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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Mon, 17 Oct 2016 15:45:32 +0100

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Oct/17/t1476715558m22a3zcyd9gm3vp.htm/, Retrieved Sun, 05 May 2024 04:19:52 +0200

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Sun, 05 May 2024 04:19:52 +0200

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Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	'Sir Maurice George Kendall' @ kendall.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 & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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 Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	'Sir Maurice George Kendall' @ kendall.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.144397	1.1091	0.135936
2	0.010036	0.0771	0.469407
3	-0.103079	-0.7918	0.215835
4	-0.103215	-0.7928	0.215533
5	-0.008524	-0.0655	0.474009
6	-0.131579	-1.0107	0.158149
7	-0.032698	-0.2512	0.401283
8	-0.147117	-1.13	0.131519
9	-0.156083	-1.1989	0.117681
10	-0.009767	-0.075	0.470226
11	0.097408	0.7482	0.228654
12	0.107752	0.8277	0.2056
13	0.106642	0.8191	0.208005
14	-0.060668	-0.466	0.321467
15	-0.061692	-0.4739	0.318672
16	-0.082535	-0.634	0.264278
17	-0.004624	-0.0355	0.485895

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.144397 & 1.1091 & 0.135936 \tabularnewline
2 & 0.010036 & 0.0771 & 0.469407 \tabularnewline
3 & -0.103079 & -0.7918 & 0.215835 \tabularnewline
4 & -0.103215 & -0.7928 & 0.215533 \tabularnewline
5 & -0.008524 & -0.0655 & 0.474009 \tabularnewline
6 & -0.131579 & -1.0107 & 0.158149 \tabularnewline
7 & -0.032698 & -0.2512 & 0.401283 \tabularnewline
8 & -0.147117 & -1.13 & 0.131519 \tabularnewline
9 & -0.156083 & -1.1989 & 0.117681 \tabularnewline
10 & -0.009767 & -0.075 & 0.470226 \tabularnewline
11 & 0.097408 & 0.7482 & 0.228654 \tabularnewline
12 & 0.107752 & 0.8277 & 0.2056 \tabularnewline
13 & 0.106642 & 0.8191 & 0.208005 \tabularnewline
14 & -0.060668 & -0.466 & 0.321467 \tabularnewline
15 & -0.061692 & -0.4739 & 0.318672 \tabularnewline
16 & -0.082535 & -0.634 & 0.264278 \tabularnewline
17 & -0.004624 & -0.0355 & 0.485895 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]0.144397[/C][C]1.1091[/C][C]0.135936[/C][/ROW]
[ROW][C]2[/C][C]0.010036[/C][C]0.0771[/C][C]0.469407[/C][/ROW]
[ROW][C]3[/C][C]-0.103079[/C][C]-0.7918[/C][C]0.215835[/C][/ROW]
[ROW][C]4[/C][C]-0.103215[/C][C]-0.7928[/C][C]0.215533[/C][/ROW]
[ROW][C]5[/C][C]-0.008524[/C][C]-0.0655[/C][C]0.474009[/C][/ROW]
[ROW][C]6[/C][C]-0.131579[/C][C]-1.0107[/C][C]0.158149[/C][/ROW]
[ROW][C]7[/C][C]-0.032698[/C][C]-0.2512[/C][C]0.401283[/C][/ROW]
[ROW][C]8[/C][C]-0.147117[/C][C]-1.13[/C][C]0.131519[/C][/ROW]
[ROW][C]9[/C][C]-0.156083[/C][C]-1.1989[/C][C]0.117681[/C][/ROW]
[ROW][C]10[/C][C]-0.009767[/C][C]-0.075[/C][C]0.470226[/C][/ROW]
[ROW][C]11[/C][C]0.097408[/C][C]0.7482[/C][C]0.228654[/C][/ROW]
[ROW][C]12[/C][C]0.107752[/C][C]0.8277[/C][C]0.2056[/C][/ROW]
[ROW][C]13[/C][C]0.106642[/C][C]0.8191[/C][C]0.208005[/C][/ROW]
[ROW][C]14[/C][C]-0.060668[/C][C]-0.466[/C][C]0.321467[/C][/ROW]
[ROW][C]15[/C][C]-0.061692[/C][C]-0.4739[/C][C]0.318672[/C][/ROW]
[ROW][C]16[/C][C]-0.082535[/C][C]-0.634[/C][C]0.264278[/C][/ROW]
[ROW][C]17[/C][C]-0.004624[/C][C]-0.0355[/C][C]0.485895[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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 k	ACF(k)	T-STAT	P-value
1	0.144397	1.1091	0.135936
2	0.010036	0.0771	0.469407
3	-0.103079	-0.7918	0.215835
4	-0.103215	-0.7928	0.215533
5	-0.008524	-0.0655	0.474009
6	-0.131579	-1.0107	0.158149
7	-0.032698	-0.2512	0.401283
8	-0.147117	-1.13	0.131519
9	-0.156083	-1.1989	0.117681
10	-0.009767	-0.075	0.470226
11	0.097408	0.7482	0.228654
12	0.107752	0.8277	0.2056
13	0.106642	0.8191	0.208005
14	-0.060668	-0.466	0.321467
15	-0.061692	-0.4739	0.318672
16	-0.082535	-0.634	0.264278
17	-0.004624	-0.0355	0.485895

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.144397	1.1091	0.135936
2	-0.011045	-0.0848	0.466339
3	-0.105155	-0.8077	0.211252
4	-0.075547	-0.5803	0.281965
5	0.018632	0.1431	0.443344
6	-0.1469	-1.1284	0.131868
7	-0.013254	-0.1018	0.459628
8	-0.153849	-1.1817	0.121025
9	-0.154233	-1.1847	0.120446
10	-0.004507	-0.0346	0.486251
11	0.068651	0.5273	0.299974
12	0.007249	0.0557	0.477892
13	0.067677	0.5198	0.302562
14	-0.112139	-0.8614	0.196264
15	-0.068183	-0.5237	0.301217
16	-0.076718	-0.5893	0.27896
17	-0.012821	-0.0985	0.460942

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.144397 & 1.1091 & 0.135936 \tabularnewline
2 & -0.011045 & -0.0848 & 0.466339 \tabularnewline
3 & -0.105155 & -0.8077 & 0.211252 \tabularnewline
4 & -0.075547 & -0.5803 & 0.281965 \tabularnewline
5 & 0.018632 & 0.1431 & 0.443344 \tabularnewline
6 & -0.1469 & -1.1284 & 0.131868 \tabularnewline
7 & -0.013254 & -0.1018 & 0.459628 \tabularnewline
8 & -0.153849 & -1.1817 & 0.121025 \tabularnewline
9 & -0.154233 & -1.1847 & 0.120446 \tabularnewline
10 & -0.004507 & -0.0346 & 0.486251 \tabularnewline
11 & 0.068651 & 0.5273 & 0.299974 \tabularnewline
12 & 0.007249 & 0.0557 & 0.477892 \tabularnewline
13 & 0.067677 & 0.5198 & 0.302562 \tabularnewline
14 & -0.112139 & -0.8614 & 0.196264 \tabularnewline
15 & -0.068183 & -0.5237 & 0.301217 \tabularnewline
16 & -0.076718 & -0.5893 & 0.27896 \tabularnewline
17 & -0.012821 & -0.0985 & 0.460942 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]0.144397[/C][C]1.1091[/C][C]0.135936[/C][/ROW]
[ROW][C]2[/C][C]-0.011045[/C][C]-0.0848[/C][C]0.466339[/C][/ROW]
[ROW][C]3[/C][C]-0.105155[/C][C]-0.8077[/C][C]0.211252[/C][/ROW]
[ROW][C]4[/C][C]-0.075547[/C][C]-0.5803[/C][C]0.281965[/C][/ROW]
[ROW][C]5[/C][C]0.018632[/C][C]0.1431[/C][C]0.443344[/C][/ROW]
[ROW][C]6[/C][C]-0.1469[/C][C]-1.1284[/C][C]0.131868[/C][/ROW]
[ROW][C]7[/C][C]-0.013254[/C][C]-0.1018[/C][C]0.459628[/C][/ROW]
[ROW][C]8[/C][C]-0.153849[/C][C]-1.1817[/C][C]0.121025[/C][/ROW]
[ROW][C]9[/C][C]-0.154233[/C][C]-1.1847[/C][C]0.120446[/C][/ROW]
[ROW][C]10[/C][C]-0.004507[/C][C]-0.0346[/C][C]0.486251[/C][/ROW]
[ROW][C]11[/C][C]0.068651[/C][C]0.5273[/C][C]0.299974[/C][/ROW]
[ROW][C]12[/C][C]0.007249[/C][C]0.0557[/C][C]0.477892[/C][/ROW]
[ROW][C]13[/C][C]0.067677[/C][C]0.5198[/C][C]0.302562[/C][/ROW]
[ROW][C]14[/C][C]-0.112139[/C][C]-0.8614[/C][C]0.196264[/C][/ROW]
[ROW][C]15[/C][C]-0.068183[/C][C]-0.5237[/C][C]0.301217[/C][/ROW]
[ROW][C]16[/C][C]-0.076718[/C][C]-0.5893[/C][C]0.27896[/C][/ROW]
[ROW][C]17[/C][C]-0.012821[/C][C]-0.0985[/C][C]0.460942[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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 k	PACF(k)	T-STAT	P-value
1	0.144397	1.1091	0.135936
2	-0.011045	-0.0848	0.466339
3	-0.105155	-0.8077	0.211252
4	-0.075547	-0.5803	0.281965
5	0.018632	0.1431	0.443344
6	-0.1469	-1.1284	0.131868
7	-0.013254	-0.1018	0.459628
8	-0.153849	-1.1817	0.121025
9	-0.154233	-1.1847	0.120446
10	-0.004507	-0.0346	0.486251
11	0.068651	0.5273	0.299974
12	0.007249	0.0557	0.477892
13	0.067677	0.5198	0.302562
14	-0.112139	-0.8614	0.196264
15	-0.068183	-0.5237	0.301217
16	-0.076718	-0.5893	0.27896
17	-0.012821	-0.0985	0.460942

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; 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)
x <- na.omit(x)
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')

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Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code