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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sat, 06 Dec 2008 06:06:08 -0700

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/2008/Dec/06/t1228568860xttw0xhded480pz.htm/, Retrieved Sat, 25 May 2024 19:51:24 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=29567, Retrieved Sat, 25 May 2024 19:51:24 +0000

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Estimated Impact

212

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

-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
F RMP   [Standard Deviation-Mean Plot] [sdm ] [2008-12-05 13:33:27] [de72ca3f4fcfd0997c84e1ac92aea119]
F RM D    [Variance Reduction Matrix] [Q2 eigen tijdreeks] [2008-12-06 10:45:14] [de72ca3f4fcfd0997c84e1ac92aea119]
F RMP       [(Partial) Autocorrelation Function] [Q2 eigen tijdreeks] [2008-12-06 10:52:06] [de72ca3f4fcfd0997c84e1ac92aea119]
-   P           [(Partial) Autocorrelation Function] [Q3 Eigen tijdreeks] [2008-12-06 13:06:08] [56fd94b954e08a6655cb7790b21ee404] [Current]
-   P             [(Partial) Autocorrelation Function] [Q3 Eigen tijdreeks] [2008-12-06 13:14:50] [de72ca3f4fcfd0997c84e1ac92aea119] 

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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	11 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 & 11 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=29567&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]11 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=29567&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=29567&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	11 seconds
R Server	'George Udny Yule' @ 72.249.76.132

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.251682	2.1504	0.017419
2	-0.135433	-1.1571	0.125494
3	-0.134585	-1.1499	0.126971
4	0.112484	0.9611	0.169847
5	0.015627	0.1335	0.447077
6	-0.20151	-1.7217	0.04468
7	-0.011138	-0.0952	0.462225
8	0.021464	0.1834	0.427502
9	0.04162	0.3556	0.361583
10	0.040311	0.3444	0.365763
11	0.090816	0.7759	0.220147
12	-0.008275	-0.0707	0.471913
13	-0.046293	-0.3955	0.346804
14	0.030877	0.2638	0.396332
15	-0.080167	-0.6849	0.247773
16	-0.161829	-1.3827	0.085491
17	0.021817	0.1864	0.426323
18	0.162509	1.3885	0.084607

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.251682 & 2.1504 & 0.017419 \tabularnewline
2 & -0.135433 & -1.1571 & 0.125494 \tabularnewline
3 & -0.134585 & -1.1499 & 0.126971 \tabularnewline
4 & 0.112484 & 0.9611 & 0.169847 \tabularnewline
5 & 0.015627 & 0.1335 & 0.447077 \tabularnewline
6 & -0.20151 & -1.7217 & 0.04468 \tabularnewline
7 & -0.011138 & -0.0952 & 0.462225 \tabularnewline
8 & 0.021464 & 0.1834 & 0.427502 \tabularnewline
9 & 0.04162 & 0.3556 & 0.361583 \tabularnewline
10 & 0.040311 & 0.3444 & 0.365763 \tabularnewline
11 & 0.090816 & 0.7759 & 0.220147 \tabularnewline
12 & -0.008275 & -0.0707 & 0.471913 \tabularnewline
13 & -0.046293 & -0.3955 & 0.346804 \tabularnewline
14 & 0.030877 & 0.2638 & 0.396332 \tabularnewline
15 & -0.080167 & -0.6849 & 0.247773 \tabularnewline
16 & -0.161829 & -1.3827 & 0.085491 \tabularnewline
17 & 0.021817 & 0.1864 & 0.426323 \tabularnewline
18 & 0.162509 & 1.3885 & 0.084607 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=29567&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]0.251682[/C][C]2.1504[/C][C]0.017419[/C][/ROW]
[ROW][C]2[/C][C]-0.135433[/C][C]-1.1571[/C][C]0.125494[/C][/ROW]
[ROW][C]3[/C][C]-0.134585[/C][C]-1.1499[/C][C]0.126971[/C][/ROW]
[ROW][C]4[/C][C]0.112484[/C][C]0.9611[/C][C]0.169847[/C][/ROW]
[ROW][C]5[/C][C]0.015627[/C][C]0.1335[/C][C]0.447077[/C][/ROW]
[ROW][C]6[/C][C]-0.20151[/C][C]-1.7217[/C][C]0.04468[/C][/ROW]
[ROW][C]7[/C][C]-0.011138[/C][C]-0.0952[/C][C]0.462225[/C][/ROW]
[ROW][C]8[/C][C]0.021464[/C][C]0.1834[/C][C]0.427502[/C][/ROW]
[ROW][C]9[/C][C]0.04162[/C][C]0.3556[/C][C]0.361583[/C][/ROW]
[ROW][C]10[/C][C]0.040311[/C][C]0.3444[/C][C]0.365763[/C][/ROW]
[ROW][C]11[/C][C]0.090816[/C][C]0.7759[/C][C]0.220147[/C][/ROW]
[ROW][C]12[/C][C]-0.008275[/C][C]-0.0707[/C][C]0.471913[/C][/ROW]
[ROW][C]13[/C][C]-0.046293[/C][C]-0.3955[/C][C]0.346804[/C][/ROW]
[ROW][C]14[/C][C]0.030877[/C][C]0.2638[/C][C]0.396332[/C][/ROW]
[ROW][C]15[/C][C]-0.080167[/C][C]-0.6849[/C][C]0.247773[/C][/ROW]
[ROW][C]16[/C][C]-0.161829[/C][C]-1.3827[/C][C]0.085491[/C][/ROW]
[ROW][C]17[/C][C]0.021817[/C][C]0.1864[/C][C]0.426323[/C][/ROW]
[ROW][C]18[/C][C]0.162509[/C][C]1.3885[/C][C]0.084607[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=29567&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=29567&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	0.251682	2.1504	0.017419
2	-0.135433	-1.1571	0.125494
3	-0.134585	-1.1499	0.126971
4	0.112484	0.9611	0.169847
5	0.015627	0.1335	0.447077
6	-0.20151	-1.7217	0.04468
7	-0.011138	-0.0952	0.462225
8	0.021464	0.1834	0.427502
9	0.04162	0.3556	0.361583
10	0.040311	0.3444	0.365763
11	0.090816	0.7759	0.220147
12	-0.008275	-0.0707	0.471913
13	-0.046293	-0.3955	0.346804
14	0.030877	0.2638	0.396332
15	-0.080167	-0.6849	0.247773
16	-0.161829	-1.3827	0.085491
17	0.021817	0.1864	0.426323
18	0.162509	1.3885	0.084607

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.251682	2.1504	0.017419
2	-0.212219	-1.8132	0.036956
3	-0.044555	-0.3807	0.352274
4	0.153003	1.3073	0.097613
5	-0.105191	-0.8987	0.185871
6	-0.173359	-1.4812	0.071431
7	0.147605	1.2611	0.105637
8	-0.110417	-0.9434	0.174293
9	0.031182	0.2664	0.395335
10	0.116985	0.9995	0.160422
11	0.021169	0.1809	0.428486
12	-0.081515	-0.6965	0.244174
13	0.061575	0.5261	0.300208
14	0.016427	0.1404	0.444382
15	-0.172271	-1.4719	0.072675
16	-0.055319	-0.4726	0.318937
17	0.163776	1.3993	0.082978
18	-0.009287	-0.0793	0.468486

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.251682 & 2.1504 & 0.017419 \tabularnewline
2 & -0.212219 & -1.8132 & 0.036956 \tabularnewline
3 & -0.044555 & -0.3807 & 0.352274 \tabularnewline
4 & 0.153003 & 1.3073 & 0.097613 \tabularnewline
5 & -0.105191 & -0.8987 & 0.185871 \tabularnewline
6 & -0.173359 & -1.4812 & 0.071431 \tabularnewline
7 & 0.147605 & 1.2611 & 0.105637 \tabularnewline
8 & -0.110417 & -0.9434 & 0.174293 \tabularnewline
9 & 0.031182 & 0.2664 & 0.395335 \tabularnewline
10 & 0.116985 & 0.9995 & 0.160422 \tabularnewline
11 & 0.021169 & 0.1809 & 0.428486 \tabularnewline
12 & -0.081515 & -0.6965 & 0.244174 \tabularnewline
13 & 0.061575 & 0.5261 & 0.300208 \tabularnewline
14 & 0.016427 & 0.1404 & 0.444382 \tabularnewline
15 & -0.172271 & -1.4719 & 0.072675 \tabularnewline
16 & -0.055319 & -0.4726 & 0.318937 \tabularnewline
17 & 0.163776 & 1.3993 & 0.082978 \tabularnewline
18 & -0.009287 & -0.0793 & 0.468486 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=29567&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]0.251682[/C][C]2.1504[/C][C]0.017419[/C][/ROW]
[ROW][C]2[/C][C]-0.212219[/C][C]-1.8132[/C][C]0.036956[/C][/ROW]
[ROW][C]3[/C][C]-0.044555[/C][C]-0.3807[/C][C]0.352274[/C][/ROW]
[ROW][C]4[/C][C]0.153003[/C][C]1.3073[/C][C]0.097613[/C][/ROW]
[ROW][C]5[/C][C]-0.105191[/C][C]-0.8987[/C][C]0.185871[/C][/ROW]
[ROW][C]6[/C][C]-0.173359[/C][C]-1.4812[/C][C]0.071431[/C][/ROW]
[ROW][C]7[/C][C]0.147605[/C][C]1.2611[/C][C]0.105637[/C][/ROW]
[ROW][C]8[/C][C]-0.110417[/C][C]-0.9434[/C][C]0.174293[/C][/ROW]
[ROW][C]9[/C][C]0.031182[/C][C]0.2664[/C][C]0.395335[/C][/ROW]
[ROW][C]10[/C][C]0.116985[/C][C]0.9995[/C][C]0.160422[/C][/ROW]
[ROW][C]11[/C][C]0.021169[/C][C]0.1809[/C][C]0.428486[/C][/ROW]
[ROW][C]12[/C][C]-0.081515[/C][C]-0.6965[/C][C]0.244174[/C][/ROW]
[ROW][C]13[/C][C]0.061575[/C][C]0.5261[/C][C]0.300208[/C][/ROW]
[ROW][C]14[/C][C]0.016427[/C][C]0.1404[/C][C]0.444382[/C][/ROW]
[ROW][C]15[/C][C]-0.172271[/C][C]-1.4719[/C][C]0.072675[/C][/ROW]
[ROW][C]16[/C][C]-0.055319[/C][C]-0.4726[/C][C]0.318937[/C][/ROW]
[ROW][C]17[/C][C]0.163776[/C][C]1.3993[/C][C]0.082978[/C][/ROW]
[ROW][C]18[/C][C]-0.009287[/C][C]-0.0793[/C][C]0.468486[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=29567&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=29567&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	0.251682	2.1504	0.017419
2	-0.212219	-1.8132	0.036956
3	-0.044555	-0.3807	0.352274
4	0.153003	1.3073	0.097613
5	-0.105191	-0.8987	0.185871
6	-0.173359	-1.4812	0.071431
7	0.147605	1.2611	0.105637
8	-0.110417	-0.9434	0.174293
9	0.031182	0.2664	0.395335
10	0.116985	0.9995	0.160422
11	0.021169	0.1809	0.428486
12	-0.081515	-0.6965	0.244174
13	0.061575	0.5261	0.300208
14	0.016427	0.1404	0.444382
15	-0.172271	-1.4719	0.072675
16	-0.055319	-0.4726	0.318937
17	0.163776	1.3993	0.082978
18	-0.009287	-0.0793	0.468486

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = 1.8 ; par3 = 1 ; par4 = 0 ; par5 = 12 ;

Parameters (R input):

par1 = Default ; par2 = 1.8 ; par3 = 1 ; par4 = 0 ; par5 = 12 ;

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 (par2 == 0) {
x <- log(x)
} else {
x <- (x ^ par2 - 1) / par2
}
if (par3 > 0) x <- diff(x,lag=1,difference=par3)
if (par4 > 0) x <- diff(x,lag=par5,difference=par4)
bitmap(file='pic1.png')
racf <- acf(x,par1,main='Autocorrelation',xlab='lags',ylab='ACF')
dev.off()
bitmap(file='pic2.png')
rpacf <- pacf(x,par1,main='Partial Autocorrelation',xlab='lags',ylab='PACF')
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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