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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sat, 25 Dec 2010 09:05:34 +0000

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/2010/Dec/25/t1293267855nunehwbnzo2wh8t.htm/, Retrieved Mon, 29 Apr 2024 07:47:36 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=115311, Retrieved Mon, 29 Apr 2024 07:47:36 +0000

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No (this computation is public)

User-defined keywords

Estimated Impact

174

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

F     [(Partial) Autocorrelation Function] [(P)ACF Algemeen i...] [2008-12-03 16:58:16] [74be16979710d4c4e7c6647856088456]
- RMPD    [(Partial) Autocorrelation Function] [paper (p)ACF] [2010-12-25 09:05:34] [b7765ad69c3ab250b1ef04c2ab1247ec] [Current]
-    D      [(Partial) Autocorrelation Function] [] [2010-12-26 09:57:06] [a2638725f7f7c6bd63902ba17eba666b] 
-   P       [(Partial) Autocorrelation Function] [] [2010-12-26 10:56:45] [c4f608d390ad7371b1365a9b84541edb] 

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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	14 seconds
R Server	'George Udny Yule' @ 72.249.76.132

\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 & 14 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115311&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]14 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115311&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115311&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	14 seconds
R Server	'George Udny Yule' @ 72.249.76.132

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.516585	3.9001	0.000128
2	0.363097	2.7413	0.00408
3	0.509559	3.8471	0.000152
4	0.416402	3.1438	0.001324
5	0.281023	2.1217	0.019112
6	0.268144	2.0244	0.02381
7	0.08489	0.6409	0.262076
8	0.10237	0.7729	0.221395
9	-0.048526	-0.3664	0.357724
10	-0.243074	-1.8352	0.03585
11	-0.144031	-1.0874	0.140716
12	0.054738	0.4133	0.340482
13	-0.249805	-1.886	0.032198
14	-0.357951	-2.7025	0.004526
15	-0.260844	-1.9693	0.026892
16	-0.234957	-1.7739	0.040712
17	-0.249183	-1.8813	0.032521

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.516585 & 3.9001 & 0.000128 \tabularnewline
2 & 0.363097 & 2.7413 & 0.00408 \tabularnewline
3 & 0.509559 & 3.8471 & 0.000152 \tabularnewline
4 & 0.416402 & 3.1438 & 0.001324 \tabularnewline
5 & 0.281023 & 2.1217 & 0.019112 \tabularnewline
6 & 0.268144 & 2.0244 & 0.02381 \tabularnewline
7 & 0.08489 & 0.6409 & 0.262076 \tabularnewline
8 & 0.10237 & 0.7729 & 0.221395 \tabularnewline
9 & -0.048526 & -0.3664 & 0.357724 \tabularnewline
10 & -0.243074 & -1.8352 & 0.03585 \tabularnewline
11 & -0.144031 & -1.0874 & 0.140716 \tabularnewline
12 & 0.054738 & 0.4133 & 0.340482 \tabularnewline
13 & -0.249805 & -1.886 & 0.032198 \tabularnewline
14 & -0.357951 & -2.7025 & 0.004526 \tabularnewline
15 & -0.260844 & -1.9693 & 0.026892 \tabularnewline
16 & -0.234957 & -1.7739 & 0.040712 \tabularnewline
17 & -0.249183 & -1.8813 & 0.032521 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115311&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]0.516585[/C][C]3.9001[/C][C]0.000128[/C][/ROW]
[ROW][C]2[/C][C]0.363097[/C][C]2.7413[/C][C]0.00408[/C][/ROW]
[ROW][C]3[/C][C]0.509559[/C][C]3.8471[/C][C]0.000152[/C][/ROW]
[ROW][C]4[/C][C]0.416402[/C][C]3.1438[/C][C]0.001324[/C][/ROW]
[ROW][C]5[/C][C]0.281023[/C][C]2.1217[/C][C]0.019112[/C][/ROW]
[ROW][C]6[/C][C]0.268144[/C][C]2.0244[/C][C]0.02381[/C][/ROW]
[ROW][C]7[/C][C]0.08489[/C][C]0.6409[/C][C]0.262076[/C][/ROW]
[ROW][C]8[/C][C]0.10237[/C][C]0.7729[/C][C]0.221395[/C][/ROW]
[ROW][C]9[/C][C]-0.048526[/C][C]-0.3664[/C][C]0.357724[/C][/ROW]
[ROW][C]10[/C][C]-0.243074[/C][C]-1.8352[/C][C]0.03585[/C][/ROW]
[ROW][C]11[/C][C]-0.144031[/C][C]-1.0874[/C][C]0.140716[/C][/ROW]
[ROW][C]12[/C][C]0.054738[/C][C]0.4133[/C][C]0.340482[/C][/ROW]
[ROW][C]13[/C][C]-0.249805[/C][C]-1.886[/C][C]0.032198[/C][/ROW]
[ROW][C]14[/C][C]-0.357951[/C][C]-2.7025[/C][C]0.004526[/C][/ROW]
[ROW][C]15[/C][C]-0.260844[/C][C]-1.9693[/C][C]0.026892[/C][/ROW]
[ROW][C]16[/C][C]-0.234957[/C][C]-1.7739[/C][C]0.040712[/C][/ROW]
[ROW][C]17[/C][C]-0.249183[/C][C]-1.8813[/C][C]0.032521[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115311&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115311&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	0.516585	3.9001	0.000128
2	0.363097	2.7413	0.00408
3	0.509559	3.8471	0.000152
4	0.416402	3.1438	0.001324
5	0.281023	2.1217	0.019112
6	0.268144	2.0244	0.02381
7	0.08489	0.6409	0.262076
8	0.10237	0.7729	0.221395
9	-0.048526	-0.3664	0.357724
10	-0.243074	-1.8352	0.03585
11	-0.144031	-1.0874	0.140716
12	0.054738	0.4133	0.340482
13	-0.249805	-1.886	0.032198
14	-0.357951	-2.7025	0.004526
15	-0.260844	-1.9693	0.026892
16	-0.234957	-1.7739	0.040712
17	-0.249183	-1.8813	0.032521

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.516585	3.9001	0.000128
2	0.131267	0.991	0.162927
3	0.38695	2.9214	0.002493
4	0.047508	0.3587	0.360581
5	-0.023963	-0.1809	0.428539
6	-0.034266	-0.2587	0.398397
7	-0.284141	-2.1452	0.018105
8	0.054256	0.4096	0.341809
9	-0.31051	-2.3443	0.011286
10	-0.218568	-1.6502	0.052206
11	0.056389	0.4257	0.335956
12	0.420688	3.1761	0.001205
13	-0.134714	-1.0171	0.15671
14	-0.210695	-1.5907	0.058603
15	-0.202957	-1.5323	0.065491
16	-0.018353	-0.1386	0.445142
17	0.085872	0.6483	0.25969

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.516585 & 3.9001 & 0.000128 \tabularnewline
2 & 0.131267 & 0.991 & 0.162927 \tabularnewline
3 & 0.38695 & 2.9214 & 0.002493 \tabularnewline
4 & 0.047508 & 0.3587 & 0.360581 \tabularnewline
5 & -0.023963 & -0.1809 & 0.428539 \tabularnewline
6 & -0.034266 & -0.2587 & 0.398397 \tabularnewline
7 & -0.284141 & -2.1452 & 0.018105 \tabularnewline
8 & 0.054256 & 0.4096 & 0.341809 \tabularnewline
9 & -0.31051 & -2.3443 & 0.011286 \tabularnewline
10 & -0.218568 & -1.6502 & 0.052206 \tabularnewline
11 & 0.056389 & 0.4257 & 0.335956 \tabularnewline
12 & 0.420688 & 3.1761 & 0.001205 \tabularnewline
13 & -0.134714 & -1.0171 & 0.15671 \tabularnewline
14 & -0.210695 & -1.5907 & 0.058603 \tabularnewline
15 & -0.202957 & -1.5323 & 0.065491 \tabularnewline
16 & -0.018353 & -0.1386 & 0.445142 \tabularnewline
17 & 0.085872 & 0.6483 & 0.25969 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115311&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]0.516585[/C][C]3.9001[/C][C]0.000128[/C][/ROW]
[ROW][C]2[/C][C]0.131267[/C][C]0.991[/C][C]0.162927[/C][/ROW]
[ROW][C]3[/C][C]0.38695[/C][C]2.9214[/C][C]0.002493[/C][/ROW]
[ROW][C]4[/C][C]0.047508[/C][C]0.3587[/C][C]0.360581[/C][/ROW]
[ROW][C]5[/C][C]-0.023963[/C][C]-0.1809[/C][C]0.428539[/C][/ROW]
[ROW][C]6[/C][C]-0.034266[/C][C]-0.2587[/C][C]0.398397[/C][/ROW]
[ROW][C]7[/C][C]-0.284141[/C][C]-2.1452[/C][C]0.018105[/C][/ROW]
[ROW][C]8[/C][C]0.054256[/C][C]0.4096[/C][C]0.341809[/C][/ROW]
[ROW][C]9[/C][C]-0.31051[/C][C]-2.3443[/C][C]0.011286[/C][/ROW]
[ROW][C]10[/C][C]-0.218568[/C][C]-1.6502[/C][C]0.052206[/C][/ROW]
[ROW][C]11[/C][C]0.056389[/C][C]0.4257[/C][C]0.335956[/C][/ROW]
[ROW][C]12[/C][C]0.420688[/C][C]3.1761[/C][C]0.001205[/C][/ROW]
[ROW][C]13[/C][C]-0.134714[/C][C]-1.0171[/C][C]0.15671[/C][/ROW]
[ROW][C]14[/C][C]-0.210695[/C][C]-1.5907[/C][C]0.058603[/C][/ROW]
[ROW][C]15[/C][C]-0.202957[/C][C]-1.5323[/C][C]0.065491[/C][/ROW]
[ROW][C]16[/C][C]-0.018353[/C][C]-0.1386[/C][C]0.445142[/C][/ROW]
[ROW][C]17[/C][C]0.085872[/C][C]0.6483[/C][C]0.25969[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115311&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115311&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	0.516585	3.9001	0.000128
2	0.131267	0.991	0.162927
3	0.38695	2.9214	0.002493
4	0.047508	0.3587	0.360581
5	-0.023963	-0.1809	0.428539
6	-0.034266	-0.2587	0.398397
7	-0.284141	-2.1452	0.018105
8	0.054256	0.4096	0.341809
9	-0.31051	-2.3443	0.011286
10	-0.218568	-1.6502	0.052206
11	0.056389	0.4257	0.335956
12	0.420688	3.1761	0.001205
13	-0.134714	-1.0171	0.15671
14	-0.210695	-1.5907	0.058603
15	-0.202957	-1.5323	0.065491
16	-0.018353	-0.1386	0.445142
17	0.085872	0.6483	0.25969

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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