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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 19:33:05 -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/t1324600408pcrhdal0zgd36fj.htm/, Retrieved Fri, 03 May 2024 10:46:38 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=160116, Retrieved Fri, 03 May 2024 10:46:38 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact126

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 00:33:05] [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'Gertrude Mary Cox' @ cox.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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160116&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160116&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160116&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'Gertrude Mary Cox' @ cox.wessa.net






Autocorrelation Function
Time lag kACF(k)T-STATP-value
10.94054210.30310
20.8585229.40460
30.7570128.29260
40.6372676.98090
50.4914135.38320
60.3451153.78050.000123
70.1919022.10220.018814
80.0331380.3630.358619
9-0.113793-1.24650.107497
10-0.244594-2.67940.004206
11-0.357487-3.91617.5e-05
12-0.470742-5.15671e-06
13-0.524228-5.74260
14-0.556102-6.09180
15-0.572516-6.27160
16-0.580009-6.35370
17-0.561576-6.15180
18-0.531907-5.82680
19-0.488197-5.34790
20-0.442765-4.85022e-06

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.940542 & 10.3031 & 0 \tabularnewline
2 & 0.858522 & 9.4046 & 0 \tabularnewline
3 & 0.757012 & 8.2926 & 0 \tabularnewline
4 & 0.637267 & 6.9809 & 0 \tabularnewline
5 & 0.491413 & 5.3832 & 0 \tabularnewline
6 & 0.345115 & 3.7805 & 0.000123 \tabularnewline
7 & 0.191902 & 2.1022 & 0.018814 \tabularnewline
8 & 0.033138 & 0.363 & 0.358619 \tabularnewline
9 & -0.113793 & -1.2465 & 0.107497 \tabularnewline
10 & -0.244594 & -2.6794 & 0.004206 \tabularnewline
11 & -0.357487 & -3.9161 & 7.5e-05 \tabularnewline
12 & -0.470742 & -5.1567 & 1e-06 \tabularnewline
13 & -0.524228 & -5.7426 & 0 \tabularnewline
14 & -0.556102 & -6.0918 & 0 \tabularnewline
15 & -0.572516 & -6.2716 & 0 \tabularnewline
16 & -0.580009 & -6.3537 & 0 \tabularnewline
17 & -0.561576 & -6.1518 & 0 \tabularnewline
18 & -0.531907 & -5.8268 & 0 \tabularnewline
19 & -0.488197 & -5.3479 & 0 \tabularnewline
20 & -0.442765 & -4.8502 & 2e-06 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160116&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]0.940542[/C][C]10.3031[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.858522[/C][C]9.4046[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.757012[/C][C]8.2926[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.637267[/C][C]6.9809[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.491413[/C][C]5.3832[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.345115[/C][C]3.7805[/C][C]0.000123[/C][/ROW]
[ROW][C]7[/C][C]0.191902[/C][C]2.1022[/C][C]0.018814[/C][/ROW]
[ROW][C]8[/C][C]0.033138[/C][C]0.363[/C][C]0.358619[/C][/ROW]
[ROW][C]9[/C][C]-0.113793[/C][C]-1.2465[/C][C]0.107497[/C][/ROW]
[ROW][C]10[/C][C]-0.244594[/C][C]-2.6794[/C][C]0.004206[/C][/ROW]
[ROW][C]11[/C][C]-0.357487[/C][C]-3.9161[/C][C]7.5e-05[/C][/ROW]
[ROW][C]12[/C][C]-0.470742[/C][C]-5.1567[/C][C]1e-06[/C][/ROW]
[ROW][C]13[/C][C]-0.524228[/C][C]-5.7426[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]-0.556102[/C][C]-6.0918[/C][C]0[/C][/ROW]
[ROW][C]15[/C][C]-0.572516[/C][C]-6.2716[/C][C]0[/C][/ROW]
[ROW][C]16[/C][C]-0.580009[/C][C]-6.3537[/C][C]0[/C][/ROW]
[ROW][C]17[/C][C]-0.561576[/C][C]-6.1518[/C][C]0[/C][/ROW]
[ROW][C]18[/C][C]-0.531907[/C][C]-5.8268[/C][C]0[/C][/ROW]
[ROW][C]19[/C][C]-0.488197[/C][C]-5.3479[/C][C]0[/C][/ROW]
[ROW][C]20[/C][C]-0.442765[/C][C]-4.8502[/C][C]2e-06[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160116&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160116&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
10.94054210.30310
20.8585229.40460
30.7570128.29260
40.6372676.98090
50.4914135.38320
60.3451153.78050.000123
70.1919022.10220.018814
80.0331380.3630.358619
9-0.113793-1.24650.107497
10-0.244594-2.67940.004206
11-0.357487-3.91617.5e-05
12-0.470742-5.15671e-06
13-0.524228-5.74260
14-0.556102-6.09180
15-0.572516-6.27160
16-0.580009-6.35370
17-0.561576-6.15180
18-0.531907-5.82680
19-0.488197-5.34790
20-0.442765-4.85022e-06






Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
10.94054210.30310
2-0.226183-2.47770.007307
3-0.186032-2.03790.02188
4-0.179417-1.96540.025838
5-0.271372-2.97270.001784
6-0.034713-0.38030.352211
7-0.144668-1.58480.057826
8-0.162462-1.77970.03883
9-0.004261-0.04670.481425
10-0.039168-0.42910.334321
11-0.007505-0.08220.467309
12-0.240453-2.6340.004775
130.3819814.18442.7e-05
14-0.093042-1.01920.155074
15-0.103706-1.1360.129101
16-0.126402-1.38470.084362
17-0.093351-1.02260.154274
180.0039250.0430.482889
19-0.058265-0.63830.262262
20-0.213393-2.33760.010532

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.940542 & 10.3031 & 0 \tabularnewline
2 & -0.226183 & -2.4777 & 0.007307 \tabularnewline
3 & -0.186032 & -2.0379 & 0.02188 \tabularnewline
4 & -0.179417 & -1.9654 & 0.025838 \tabularnewline
5 & -0.271372 & -2.9727 & 0.001784 \tabularnewline
6 & -0.034713 & -0.3803 & 0.352211 \tabularnewline
7 & -0.144668 & -1.5848 & 0.057826 \tabularnewline
8 & -0.162462 & -1.7797 & 0.03883 \tabularnewline
9 & -0.004261 & -0.0467 & 0.481425 \tabularnewline
10 & -0.039168 & -0.4291 & 0.334321 \tabularnewline
11 & -0.007505 & -0.0822 & 0.467309 \tabularnewline
12 & -0.240453 & -2.634 & 0.004775 \tabularnewline
13 & 0.381981 & 4.1844 & 2.7e-05 \tabularnewline
14 & -0.093042 & -1.0192 & 0.155074 \tabularnewline
15 & -0.103706 & -1.136 & 0.129101 \tabularnewline
16 & -0.126402 & -1.3847 & 0.084362 \tabularnewline
17 & -0.093351 & -1.0226 & 0.154274 \tabularnewline
18 & 0.003925 & 0.043 & 0.482889 \tabularnewline
19 & -0.058265 & -0.6383 & 0.262262 \tabularnewline
20 & -0.213393 & -2.3376 & 0.010532 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160116&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]0.940542[/C][C]10.3031[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.226183[/C][C]-2.4777[/C][C]0.007307[/C][/ROW]
[ROW][C]3[/C][C]-0.186032[/C][C]-2.0379[/C][C]0.02188[/C][/ROW]
[ROW][C]4[/C][C]-0.179417[/C][C]-1.9654[/C][C]0.025838[/C][/ROW]
[ROW][C]5[/C][C]-0.271372[/C][C]-2.9727[/C][C]0.001784[/C][/ROW]
[ROW][C]6[/C][C]-0.034713[/C][C]-0.3803[/C][C]0.352211[/C][/ROW]
[ROW][C]7[/C][C]-0.144668[/C][C]-1.5848[/C][C]0.057826[/C][/ROW]
[ROW][C]8[/C][C]-0.162462[/C][C]-1.7797[/C][C]0.03883[/C][/ROW]
[ROW][C]9[/C][C]-0.004261[/C][C]-0.0467[/C][C]0.481425[/C][/ROW]
[ROW][C]10[/C][C]-0.039168[/C][C]-0.4291[/C][C]0.334321[/C][/ROW]
[ROW][C]11[/C][C]-0.007505[/C][C]-0.0822[/C][C]0.467309[/C][/ROW]
[ROW][C]12[/C][C]-0.240453[/C][C]-2.634[/C][C]0.004775[/C][/ROW]
[ROW][C]13[/C][C]0.381981[/C][C]4.1844[/C][C]2.7e-05[/C][/ROW]
[ROW][C]14[/C][C]-0.093042[/C][C]-1.0192[/C][C]0.155074[/C][/ROW]
[ROW][C]15[/C][C]-0.103706[/C][C]-1.136[/C][C]0.129101[/C][/ROW]
[ROW][C]16[/C][C]-0.126402[/C][C]-1.3847[/C][C]0.084362[/C][/ROW]
[ROW][C]17[/C][C]-0.093351[/C][C]-1.0226[/C][C]0.154274[/C][/ROW]
[ROW][C]18[/C][C]0.003925[/C][C]0.043[/C][C]0.482889[/C][/ROW]
[ROW][C]19[/C][C]-0.058265[/C][C]-0.6383[/C][C]0.262262[/C][/ROW]
[ROW][C]20[/C][C]-0.213393[/C][C]-2.3376[/C][C]0.010532[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160116&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160116&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
10.94054210.30310
2-0.226183-2.47770.007307
3-0.186032-2.03790.02188
4-0.179417-1.96540.025838
5-0.271372-2.97270.001784
6-0.034713-0.38030.352211
7-0.144668-1.58480.057826
8-0.162462-1.77970.03883
9-0.004261-0.04670.481425
10-0.039168-0.42910.334321
11-0.007505-0.08220.467309
12-0.240453-2.6340.004775
130.3819814.18442.7e-05
14-0.093042-1.01920.155074
15-0.103706-1.1360.129101
16-0.126402-1.38470.084362
17-0.093351-1.02260.154274
180.0039250.0430.482889
19-0.058265-0.63830.262262
20-0.213393-2.33760.010532


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = multiplicative ; par2 = 12 ;
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')