Free Statistics

of Irreproducible Research!

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 computationThu, 01 Dec 2011 11:11:16 -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/01/t1322755892887c510a7322xq3.htm/, Retrieved Thu, 28 Mar 2024 15:24:41 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=149845, Retrieved Thu, 28 Mar 2024 15:24:41 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact119
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         [Spectral Analysis] [Births] [2010-11-29 09:38:20] [b98453cac15ba1066b407e146608df68]
- R  D          [Spectral Analysis] [WS9 3.2 CP d=0, D=0] [2010-12-07 10:39:32] [afe9379cca749d06b3d6872e02cc47ed]
- R P             [Spectral Analysis] [] [2011-12-01 15:46:44] [c53df38315e3cbde2dbe0de809195ef2]
- RM                  [(Partial) Autocorrelation Function] [] [2011-12-01 16:11:16] [ff205c8f94ca61ac7cf7eb30cad83105] [Current]
Feedback Forum

Post a new message
Dataseries X:
12008
9169
8788
8417
8247
8197
8236
8253
7733
8366
8626
8863
10102
8463
9114
8563
8872
8301
8301
8278
7736
7973
8268
9476
11100
8962
9173
8738
8459
8078
8411
8291
7810
8616
8312
9692
9911
8915
9452
9112
8472
8230
8384
8625
8221
8649
8625
10443
10357
8586
8892
8329
8101
7922
8120
7838
7735
8406
8209
9451
10041
9411
10405
8467
8464
8102
7627
7513
7510
8291
8064
9383
9706
8579
9474
8318
8213
8059
9111
7708
7680
8014
8007
8718
9486
9113
9025
8476
7952
7759
7835
7600
7651
8319
8812
8630




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'AstonUniversity' @ aston.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 & 2 seconds \tabularnewline
R Server & 'AstonUniversity' @ aston.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=149845&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]'AstonUniversity' @ aston.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=149845&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=149845&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'AstonUniversity' @ aston.wessa.net







Autocorrelation Function
Time lag kACF(k)T-STATP-value
10.4456794.36671.6e-05
20.2386352.33810.010728
3-0.010388-0.10180.459571
4-0.268135-2.62720.005012
5-0.352368-3.45250.000414
6-0.405123-3.96947e-05
7-0.32367-3.17130.001019
8-0.295987-2.90010.002312
9-0.014715-0.14420.442833
100.1609721.57720.05902
110.3223343.15820.001061
120.6446096.31590
130.311073.04780.001489
140.2497922.44740.008102
150.0339150.33230.370193
16-0.170795-1.67340.048748
17-0.284227-2.78480.003226
18-0.361752-3.54440.000305
19-0.307704-3.01490.001645

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.445679 & 4.3667 & 1.6e-05 \tabularnewline
2 & 0.238635 & 2.3381 & 0.010728 \tabularnewline
3 & -0.010388 & -0.1018 & 0.459571 \tabularnewline
4 & -0.268135 & -2.6272 & 0.005012 \tabularnewline
5 & -0.352368 & -3.4525 & 0.000414 \tabularnewline
6 & -0.405123 & -3.9694 & 7e-05 \tabularnewline
7 & -0.32367 & -3.1713 & 0.001019 \tabularnewline
8 & -0.295987 & -2.9001 & 0.002312 \tabularnewline
9 & -0.014715 & -0.1442 & 0.442833 \tabularnewline
10 & 0.160972 & 1.5772 & 0.05902 \tabularnewline
11 & 0.322334 & 3.1582 & 0.001061 \tabularnewline
12 & 0.644609 & 6.3159 & 0 \tabularnewline
13 & 0.31107 & 3.0478 & 0.001489 \tabularnewline
14 & 0.249792 & 2.4474 & 0.008102 \tabularnewline
15 & 0.033915 & 0.3323 & 0.370193 \tabularnewline
16 & -0.170795 & -1.6734 & 0.048748 \tabularnewline
17 & -0.284227 & -2.7848 & 0.003226 \tabularnewline
18 & -0.361752 & -3.5444 & 0.000305 \tabularnewline
19 & -0.307704 & -3.0149 & 0.001645 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=149845&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]0.445679[/C][C]4.3667[/C][C]1.6e-05[/C][/ROW]
[ROW][C]2[/C][C]0.238635[/C][C]2.3381[/C][C]0.010728[/C][/ROW]
[ROW][C]3[/C][C]-0.010388[/C][C]-0.1018[/C][C]0.459571[/C][/ROW]
[ROW][C]4[/C][C]-0.268135[/C][C]-2.6272[/C][C]0.005012[/C][/ROW]
[ROW][C]5[/C][C]-0.352368[/C][C]-3.4525[/C][C]0.000414[/C][/ROW]
[ROW][C]6[/C][C]-0.405123[/C][C]-3.9694[/C][C]7e-05[/C][/ROW]
[ROW][C]7[/C][C]-0.32367[/C][C]-3.1713[/C][C]0.001019[/C][/ROW]
[ROW][C]8[/C][C]-0.295987[/C][C]-2.9001[/C][C]0.002312[/C][/ROW]
[ROW][C]9[/C][C]-0.014715[/C][C]-0.1442[/C][C]0.442833[/C][/ROW]
[ROW][C]10[/C][C]0.160972[/C][C]1.5772[/C][C]0.05902[/C][/ROW]
[ROW][C]11[/C][C]0.322334[/C][C]3.1582[/C][C]0.001061[/C][/ROW]
[ROW][C]12[/C][C]0.644609[/C][C]6.3159[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.31107[/C][C]3.0478[/C][C]0.001489[/C][/ROW]
[ROW][C]14[/C][C]0.249792[/C][C]2.4474[/C][C]0.008102[/C][/ROW]
[ROW][C]15[/C][C]0.033915[/C][C]0.3323[/C][C]0.370193[/C][/ROW]
[ROW][C]16[/C][C]-0.170795[/C][C]-1.6734[/C][C]0.048748[/C][/ROW]
[ROW][C]17[/C][C]-0.284227[/C][C]-2.7848[/C][C]0.003226[/C][/ROW]
[ROW][C]18[/C][C]-0.361752[/C][C]-3.5444[/C][C]0.000305[/C][/ROW]
[ROW][C]19[/C][C]-0.307704[/C][C]-3.0149[/C][C]0.001645[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=149845&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=149845&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
10.4456794.36671.6e-05
20.2386352.33810.010728
3-0.010388-0.10180.459571
4-0.268135-2.62720.005012
5-0.352368-3.45250.000414
6-0.405123-3.96947e-05
7-0.32367-3.17130.001019
8-0.295987-2.90010.002312
9-0.014715-0.14420.442833
100.1609721.57720.05902
110.3223343.15820.001061
120.6446096.31590
130.311073.04780.001489
140.2497922.44740.008102
150.0339150.33230.370193
16-0.170795-1.67340.048748
17-0.284227-2.78480.003226
18-0.361752-3.54440.000305
19-0.307704-3.01490.001645







Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
10.4456794.36671.6e-05
20.0499210.48910.312935
3-0.167234-1.63850.05229
4-0.280467-2.7480.003581
5-0.155827-1.52680.065051
6-0.176867-1.73290.043159
7-0.097218-0.95250.171608
8-0.225464-2.20910.014774
90.0910480.89210.187288
100.0566480.5550.290082
110.1100861.07860.14173
120.471524.61996e-06
13-0.230962-2.2630.012946
140.113361.11070.134736
150.025760.25240.400637
16-0.005459-0.05350.478729
170.0183410.17970.428881
18-0.056239-0.5510.291447
19-0.017588-0.17230.431773

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.445679 & 4.3667 & 1.6e-05 \tabularnewline
2 & 0.049921 & 0.4891 & 0.312935 \tabularnewline
3 & -0.167234 & -1.6385 & 0.05229 \tabularnewline
4 & -0.280467 & -2.748 & 0.003581 \tabularnewline
5 & -0.155827 & -1.5268 & 0.065051 \tabularnewline
6 & -0.176867 & -1.7329 & 0.043159 \tabularnewline
7 & -0.097218 & -0.9525 & 0.171608 \tabularnewline
8 & -0.225464 & -2.2091 & 0.014774 \tabularnewline
9 & 0.091048 & 0.8921 & 0.187288 \tabularnewline
10 & 0.056648 & 0.555 & 0.290082 \tabularnewline
11 & 0.110086 & 1.0786 & 0.14173 \tabularnewline
12 & 0.47152 & 4.6199 & 6e-06 \tabularnewline
13 & -0.230962 & -2.263 & 0.012946 \tabularnewline
14 & 0.11336 & 1.1107 & 0.134736 \tabularnewline
15 & 0.02576 & 0.2524 & 0.400637 \tabularnewline
16 & -0.005459 & -0.0535 & 0.478729 \tabularnewline
17 & 0.018341 & 0.1797 & 0.428881 \tabularnewline
18 & -0.056239 & -0.551 & 0.291447 \tabularnewline
19 & -0.017588 & -0.1723 & 0.431773 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=149845&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]0.445679[/C][C]4.3667[/C][C]1.6e-05[/C][/ROW]
[ROW][C]2[/C][C]0.049921[/C][C]0.4891[/C][C]0.312935[/C][/ROW]
[ROW][C]3[/C][C]-0.167234[/C][C]-1.6385[/C][C]0.05229[/C][/ROW]
[ROW][C]4[/C][C]-0.280467[/C][C]-2.748[/C][C]0.003581[/C][/ROW]
[ROW][C]5[/C][C]-0.155827[/C][C]-1.5268[/C][C]0.065051[/C][/ROW]
[ROW][C]6[/C][C]-0.176867[/C][C]-1.7329[/C][C]0.043159[/C][/ROW]
[ROW][C]7[/C][C]-0.097218[/C][C]-0.9525[/C][C]0.171608[/C][/ROW]
[ROW][C]8[/C][C]-0.225464[/C][C]-2.2091[/C][C]0.014774[/C][/ROW]
[ROW][C]9[/C][C]0.091048[/C][C]0.8921[/C][C]0.187288[/C][/ROW]
[ROW][C]10[/C][C]0.056648[/C][C]0.555[/C][C]0.290082[/C][/ROW]
[ROW][C]11[/C][C]0.110086[/C][C]1.0786[/C][C]0.14173[/C][/ROW]
[ROW][C]12[/C][C]0.47152[/C][C]4.6199[/C][C]6e-06[/C][/ROW]
[ROW][C]13[/C][C]-0.230962[/C][C]-2.263[/C][C]0.012946[/C][/ROW]
[ROW][C]14[/C][C]0.11336[/C][C]1.1107[/C][C]0.134736[/C][/ROW]
[ROW][C]15[/C][C]0.02576[/C][C]0.2524[/C][C]0.400637[/C][/ROW]
[ROW][C]16[/C][C]-0.005459[/C][C]-0.0535[/C][C]0.478729[/C][/ROW]
[ROW][C]17[/C][C]0.018341[/C][C]0.1797[/C][C]0.428881[/C][/ROW]
[ROW][C]18[/C][C]-0.056239[/C][C]-0.551[/C][C]0.291447[/C][/ROW]
[ROW][C]19[/C][C]-0.017588[/C][C]-0.1723[/C][C]0.431773[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=149845&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=149845&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
10.4456794.36671.6e-05
20.0499210.48910.312935
3-0.167234-1.63850.05229
4-0.280467-2.7480.003581
5-0.155827-1.52680.065051
6-0.176867-1.73290.043159
7-0.097218-0.95250.171608
8-0.225464-2.20910.014774
90.0910480.89210.187288
100.0566480.5550.290082
110.1100861.07860.14173
120.471524.61996e-06
13-0.230962-2.2630.012946
140.113361.11070.134736
150.025760.25240.400637
16-0.005459-0.05350.478729
170.0183410.17970.428881
18-0.056239-0.5510.291447
19-0.017588-0.17230.431773



Parameters (Session):
par1 = 0 ;
Parameters (R input):
par1 = Default ; par2 = 1.0 ; 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')