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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Mon, 06 Dec 2010 23:38:48 +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/07/t129167861874kduo0yi9mxjvf.htm/, Retrieved Fri, 03 May 2024 18:59:00 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=105975, Retrieved Fri, 03 May 2024 18:59:00 +0000

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User-defined keywords

Estimated Impact

154

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]
- RMP   [(Partial) Autocorrelation Function] [Unemployment] [2010-11-29 09:05:21] [b98453cac15ba1066b407e146608df68]
-    D    [(Partial) Autocorrelation Function] [ACF 1] [2010-12-06 22:52:14] [b8e188bcc949964bed729335b3416734]
-    D        [(Partial) Autocorrelation Function] [ACF 2] [2010-12-06 23:38:48] [278a0539dc236556c5f30b5bc56ff9eb] [Current]
-   P           [(Partial) Autocorrelation Function] [ACF 2.1] [2010-12-06 23:51:36] [b8e188bcc949964bed729335b3416734] 
-   P             [(Partial) Autocorrelation Function] [ACF 2.2] [2010-12-07 15:16:06] [b8e188bcc949964bed729335b3416734] 

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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=105975&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=105975&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=105975&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	0.270067	2.2106	0.015241
2	0.253769	2.0772	0.02081
3	0.311216	2.5474	0.006577
4	0.165965	1.3585	0.089434
5	0.306561	2.5093	0.00726
6	0.165432	1.3541	0.090124
7	0.10564	0.8647	0.195145
8	0.124632	1.0202	0.155662
9	0.238123	1.9491	0.027734
10	0.156479	1.2808	0.102334
11	0.143567	1.1752	0.122047
12	0.312007	2.5539	0.006467
13	0.12979	1.0624	0.14594
14	0.175191	1.434	0.078111
15	0.063024	0.5159	0.303819
16	-0.039548	-0.3237	0.373582
17	0.0374	0.3061	0.380227
18	-0.061555	-0.5038	0.308011

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.270067 & 2.2106 & 0.015241 \tabularnewline
2 & 0.253769 & 2.0772 & 0.02081 \tabularnewline
3 & 0.311216 & 2.5474 & 0.006577 \tabularnewline
4 & 0.165965 & 1.3585 & 0.089434 \tabularnewline
5 & 0.306561 & 2.5093 & 0.00726 \tabularnewline
6 & 0.165432 & 1.3541 & 0.090124 \tabularnewline
7 & 0.10564 & 0.8647 & 0.195145 \tabularnewline
8 & 0.124632 & 1.0202 & 0.155662 \tabularnewline
9 & 0.238123 & 1.9491 & 0.027734 \tabularnewline
10 & 0.156479 & 1.2808 & 0.102334 \tabularnewline
11 & 0.143567 & 1.1752 & 0.122047 \tabularnewline
12 & 0.312007 & 2.5539 & 0.006467 \tabularnewline
13 & 0.12979 & 1.0624 & 0.14594 \tabularnewline
14 & 0.175191 & 1.434 & 0.078111 \tabularnewline
15 & 0.063024 & 0.5159 & 0.303819 \tabularnewline
16 & -0.039548 & -0.3237 & 0.373582 \tabularnewline
17 & 0.0374 & 0.3061 & 0.380227 \tabularnewline
18 & -0.061555 & -0.5038 & 0.308011 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=105975&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]0.270067[/C][C]2.2106[/C][C]0.015241[/C][/ROW]
[ROW][C]2[/C][C]0.253769[/C][C]2.0772[/C][C]0.02081[/C][/ROW]
[ROW][C]3[/C][C]0.311216[/C][C]2.5474[/C][C]0.006577[/C][/ROW]
[ROW][C]4[/C][C]0.165965[/C][C]1.3585[/C][C]0.089434[/C][/ROW]
[ROW][C]5[/C][C]0.306561[/C][C]2.5093[/C][C]0.00726[/C][/ROW]
[ROW][C]6[/C][C]0.165432[/C][C]1.3541[/C][C]0.090124[/C][/ROW]
[ROW][C]7[/C][C]0.10564[/C][C]0.8647[/C][C]0.195145[/C][/ROW]
[ROW][C]8[/C][C]0.124632[/C][C]1.0202[/C][C]0.155662[/C][/ROW]
[ROW][C]9[/C][C]0.238123[/C][C]1.9491[/C][C]0.027734[/C][/ROW]
[ROW][C]10[/C][C]0.156479[/C][C]1.2808[/C][C]0.102334[/C][/ROW]
[ROW][C]11[/C][C]0.143567[/C][C]1.1752[/C][C]0.122047[/C][/ROW]
[ROW][C]12[/C][C]0.312007[/C][C]2.5539[/C][C]0.006467[/C][/ROW]
[ROW][C]13[/C][C]0.12979[/C][C]1.0624[/C][C]0.14594[/C][/ROW]
[ROW][C]14[/C][C]0.175191[/C][C]1.434[/C][C]0.078111[/C][/ROW]
[ROW][C]15[/C][C]0.063024[/C][C]0.5159[/C][C]0.303819[/C][/ROW]
[ROW][C]16[/C][C]-0.039548[/C][C]-0.3237[/C][C]0.373582[/C][/ROW]
[ROW][C]17[/C][C]0.0374[/C][C]0.3061[/C][C]0.380227[/C][/ROW]
[ROW][C]18[/C][C]-0.061555[/C][C]-0.5038[/C][C]0.308011[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=105975&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=105975&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	0.270067	2.2106	0.015241
2	0.253769	2.0772	0.02081
3	0.311216	2.5474	0.006577
4	0.165965	1.3585	0.089434
5	0.306561	2.5093	0.00726
6	0.165432	1.3541	0.090124
7	0.10564	0.8647	0.195145
8	0.124632	1.0202	0.155662
9	0.238123	1.9491	0.027734
10	0.156479	1.2808	0.102334
11	0.143567	1.1752	0.122047
12	0.312007	2.5539	0.006467
13	0.12979	1.0624	0.14594
14	0.175191	1.434	0.078111
15	0.063024	0.5159	0.303819
16	-0.039548	-0.3237	0.373582
17	0.0374	0.3061	0.380227
18	-0.061555	-0.5038	0.308011

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.270067	2.2106	0.015241
2	0.19506	1.5966	0.057526
3	0.228047	1.8666	0.033164
4	0.016142	0.1321	0.447641
5	0.203986	1.6697	0.049823
6	-0.016059	-0.1314	0.447907
7	-0.034562	-0.2829	0.389063
8	-0.028519	-0.2334	0.408065
9	0.194587	1.5928	0.05796
10	0.010343	0.0847	0.46639
11	0.032406	0.2653	0.395814
12	0.221141	1.8101	0.037381
13	-0.027491	-0.225	0.411323
14	-0.023888	-0.1955	0.422784
15	-0.154102	-1.2614	0.105773
16	-0.132419	-1.0839	0.141149
17	-0.101342	-0.8295	0.204878
18	-0.106878	-0.8748	0.192394

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.270067 & 2.2106 & 0.015241 \tabularnewline
2 & 0.19506 & 1.5966 & 0.057526 \tabularnewline
3 & 0.228047 & 1.8666 & 0.033164 \tabularnewline
4 & 0.016142 & 0.1321 & 0.447641 \tabularnewline
5 & 0.203986 & 1.6697 & 0.049823 \tabularnewline
6 & -0.016059 & -0.1314 & 0.447907 \tabularnewline
7 & -0.034562 & -0.2829 & 0.389063 \tabularnewline
8 & -0.028519 & -0.2334 & 0.408065 \tabularnewline
9 & 0.194587 & 1.5928 & 0.05796 \tabularnewline
10 & 0.010343 & 0.0847 & 0.46639 \tabularnewline
11 & 0.032406 & 0.2653 & 0.395814 \tabularnewline
12 & 0.221141 & 1.8101 & 0.037381 \tabularnewline
13 & -0.027491 & -0.225 & 0.411323 \tabularnewline
14 & -0.023888 & -0.1955 & 0.422784 \tabularnewline
15 & -0.154102 & -1.2614 & 0.105773 \tabularnewline
16 & -0.132419 & -1.0839 & 0.141149 \tabularnewline
17 & -0.101342 & -0.8295 & 0.204878 \tabularnewline
18 & -0.106878 & -0.8748 & 0.192394 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=105975&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]0.270067[/C][C]2.2106[/C][C]0.015241[/C][/ROW]
[ROW][C]2[/C][C]0.19506[/C][C]1.5966[/C][C]0.057526[/C][/ROW]
[ROW][C]3[/C][C]0.228047[/C][C]1.8666[/C][C]0.033164[/C][/ROW]
[ROW][C]4[/C][C]0.016142[/C][C]0.1321[/C][C]0.447641[/C][/ROW]
[ROW][C]5[/C][C]0.203986[/C][C]1.6697[/C][C]0.049823[/C][/ROW]
[ROW][C]6[/C][C]-0.016059[/C][C]-0.1314[/C][C]0.447907[/C][/ROW]
[ROW][C]7[/C][C]-0.034562[/C][C]-0.2829[/C][C]0.389063[/C][/ROW]
[ROW][C]8[/C][C]-0.028519[/C][C]-0.2334[/C][C]0.408065[/C][/ROW]
[ROW][C]9[/C][C]0.194587[/C][C]1.5928[/C][C]0.05796[/C][/ROW]
[ROW][C]10[/C][C]0.010343[/C][C]0.0847[/C][C]0.46639[/C][/ROW]
[ROW][C]11[/C][C]0.032406[/C][C]0.2653[/C][C]0.395814[/C][/ROW]
[ROW][C]12[/C][C]0.221141[/C][C]1.8101[/C][C]0.037381[/C][/ROW]
[ROW][C]13[/C][C]-0.027491[/C][C]-0.225[/C][C]0.411323[/C][/ROW]
[ROW][C]14[/C][C]-0.023888[/C][C]-0.1955[/C][C]0.422784[/C][/ROW]
[ROW][C]15[/C][C]-0.154102[/C][C]-1.2614[/C][C]0.105773[/C][/ROW]
[ROW][C]16[/C][C]-0.132419[/C][C]-1.0839[/C][C]0.141149[/C][/ROW]
[ROW][C]17[/C][C]-0.101342[/C][C]-0.8295[/C][C]0.204878[/C][/ROW]
[ROW][C]18[/C][C]-0.106878[/C][C]-0.8748[/C][C]0.192394[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=105975&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=105975&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	0.270067	2.2106	0.015241
2	0.19506	1.5966	0.057526
3	0.228047	1.8666	0.033164
4	0.016142	0.1321	0.447641
5	0.203986	1.6697	0.049823
6	-0.016059	-0.1314	0.447907
7	-0.034562	-0.2829	0.389063
8	-0.028519	-0.2334	0.408065
9	0.194587	1.5928	0.05796
10	0.010343	0.0847	0.46639
11	0.032406	0.2653	0.395814
12	0.221141	1.8101	0.037381
13	-0.027491	-0.225	0.411323
14	-0.023888	-0.1955	0.422784
15	-0.154102	-1.2614	0.105773
16	-0.132419	-1.0839	0.141149
17	-0.101342	-0.8295	0.204878
18	-0.106878	-0.8748	0.192394

Figure 1

PNG link

Postscript link

PDF link

Figure 2

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 ;

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 (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='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep=''))
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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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code