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Author's title

Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sun, 16 Nov 2014 09:39:28 +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/2014/Nov/16/t1416130839t5bw2oq8k0517l5.htm/, Retrieved Fri, 17 May 2024 03:22:28 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=255049, Retrieved Fri, 17 May 2024 03:22:28 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

135

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

-       [(Partial) Autocorrelation Function] [] [2014-11-16 09:39:28] [4b199ad8119df16cb977784959786033] [Current]

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Dataseries X:

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Histogram

Boxplots

1,11
1,11
1,2
1,21
1,31
1,37
1,37
1,26
1,23
1,17
1,06
0,95
0,92
0,92
0,9
0,93
0,93
0,97
0,96
0,99
0,98
0,96
1
0,99
1,03
1,02
1,07
1,13
1,15
1,16
1,14
1,15
1,15
1,16
1,17
1,22
1,26
1,29
1,36
1,38
1,37
1,37
1,37
1,36
1,38
1,4
1,44
1,42
1,45
1,45
1,49
1,48
1,44
1,39
1,41
1,48
1,51
1,49
1,46
1,43
1,42
1,43
1,42
1,39
1,36
1,36
1,39
1,39
1,43
1,38
1,36
1,38

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 Ronald Aylmer Fisher' @ fisher.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 Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=255049&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 Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=255049&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=255049&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 Ronald Aylmer Fisher' @ fisher.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.969142	8.2234	0
2	0.92015	7.8077	0
3	0.863211	7.3246	0
4	0.802869	6.8126	0
5	0.748539	6.3516	0
6	0.702669	5.9623	0
7	0.666471	5.6552	0
8	0.629576	5.3421	1e-06
9	0.599408	5.0861	1e-06
10	0.566438	4.8064	4e-06
11	0.522901	4.437	1.6e-05
12	0.46477	3.9437	9.2e-05
13	0.401143	3.4038	0.000545
14	0.335059	2.8431	0.002905
15	0.270317	2.2937	0.012364
16	0.212447	1.8027	0.037812
17	0.160377	1.3608	0.088904
18	0.116674	0.99	0.162742

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.969142 & 8.2234 & 0 \tabularnewline
2 & 0.92015 & 7.8077 & 0 \tabularnewline
3 & 0.863211 & 7.3246 & 0 \tabularnewline
4 & 0.802869 & 6.8126 & 0 \tabularnewline
5 & 0.748539 & 6.3516 & 0 \tabularnewline
6 & 0.702669 & 5.9623 & 0 \tabularnewline
7 & 0.666471 & 5.6552 & 0 \tabularnewline
8 & 0.629576 & 5.3421 & 1e-06 \tabularnewline
9 & 0.599408 & 5.0861 & 1e-06 \tabularnewline
10 & 0.566438 & 4.8064 & 4e-06 \tabularnewline
11 & 0.522901 & 4.437 & 1.6e-05 \tabularnewline
12 & 0.46477 & 3.9437 & 9.2e-05 \tabularnewline
13 & 0.401143 & 3.4038 & 0.000545 \tabularnewline
14 & 0.335059 & 2.8431 & 0.002905 \tabularnewline
15 & 0.270317 & 2.2937 & 0.012364 \tabularnewline
16 & 0.212447 & 1.8027 & 0.037812 \tabularnewline
17 & 0.160377 & 1.3608 & 0.088904 \tabularnewline
18 & 0.116674 & 0.99 & 0.162742 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=255049&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]0.969142[/C][C]8.2234[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.92015[/C][C]7.8077[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.863211[/C][C]7.3246[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.802869[/C][C]6.8126[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.748539[/C][C]6.3516[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.702669[/C][C]5.9623[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.666471[/C][C]5.6552[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.629576[/C][C]5.3421[/C][C]1e-06[/C][/ROW]
[ROW][C]9[/C][C]0.599408[/C][C]5.0861[/C][C]1e-06[/C][/ROW]
[ROW][C]10[/C][C]0.566438[/C][C]4.8064[/C][C]4e-06[/C][/ROW]
[ROW][C]11[/C][C]0.522901[/C][C]4.437[/C][C]1.6e-05[/C][/ROW]
[ROW][C]12[/C][C]0.46477[/C][C]3.9437[/C][C]9.2e-05[/C][/ROW]
[ROW][C]13[/C][C]0.401143[/C][C]3.4038[/C][C]0.000545[/C][/ROW]
[ROW][C]14[/C][C]0.335059[/C][C]2.8431[/C][C]0.002905[/C][/ROW]
[ROW][C]15[/C][C]0.270317[/C][C]2.2937[/C][C]0.012364[/C][/ROW]
[ROW][C]16[/C][C]0.212447[/C][C]1.8027[/C][C]0.037812[/C][/ROW]
[ROW][C]17[/C][C]0.160377[/C][C]1.3608[/C][C]0.088904[/C][/ROW]
[ROW][C]18[/C][C]0.116674[/C][C]0.99[/C][C]0.162742[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=255049&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=255049&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	0.969142	8.2234	0
2	0.92015	7.8077	0
3	0.863211	7.3246	0
4	0.802869	6.8126	0
5	0.748539	6.3516	0
6	0.702669	5.9623	0
7	0.666471	5.6552	0
8	0.629576	5.3421	1e-06
9	0.599408	5.0861	1e-06
10	0.566438	4.8064	4e-06
11	0.522901	4.437	1.6e-05
12	0.46477	3.9437	9.2e-05
13	0.401143	3.4038	0.000545
14	0.335059	2.8431	0.002905
15	0.270317	2.2937	0.012364
16	0.212447	1.8027	0.037812
17	0.160377	1.3608	0.088904
18	0.116674	0.99	0.162742

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.969142	8.2234	0
2	-0.314118	-2.6654	0.004744
3	-0.077353	-0.6564	0.256841
4	-0.039693	-0.3368	0.368621
5	0.101572	0.8619	0.19581
6	0.063232	0.5365	0.296619
7	0.065379	0.5548	0.290388
8	-0.13954	-1.184	0.120146
9	0.116339	0.9872	0.163432
10	-0.126666	-1.0748	0.143027
11	-0.153914	-1.306	0.097854
12	-0.219534	-1.8628	0.033284
13	0.042137	0.3575	0.360864
14	-0.044642	-0.3788	0.352975
15	0.027045	0.2295	0.409572
16	-0.052508	-0.4455	0.328632
17	-0.01137	-0.0965	0.461705
18	0.022349	0.1896	0.425065

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.969142 & 8.2234 & 0 \tabularnewline
2 & -0.314118 & -2.6654 & 0.004744 \tabularnewline
3 & -0.077353 & -0.6564 & 0.256841 \tabularnewline
4 & -0.039693 & -0.3368 & 0.368621 \tabularnewline
5 & 0.101572 & 0.8619 & 0.19581 \tabularnewline
6 & 0.063232 & 0.5365 & 0.296619 \tabularnewline
7 & 0.065379 & 0.5548 & 0.290388 \tabularnewline
8 & -0.13954 & -1.184 & 0.120146 \tabularnewline
9 & 0.116339 & 0.9872 & 0.163432 \tabularnewline
10 & -0.126666 & -1.0748 & 0.143027 \tabularnewline
11 & -0.153914 & -1.306 & 0.097854 \tabularnewline
12 & -0.219534 & -1.8628 & 0.033284 \tabularnewline
13 & 0.042137 & 0.3575 & 0.360864 \tabularnewline
14 & -0.044642 & -0.3788 & 0.352975 \tabularnewline
15 & 0.027045 & 0.2295 & 0.409572 \tabularnewline
16 & -0.052508 & -0.4455 & 0.328632 \tabularnewline
17 & -0.01137 & -0.0965 & 0.461705 \tabularnewline
18 & 0.022349 & 0.1896 & 0.425065 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=255049&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]0.969142[/C][C]8.2234[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.314118[/C][C]-2.6654[/C][C]0.004744[/C][/ROW]
[ROW][C]3[/C][C]-0.077353[/C][C]-0.6564[/C][C]0.256841[/C][/ROW]
[ROW][C]4[/C][C]-0.039693[/C][C]-0.3368[/C][C]0.368621[/C][/ROW]
[ROW][C]5[/C][C]0.101572[/C][C]0.8619[/C][C]0.19581[/C][/ROW]
[ROW][C]6[/C][C]0.063232[/C][C]0.5365[/C][C]0.296619[/C][/ROW]
[ROW][C]7[/C][C]0.065379[/C][C]0.5548[/C][C]0.290388[/C][/ROW]
[ROW][C]8[/C][C]-0.13954[/C][C]-1.184[/C][C]0.120146[/C][/ROW]
[ROW][C]9[/C][C]0.116339[/C][C]0.9872[/C][C]0.163432[/C][/ROW]
[ROW][C]10[/C][C]-0.126666[/C][C]-1.0748[/C][C]0.143027[/C][/ROW]
[ROW][C]11[/C][C]-0.153914[/C][C]-1.306[/C][C]0.097854[/C][/ROW]
[ROW][C]12[/C][C]-0.219534[/C][C]-1.8628[/C][C]0.033284[/C][/ROW]
[ROW][C]13[/C][C]0.042137[/C][C]0.3575[/C][C]0.360864[/C][/ROW]
[ROW][C]14[/C][C]-0.044642[/C][C]-0.3788[/C][C]0.352975[/C][/ROW]
[ROW][C]15[/C][C]0.027045[/C][C]0.2295[/C][C]0.409572[/C][/ROW]
[ROW][C]16[/C][C]-0.052508[/C][C]-0.4455[/C][C]0.328632[/C][/ROW]
[ROW][C]17[/C][C]-0.01137[/C][C]-0.0965[/C][C]0.461705[/C][/ROW]
[ROW][C]18[/C][C]0.022349[/C][C]0.1896[/C][C]0.425065[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=255049&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=255049&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	0.969142	8.2234	0
2	-0.314118	-2.6654	0.004744
3	-0.077353	-0.6564	0.256841
4	-0.039693	-0.3368	0.368621
5	0.101572	0.8619	0.19581
6	0.063232	0.5365	0.296619
7	0.065379	0.5548	0.290388
8	-0.13954	-1.184	0.120146
9	0.116339	0.9872	0.163432
10	-0.126666	-1.0748	0.143027
11	-0.153914	-1.306	0.097854
12	-0.219534	-1.8628	0.033284
13	0.042137	0.3575	0.360864
14	-0.044642	-0.3788	0.352975
15	0.027045	0.2295	0.409572
16	-0.052508	-0.4455	0.328632
17	-0.01137	-0.0965	0.461705
18	0.022349	0.1896	0.425065

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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code