit_ACF1] [2010-12-19 14:03:11] [7e261c986c934df955dd3ac53e9d45c6]
-   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=112326&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=112326&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112326&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
10.6759127.4350
20.5568856.12570
30.6459027.10490
40.6398597.03850
50.5624686.18710
60.5999426.59940
70.4743465.21780
80.5040075.54410
90.4190054.60915e-06
100.2731213.00430.001618
110.3737384.11113.6e-05
120.5717686.28950
130.3021953.32410.000587
140.220692.42760.008336
150.2714142.98560.001713
160.2941243.23540.000783
170.280333.08360.001267
180.3150323.46540.000367
190.2473832.72120.003732
200.3260213.58620.000243

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.675912 & 7.435 & 0 \tabularnewline
2 & 0.556885 & 6.1257 & 0 \tabularnewline
3 & 0.645902 & 7.1049 & 0 \tabularnewline
4 & 0.639859 & 7.0385 & 0 \tabularnewline
5 & 0.562468 & 6.1871 & 0 \tabularnewline
6 & 0.599942 & 6.5994 & 0 \tabularnewline
7 & 0.474346 & 5.2178 & 0 \tabularnewline
8 & 0.504007 & 5.5441 & 0 \tabularnewline
9 & 0.419005 & 4.6091 & 5e-06 \tabularnewline
10 & 0.273121 & 3.0043 & 0.001618 \tabularnewline
11 & 0.373738 & 4.1111 & 3.6e-05 \tabularnewline
12 & 0.571768 & 6.2895 & 0 \tabularnewline
13 & 0.302195 & 3.3241 & 0.000587 \tabularnewline
14 & 0.22069 & 2.4276 & 0.008336 \tabularnewline
15 & 0.271414 & 2.9856 & 0.001713 \tabularnewline
16 & 0.294124 & 3.2354 & 0.000783 \tabularnewline
17 & 0.28033 & 3.0836 & 0.001267 \tabularnewline
18 & 0.315032 & 3.4654 & 0.000367 \tabularnewline
19 & 0.247383 & 2.7212 & 0.003732 \tabularnewline
20 & 0.326021 & 3.5862 & 0.000243 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112326&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]0.675912[/C][C]7.435[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.556885[/C][C]6.1257[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.645902[/C][C]7.1049[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.639859[/C][C]7.0385[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.562468[/C][C]6.1871[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.599942[/C][C]6.5994[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.474346[/C][C]5.2178[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.504007[/C][C]5.5441[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.419005[/C][C]4.6091[/C][C]5e-06[/C][/ROW]
[ROW][C]10[/C][C]0.273121[/C][C]3.0043[/C][C]0.001618[/C][/ROW]
[ROW][C]11[/C][C]0.373738[/C][C]4.1111[/C][C]3.6e-05[/C][/ROW]
[ROW][C]12[/C][C]0.571768[/C][C]6.2895[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.302195[/C][C]3.3241[/C][C]0.000587[/C][/ROW]
[ROW][C]14[/C][C]0.22069[/C][C]2.4276[/C][C]0.008336[/C][/ROW]
[ROW][C]15[/C][C]0.271414[/C][C]2.9856[/C][C]0.001713[/C][/ROW]
[ROW][C]16[/C][C]0.294124[/C][C]3.2354[/C][C]0.000783[/C][/ROW]
[ROW][C]17[/C][C]0.28033[/C][C]3.0836[/C][C]0.001267[/C][/ROW]
[ROW][C]18[/C][C]0.315032[/C][C]3.4654[/C][C]0.000367[/C][/ROW]
[ROW][C]19[/C][C]0.247383[/C][C]2.7212[/C][C]0.003732[/C][/ROW]
[ROW][C]20[/C][C]0.326021[/C][C]3.5862[/C][C]0.000243[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112326&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112326&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
10.6759127.4350
20.5568856.12570
30.6459027.10490
40.6398597.03850
50.5624686.18710
60.5999426.59940
70.4743465.21780
80.5040075.54410
90.4190054.60915e-06
100.2731213.00430.001618
110.3737384.11113.6e-05
120.5717686.28950
130.3021953.32410.000587
140.220692.42760.008336
150.2714142.98560.001713
160.2941243.23540.000783
170.280333.08360.001267
180.3150323.46540.000367
190.2473832.72120.003732
200.3260213.58620.000243







Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
10.6759127.4350
20.1841642.02580.022492
30.408484.49338e-06
40.1808451.98930.024462
50.0591560.65070.258231
60.1814381.99580.0241
7-0.250289-2.75320.003406
80.1734081.90750.029414
9-0.327107-3.59820.000233
10-0.250011-2.75010.003436
110.2606522.86720.002443
120.4775455.2530
13-0.27609-3.0370.001464
14-0.122158-1.34370.090775
15-0.151872-1.67060.048694
160.1398031.53780.06335
170.1221471.34360.090793
180.088120.96930.16716
190.0933261.02660.153331
200.0273180.30050.382157

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.675912 & 7.435 & 0 \tabularnewline
2 & 0.184164 & 2.0258 & 0.022492 \tabularnewline
3 & 0.40848 & 4.4933 & 8e-06 \tabularnewline
4 & 0.180845 & 1.9893 & 0.024462 \tabularnewline
5 & 0.059156 & 0.6507 & 0.258231 \tabularnewline
6 & 0.181438 & 1.9958 & 0.0241 \tabularnewline
7 & -0.250289 & -2.7532 & 0.003406 \tabularnewline
8 & 0.173408 & 1.9075 & 0.029414 \tabularnewline
9 & -0.327107 & -3.5982 & 0.000233 \tabularnewline
10 & -0.250011 & -2.7501 & 0.003436 \tabularnewline
11 & 0.260652 & 2.8672 & 0.002443 \tabularnewline
12 & 0.477545 & 5.253 & 0 \tabularnewline
13 & -0.27609 & -3.037 & 0.001464 \tabularnewline
14 & -0.122158 & -1.3437 & 0.090775 \tabularnewline
15 & -0.151872 & -1.6706 & 0.048694 \tabularnewline
16 & 0.139803 & 1.5378 & 0.06335 \tabularnewline
17 & 0.122147 & 1.3436 & 0.090793 \tabularnewline
18 & 0.08812 & 0.9693 & 0.16716 \tabularnewline
19 & 0.093326 & 1.0266 & 0.153331 \tabularnewline
20 & 0.027318 & 0.3005 & 0.382157 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112326&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]0.675912[/C][C]7.435[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.184164[/C][C]2.0258[/C][C]0.022492[/C][/ROW]
[ROW][C]3[/C][C]0.40848[/C][C]4.4933[/C][C]8e-06[/C][/ROW]
[ROW][C]4[/C][C]0.180845[/C][C]1.9893[/C][C]0.024462[/C][/ROW]
[ROW][C]5[/C][C]0.059156[/C][C]0.6507[/C][C]0.258231[/C][/ROW]
[ROW][C]6[/C][C]0.181438[/C][C]1.9958[/C][C]0.0241[/C][/ROW]
[ROW][C]7[/C][C]-0.250289[/C][C]-2.7532[/C][C]0.003406[/C][/ROW]
[ROW][C]8[/C][C]0.173408[/C][C]1.9075[/C][C]0.029414[/C][/ROW]
[ROW][C]9[/C][C]-0.327107[/C][C]-3.5982[/C][C]0.000233[/C][/ROW]
[ROW][C]10[/C][C]-0.250011[/C][C]-2.7501[/C][C]0.003436[/C][/ROW]
[ROW][C]11[/C][C]0.260652[/C][C]2.8672[/C][C]0.002443[/C][/ROW]
[ROW][C]12[/C][C]0.477545[/C][C]5.253[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]-0.27609[/C][C]-3.037[/C][C]0.001464[/C][/ROW]
[ROW][C]14[/C][C]-0.122158[/C][C]-1.3437[/C][C]0.090775[/C][/ROW]
[ROW][C]15[/C][C]-0.151872[/C][C]-1.6706[/C][C]0.048694[/C][/ROW]
[ROW][C]16[/C][C]0.139803[/C][C]1.5378[/C][C]0.06335[/C][/ROW]
[ROW][C]17[/C][C]0.122147[/C][C]1.3436[/C][C]0.090793[/C][/ROW]
[ROW][C]18[/C][C]0.08812[/C][C]0.9693[/C][C]0.16716[/C][/ROW]
[ROW][C]19[/C][C]0.093326[/C][C]1.0266[/C][C]0.153331[/C][/ROW]
[ROW][C]20[/C][C]0.027318[/C][C]0.3005[/C][C]0.382157[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112326&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112326&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
10.6759127.4350
20.1841642.02580.022492
30.408484.49338e-06
40.1808451.98930.024462
50.0591560.65070.258231
60.1814381.99580.0241
7-0.250289-2.75320.003406
80.1734081.90750.029414
9-0.327107-3.59820.000233
10-0.250011-2.75010.003436
110.2606522.86720.002443
120.4775455.2530
13-0.27609-3.0370.001464
14-0.122158-1.34370.090775
15-0.151872-1.67060.048694
160.1398031.53780.06335
170.1221471.34360.090793
180.088120.96930.16716
190.0933261.02660.153331
200.0273180.30050.382157



Parameters (Session):
par1 = Default ; par2 = -0.6 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;
Parameters (R input):
par1 = Default ; par2 = -0.6 ; 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')