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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 computationThu, 22 Dec 2011 19:36:23 -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/22/t1324600609mb01t4ofxt8pm1c.htm/, Retrieved Fri, 03 May 2024 07:52:39 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=160118, Retrieved Fri, 03 May 2024 07:52:39 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact118

Tree of Dependent Computations

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         [(Partial) Autocorrelation Function] [Births] [2010-11-29 09:36:27] [b98453cac15ba1066b407e146608df68]
- R PD          [(Partial) Autocorrelation Function] [WS9 3.1 ACF d=0, D=0] [2010-12-07 10:00:49] [afe9379cca749d06b3d6872e02cc47ed]
- R PD            [(Partial) Autocorrelation Function] [PAPER: aantal fai...] [2011-12-22 23:47:48] [f0cb027b41af06223bae4ee77475f3bc]
-    D                [(Partial) Autocorrelation Function] [PAPER: inflatie] [2011-12-23 00:36:23] [6baf48ba14bcb50d9e72b77bece8a45b] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
0.0213
0.0218
0.0290
0.0263
0.0267
0.0181
0.0133
0.0088
0.0128
0.0126
0.0126
0.0129
0.0110
0.0137
0.0121
0.0174
0.0176
0.0148
0.0104
0.0162
0.0149
0.0179
0.0180
0.0158
0.0186
0.0174
0.0159
0.0126
0.0113
0.0192
0.0261
0.0226
0.0241
0.0226
0.0203
0.0286
0.0255
0.0227
0.0226
0.0257
0.0307
0.0276
0.0251
0.0287
0.0314
0.0311
0.0316
0.0247
0.0257
0.0289
0.0263
0.0238
0.0169
0.0196
0.0219
0.0187
0.0160
0.0163
0.0122
0.0121
0.0149
0.0164
0.0166
0.0177
0.0182
0.0178
0.0128
0.0129
0.0137
0.0112
0.0151
0.0224
0.0294
0.0309
0.0346
0.0364
0.0439
0.0415
0.0521
0.0580
0.0591
0.0539
0.0546
0.0472
0.0314
0.0263
0.0232
0.0193
0.0062
0.0060
-0.0037
-0.0110
-0.0168
-0.0078
-0.0119
-0.0097
-0.0012
0.0026
0.0062
0.0070
0.0166
0.0180
0.0227
0.0246
0.0257
0.0232
0.0291
0.0301
0.0286
0.0310
0.0322
0.0339
0.0352
0.0341
0.0335
0.0367
0.0375
0.0360
0.0355
0.0357

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' @ jenkins.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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160118&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' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160118&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160118&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' @ jenkins.wessa.net






Autocorrelation Function
Time lag kACF(k)T-STATP-value
1-0.481198-5.22710
2-0.006306-0.06850.472751
3-0.067006-0.72790.234067
40.1949852.11810.018133
5-0.162809-1.76860.039776
60.0327950.35620.361147
70.079040.85860.196152
8-0.065911-0.7160.237709
9-0.011478-0.12470.450492
10-0.122036-1.32560.093759
110.4716455.12341e-06
12-0.59179-6.42850
130.1762381.91440.028993
140.047180.51250.304628
150.0912040.99070.161923
16-0.171573-1.86380.03242
170.0930021.01030.157219
18-0.066049-0.71750.237248
190.0944431.02590.153514
20-0.059793-0.64950.258634

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.481198 & -5.2271 & 0 \tabularnewline
2 & -0.006306 & -0.0685 & 0.472751 \tabularnewline
3 & -0.067006 & -0.7279 & 0.234067 \tabularnewline
4 & 0.194985 & 2.1181 & 0.018133 \tabularnewline
5 & -0.162809 & -1.7686 & 0.039776 \tabularnewline
6 & 0.032795 & 0.3562 & 0.361147 \tabularnewline
7 & 0.07904 & 0.8586 & 0.196152 \tabularnewline
8 & -0.065911 & -0.716 & 0.237709 \tabularnewline
9 & -0.011478 & -0.1247 & 0.450492 \tabularnewline
10 & -0.122036 & -1.3256 & 0.093759 \tabularnewline
11 & 0.471645 & 5.1234 & 1e-06 \tabularnewline
12 & -0.59179 & -6.4285 & 0 \tabularnewline
13 & 0.176238 & 1.9144 & 0.028993 \tabularnewline
14 & 0.04718 & 0.5125 & 0.304628 \tabularnewline
15 & 0.091204 & 0.9907 & 0.161923 \tabularnewline
16 & -0.171573 & -1.8638 & 0.03242 \tabularnewline
17 & 0.093002 & 1.0103 & 0.157219 \tabularnewline
18 & -0.066049 & -0.7175 & 0.237248 \tabularnewline
19 & 0.094443 & 1.0259 & 0.153514 \tabularnewline
20 & -0.059793 & -0.6495 & 0.258634 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160118&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]-0.481198[/C][C]-5.2271[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.006306[/C][C]-0.0685[/C][C]0.472751[/C][/ROW]
[ROW][C]3[/C][C]-0.067006[/C][C]-0.7279[/C][C]0.234067[/C][/ROW]
[ROW][C]4[/C][C]0.194985[/C][C]2.1181[/C][C]0.018133[/C][/ROW]
[ROW][C]5[/C][C]-0.162809[/C][C]-1.7686[/C][C]0.039776[/C][/ROW]
[ROW][C]6[/C][C]0.032795[/C][C]0.3562[/C][C]0.361147[/C][/ROW]
[ROW][C]7[/C][C]0.07904[/C][C]0.8586[/C][C]0.196152[/C][/ROW]
[ROW][C]8[/C][C]-0.065911[/C][C]-0.716[/C][C]0.237709[/C][/ROW]
[ROW][C]9[/C][C]-0.011478[/C][C]-0.1247[/C][C]0.450492[/C][/ROW]
[ROW][C]10[/C][C]-0.122036[/C][C]-1.3256[/C][C]0.093759[/C][/ROW]
[ROW][C]11[/C][C]0.471645[/C][C]5.1234[/C][C]1e-06[/C][/ROW]
[ROW][C]12[/C][C]-0.59179[/C][C]-6.4285[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.176238[/C][C]1.9144[/C][C]0.028993[/C][/ROW]
[ROW][C]14[/C][C]0.04718[/C][C]0.5125[/C][C]0.304628[/C][/ROW]
[ROW][C]15[/C][C]0.091204[/C][C]0.9907[/C][C]0.161923[/C][/ROW]
[ROW][C]16[/C][C]-0.171573[/C][C]-1.8638[/C][C]0.03242[/C][/ROW]
[ROW][C]17[/C][C]0.093002[/C][C]1.0103[/C][C]0.157219[/C][/ROW]
[ROW][C]18[/C][C]-0.066049[/C][C]-0.7175[/C][C]0.237248[/C][/ROW]
[ROW][C]19[/C][C]0.094443[/C][C]1.0259[/C][C]0.153514[/C][/ROW]
[ROW][C]20[/C][C]-0.059793[/C][C]-0.6495[/C][C]0.258634[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160118&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160118&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
1-0.481198-5.22710
2-0.006306-0.06850.472751
3-0.067006-0.72790.234067
40.1949852.11810.018133
5-0.162809-1.76860.039776
60.0327950.35620.361147
70.079040.85860.196152
8-0.065911-0.7160.237709
9-0.011478-0.12470.450492
10-0.122036-1.32560.093759
110.4716455.12341e-06
12-0.59179-6.42850
130.1762381.91440.028993
140.047180.51250.304628
150.0912040.99070.161923
16-0.171573-1.86380.03242
170.0930021.01030.157219
18-0.066049-0.71750.237248
190.0944431.02590.153514
20-0.059793-0.64950.258634






Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
1-0.481198-5.22710
2-0.309529-3.36230.000521
3-0.316518-3.43830.000405
4-0.014908-0.16190.435815
5-0.102018-1.10820.135016
6-0.088353-0.95980.16957
70.0658480.71530.23792
8-0.018296-0.19870.421403
9-0.01105-0.120.452332
10-0.237479-2.57970.005558
110.4083734.43611e-05
12-0.308048-3.34630.00055
13-0.242001-2.62880.004854
14-0.089822-0.97570.165601
15-0.162078-1.76060.040447
160.0065020.07060.471907
17-0.10216-1.10970.134683
18-0.217857-2.36650.009792
190.1019041.1070.135281
20-0.042863-0.46560.321175

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.481198 & -5.2271 & 0 \tabularnewline
2 & -0.309529 & -3.3623 & 0.000521 \tabularnewline
3 & -0.316518 & -3.4383 & 0.000405 \tabularnewline
4 & -0.014908 & -0.1619 & 0.435815 \tabularnewline
5 & -0.102018 & -1.1082 & 0.135016 \tabularnewline
6 & -0.088353 & -0.9598 & 0.16957 \tabularnewline
7 & 0.065848 & 0.7153 & 0.23792 \tabularnewline
8 & -0.018296 & -0.1987 & 0.421403 \tabularnewline
9 & -0.01105 & -0.12 & 0.452332 \tabularnewline
10 & -0.237479 & -2.5797 & 0.005558 \tabularnewline
11 & 0.408373 & 4.4361 & 1e-05 \tabularnewline
12 & -0.308048 & -3.3463 & 0.00055 \tabularnewline
13 & -0.242001 & -2.6288 & 0.004854 \tabularnewline
14 & -0.089822 & -0.9757 & 0.165601 \tabularnewline
15 & -0.162078 & -1.7606 & 0.040447 \tabularnewline
16 & 0.006502 & 0.0706 & 0.471907 \tabularnewline
17 & -0.10216 & -1.1097 & 0.134683 \tabularnewline
18 & -0.217857 & -2.3665 & 0.009792 \tabularnewline
19 & 0.101904 & 1.107 & 0.135281 \tabularnewline
20 & -0.042863 & -0.4656 & 0.321175 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160118&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]-0.481198[/C][C]-5.2271[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.309529[/C][C]-3.3623[/C][C]0.000521[/C][/ROW]
[ROW][C]3[/C][C]-0.316518[/C][C]-3.4383[/C][C]0.000405[/C][/ROW]
[ROW][C]4[/C][C]-0.014908[/C][C]-0.1619[/C][C]0.435815[/C][/ROW]
[ROW][C]5[/C][C]-0.102018[/C][C]-1.1082[/C][C]0.135016[/C][/ROW]
[ROW][C]6[/C][C]-0.088353[/C][C]-0.9598[/C][C]0.16957[/C][/ROW]
[ROW][C]7[/C][C]0.065848[/C][C]0.7153[/C][C]0.23792[/C][/ROW]
[ROW][C]8[/C][C]-0.018296[/C][C]-0.1987[/C][C]0.421403[/C][/ROW]
[ROW][C]9[/C][C]-0.01105[/C][C]-0.12[/C][C]0.452332[/C][/ROW]
[ROW][C]10[/C][C]-0.237479[/C][C]-2.5797[/C][C]0.005558[/C][/ROW]
[ROW][C]11[/C][C]0.408373[/C][C]4.4361[/C][C]1e-05[/C][/ROW]
[ROW][C]12[/C][C]-0.308048[/C][C]-3.3463[/C][C]0.00055[/C][/ROW]
[ROW][C]13[/C][C]-0.242001[/C][C]-2.6288[/C][C]0.004854[/C][/ROW]
[ROW][C]14[/C][C]-0.089822[/C][C]-0.9757[/C][C]0.165601[/C][/ROW]
[ROW][C]15[/C][C]-0.162078[/C][C]-1.7606[/C][C]0.040447[/C][/ROW]
[ROW][C]16[/C][C]0.006502[/C][C]0.0706[/C][C]0.471907[/C][/ROW]
[ROW][C]17[/C][C]-0.10216[/C][C]-1.1097[/C][C]0.134683[/C][/ROW]
[ROW][C]18[/C][C]-0.217857[/C][C]-2.3665[/C][C]0.009792[/C][/ROW]
[ROW][C]19[/C][C]0.101904[/C][C]1.107[/C][C]0.135281[/C][/ROW]
[ROW][C]20[/C][C]-0.042863[/C][C]-0.4656[/C][C]0.321175[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160118&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160118&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
1-0.481198-5.22710
2-0.309529-3.36230.000521
3-0.316518-3.43830.000405
4-0.014908-0.16190.435815
5-0.102018-1.10820.135016
6-0.088353-0.95980.16957
70.0658480.71530.23792
8-0.018296-0.19870.421403
9-0.01105-0.120.452332
10-0.237479-2.57970.005558
110.4083734.43611e-05
12-0.308048-3.34630.00055
13-0.242001-2.62880.004854
14-0.089822-0.97570.165601
15-0.162078-1.76060.040447
160.0065020.07060.471907
17-0.10216-1.10970.134683
18-0.217857-2.36650.009792
190.1019041.1070.135281
20-0.042863-0.46560.321175


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = multiplicative ; par2 = 12 ;
Parameters (R input):
par1 = Default ; par2 = 1 ; par3 = 2 ; 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')