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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 29 Dec 2010 09:19:43 +0000

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/29/t1293614260xpoh5zbn6pi0uae.htm/, Retrieved Fri, 03 May 2024 13:13:51 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=116630, Retrieved Fri, 03 May 2024 13:13:51 +0000

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137

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-     [Univariate Data Series] [] [2008-12-08 19:22:39] [d2d412c7f4d35ffbf5ee5ee89db327d4]
- RMP   [(Partial) Autocorrelation Function] [autocorrelatie ru...] [2010-12-14 18:37:20] [d6e648f00513dd750579ba7880c5fbf5]
- R  D    [(Partial) Autocorrelation Function] [] [2010-12-16 10:15:17] [b10d6b9682dfaaa479f495240bcd67cf]
-             [(Partial) Autocorrelation Function] [] [2010-12-29 09:19:43] [a3cd012a7211edfe9ed4466e21aef6a6] [Current]

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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	2 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116630&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116630&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116630&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	2 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.938205	7.0209	0
2	0.878641	6.5751	0
3	0.820805	6.1423	0
4	0.759557	5.684	0
5	0.710175	5.3145	1e-06
6	0.654281	4.8962	4e-06
7	0.601738	4.503	1.7e-05
8	0.552951	4.1379	5.9e-05
9	0.503362	3.7668	2e-04
10	0.455297	3.4071	0.000611
11	0.404096	3.024	0.00188
12	0.353657	2.6465	0.00527
13	0.301359	2.2552	0.014025
14	0.249175	1.8647	0.033737
15	0.199025	1.4894	0.071001
16	0.135068	1.0108	0.158241
17	0.075037	0.5615	0.288339

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.938205 & 7.0209 & 0 \tabularnewline
2 & 0.878641 & 6.5751 & 0 \tabularnewline
3 & 0.820805 & 6.1423 & 0 \tabularnewline
4 & 0.759557 & 5.684 & 0 \tabularnewline
5 & 0.710175 & 5.3145 & 1e-06 \tabularnewline
6 & 0.654281 & 4.8962 & 4e-06 \tabularnewline
7 & 0.601738 & 4.503 & 1.7e-05 \tabularnewline
8 & 0.552951 & 4.1379 & 5.9e-05 \tabularnewline
9 & 0.503362 & 3.7668 & 2e-04 \tabularnewline
10 & 0.455297 & 3.4071 & 0.000611 \tabularnewline
11 & 0.404096 & 3.024 & 0.00188 \tabularnewline
12 & 0.353657 & 2.6465 & 0.00527 \tabularnewline
13 & 0.301359 & 2.2552 & 0.014025 \tabularnewline
14 & 0.249175 & 1.8647 & 0.033737 \tabularnewline
15 & 0.199025 & 1.4894 & 0.071001 \tabularnewline
16 & 0.135068 & 1.0108 & 0.158241 \tabularnewline
17 & 0.075037 & 0.5615 & 0.288339 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116630&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]0.938205[/C][C]7.0209[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.878641[/C][C]6.5751[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.820805[/C][C]6.1423[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.759557[/C][C]5.684[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.710175[/C][C]5.3145[/C][C]1e-06[/C][/ROW]
[ROW][C]6[/C][C]0.654281[/C][C]4.8962[/C][C]4e-06[/C][/ROW]
[ROW][C]7[/C][C]0.601738[/C][C]4.503[/C][C]1.7e-05[/C][/ROW]
[ROW][C]8[/C][C]0.552951[/C][C]4.1379[/C][C]5.9e-05[/C][/ROW]
[ROW][C]9[/C][C]0.503362[/C][C]3.7668[/C][C]2e-04[/C][/ROW]
[ROW][C]10[/C][C]0.455297[/C][C]3.4071[/C][C]0.000611[/C][/ROW]
[ROW][C]11[/C][C]0.404096[/C][C]3.024[/C][C]0.00188[/C][/ROW]
[ROW][C]12[/C][C]0.353657[/C][C]2.6465[/C][C]0.00527[/C][/ROW]
[ROW][C]13[/C][C]0.301359[/C][C]2.2552[/C][C]0.014025[/C][/ROW]
[ROW][C]14[/C][C]0.249175[/C][C]1.8647[/C][C]0.033737[/C][/ROW]
[ROW][C]15[/C][C]0.199025[/C][C]1.4894[/C][C]0.071001[/C][/ROW]
[ROW][C]16[/C][C]0.135068[/C][C]1.0108[/C][C]0.158241[/C][/ROW]
[ROW][C]17[/C][C]0.075037[/C][C]0.5615[/C][C]0.288339[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116630&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116630&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	0.938205	7.0209	0
2	0.878641	6.5751	0
3	0.820805	6.1423	0
4	0.759557	5.684	0
5	0.710175	5.3145	1e-06
6	0.654281	4.8962	4e-06
7	0.601738	4.503	1.7e-05
8	0.552951	4.1379	5.9e-05
9	0.503362	3.7668	2e-04
10	0.455297	3.4071	0.000611
11	0.404096	3.024	0.00188
12	0.353657	2.6465	0.00527
13	0.301359	2.2552	0.014025
14	0.249175	1.8647	0.033737
15	0.199025	1.4894	0.071001
16	0.135068	1.0108	0.158241
17	0.075037	0.5615	0.288339

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.938205	7.0209	0
2	-0.01325	-0.0992	0.460684
3	-0.016964	-0.1269	0.449718
4	-0.059777	-0.4473	0.328181
5	0.06389	0.4781	0.317218
6	-0.081838	-0.6124	0.271368
7	-0.003172	-0.0237	0.490572
8	-0.007533	-0.0564	0.477623
9	-0.025143	-0.1882	0.425718
10	-0.030896	-0.2312	0.409
11	-0.053446	-0.4	0.345357
12	-0.02784	-0.2083	0.417862
13	-0.056223	-0.4207	0.33778
14	-0.035061	-0.2624	0.396998
15	-0.029414	-0.2201	0.413291
16	-0.154907	-1.1592	0.125643
17	-0.027772	-0.2078	0.418058

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.938205 & 7.0209 & 0 \tabularnewline
2 & -0.01325 & -0.0992 & 0.460684 \tabularnewline
3 & -0.016964 & -0.1269 & 0.449718 \tabularnewline
4 & -0.059777 & -0.4473 & 0.328181 \tabularnewline
5 & 0.06389 & 0.4781 & 0.317218 \tabularnewline
6 & -0.081838 & -0.6124 & 0.271368 \tabularnewline
7 & -0.003172 & -0.0237 & 0.490572 \tabularnewline
8 & -0.007533 & -0.0564 & 0.477623 \tabularnewline
9 & -0.025143 & -0.1882 & 0.425718 \tabularnewline
10 & -0.030896 & -0.2312 & 0.409 \tabularnewline
11 & -0.053446 & -0.4 & 0.345357 \tabularnewline
12 & -0.02784 & -0.2083 & 0.417862 \tabularnewline
13 & -0.056223 & -0.4207 & 0.33778 \tabularnewline
14 & -0.035061 & -0.2624 & 0.396998 \tabularnewline
15 & -0.029414 & -0.2201 & 0.413291 \tabularnewline
16 & -0.154907 & -1.1592 & 0.125643 \tabularnewline
17 & -0.027772 & -0.2078 & 0.418058 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116630&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]0.938205[/C][C]7.0209[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.01325[/C][C]-0.0992[/C][C]0.460684[/C][/ROW]
[ROW][C]3[/C][C]-0.016964[/C][C]-0.1269[/C][C]0.449718[/C][/ROW]
[ROW][C]4[/C][C]-0.059777[/C][C]-0.4473[/C][C]0.328181[/C][/ROW]
[ROW][C]5[/C][C]0.06389[/C][C]0.4781[/C][C]0.317218[/C][/ROW]
[ROW][C]6[/C][C]-0.081838[/C][C]-0.6124[/C][C]0.271368[/C][/ROW]
[ROW][C]7[/C][C]-0.003172[/C][C]-0.0237[/C][C]0.490572[/C][/ROW]
[ROW][C]8[/C][C]-0.007533[/C][C]-0.0564[/C][C]0.477623[/C][/ROW]
[ROW][C]9[/C][C]-0.025143[/C][C]-0.1882[/C][C]0.425718[/C][/ROW]
[ROW][C]10[/C][C]-0.030896[/C][C]-0.2312[/C][C]0.409[/C][/ROW]
[ROW][C]11[/C][C]-0.053446[/C][C]-0.4[/C][C]0.345357[/C][/ROW]
[ROW][C]12[/C][C]-0.02784[/C][C]-0.2083[/C][C]0.417862[/C][/ROW]
[ROW][C]13[/C][C]-0.056223[/C][C]-0.4207[/C][C]0.33778[/C][/ROW]
[ROW][C]14[/C][C]-0.035061[/C][C]-0.2624[/C][C]0.396998[/C][/ROW]
[ROW][C]15[/C][C]-0.029414[/C][C]-0.2201[/C][C]0.413291[/C][/ROW]
[ROW][C]16[/C][C]-0.154907[/C][C]-1.1592[/C][C]0.125643[/C][/ROW]
[ROW][C]17[/C][C]-0.027772[/C][C]-0.2078[/C][C]0.418058[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116630&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116630&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	0.938205	7.0209	0
2	-0.01325	-0.0992	0.460684
3	-0.016964	-0.1269	0.449718
4	-0.059777	-0.4473	0.328181
5	0.06389	0.4781	0.317218
6	-0.081838	-0.6124	0.271368
7	-0.003172	-0.0237	0.490572
8	-0.007533	-0.0564	0.477623
9	-0.025143	-0.1882	0.425718
10	-0.030896	-0.2312	0.409
11	-0.053446	-0.4	0.345357
12	-0.02784	-0.2083	0.417862
13	-0.056223	-0.4207	0.33778
14	-0.035061	-0.2624	0.396998
15	-0.029414	-0.2201	0.413291
16	-0.154907	-1.1592	0.125643
17	-0.027772	-0.2078	0.418058

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 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

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')

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Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code