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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sun, 02 Dec 2012 05:34:31 -0500

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/2012/Dec/02/t1354444521hkx8fa1xxhajqfp.htm/, Retrieved Fri, 01 Nov 2024 00:29:45 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=195408, Retrieved Fri, 01 Nov 2024 00:29:45 +0000

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180

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]
- R  D    [(Partial) Autocorrelation Function] [ws9] [2012-12-02 10:24:05] [7722d8427d2b2c713c1f0d5525f2f86c]
-   PD        [(Partial) Autocorrelation Function] [ws9] [2012-12-02 10:34:31] [2bcb0f1dab9cffb75c9fd882cacbd29a] [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	4 seconds
R Server	'Gwilym Jenkins' @ jenkins.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 & 4 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=195408&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]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=195408&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=195408&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	4 seconds
R Server	'Gwilym Jenkins' @ jenkins.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.649612	-5.5121	0
2	0.202061	1.7145	0.045365
3	-0.009466	-0.0803	0.468104
4	-0.073787	-0.6261	0.266614
5	0.036971	0.3137	0.377325
6	0.02904	0.2464	0.403031
7	-0.025003	-0.2122	0.416291
8	-0.012847	-0.109	0.456749
9	0.023528	0.1996	0.421163
10	-0.042527	-0.3609	0.359634
11	0.142019	1.2051	0.116061
12	-0.217793	-1.848	0.034352
13	0.131464	1.1155	0.13417
14	0.0254	0.2155	0.414982
15	-0.062882	-0.5336	0.297642
16	0.042909	0.3641	0.358426
17	-0.082671	-0.7015	0.242631
18	0.116777	0.9909	0.16253
19	-0.09338	-0.7924	0.215379

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.649612 & -5.5121 & 0 \tabularnewline
2 & 0.202061 & 1.7145 & 0.045365 \tabularnewline
3 & -0.009466 & -0.0803 & 0.468104 \tabularnewline
4 & -0.073787 & -0.6261 & 0.266614 \tabularnewline
5 & 0.036971 & 0.3137 & 0.377325 \tabularnewline
6 & 0.02904 & 0.2464 & 0.403031 \tabularnewline
7 & -0.025003 & -0.2122 & 0.416291 \tabularnewline
8 & -0.012847 & -0.109 & 0.456749 \tabularnewline
9 & 0.023528 & 0.1996 & 0.421163 \tabularnewline
10 & -0.042527 & -0.3609 & 0.359634 \tabularnewline
11 & 0.142019 & 1.2051 & 0.116061 \tabularnewline
12 & -0.217793 & -1.848 & 0.034352 \tabularnewline
13 & 0.131464 & 1.1155 & 0.13417 \tabularnewline
14 & 0.0254 & 0.2155 & 0.414982 \tabularnewline
15 & -0.062882 & -0.5336 & 0.297642 \tabularnewline
16 & 0.042909 & 0.3641 & 0.358426 \tabularnewline
17 & -0.082671 & -0.7015 & 0.242631 \tabularnewline
18 & 0.116777 & 0.9909 & 0.16253 \tabularnewline
19 & -0.09338 & -0.7924 & 0.215379 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=195408&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]-0.649612[/C][C]-5.5121[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.202061[/C][C]1.7145[/C][C]0.045365[/C][/ROW]
[ROW][C]3[/C][C]-0.009466[/C][C]-0.0803[/C][C]0.468104[/C][/ROW]
[ROW][C]4[/C][C]-0.073787[/C][C]-0.6261[/C][C]0.266614[/C][/ROW]
[ROW][C]5[/C][C]0.036971[/C][C]0.3137[/C][C]0.377325[/C][/ROW]
[ROW][C]6[/C][C]0.02904[/C][C]0.2464[/C][C]0.403031[/C][/ROW]
[ROW][C]7[/C][C]-0.025003[/C][C]-0.2122[/C][C]0.416291[/C][/ROW]
[ROW][C]8[/C][C]-0.012847[/C][C]-0.109[/C][C]0.456749[/C][/ROW]
[ROW][C]9[/C][C]0.023528[/C][C]0.1996[/C][C]0.421163[/C][/ROW]
[ROW][C]10[/C][C]-0.042527[/C][C]-0.3609[/C][C]0.359634[/C][/ROW]
[ROW][C]11[/C][C]0.142019[/C][C]1.2051[/C][C]0.116061[/C][/ROW]
[ROW][C]12[/C][C]-0.217793[/C][C]-1.848[/C][C]0.034352[/C][/ROW]
[ROW][C]13[/C][C]0.131464[/C][C]1.1155[/C][C]0.13417[/C][/ROW]
[ROW][C]14[/C][C]0.0254[/C][C]0.2155[/C][C]0.414982[/C][/ROW]
[ROW][C]15[/C][C]-0.062882[/C][C]-0.5336[/C][C]0.297642[/C][/ROW]
[ROW][C]16[/C][C]0.042909[/C][C]0.3641[/C][C]0.358426[/C][/ROW]
[ROW][C]17[/C][C]-0.082671[/C][C]-0.7015[/C][C]0.242631[/C][/ROW]
[ROW][C]18[/C][C]0.116777[/C][C]0.9909[/C][C]0.16253[/C][/ROW]
[ROW][C]19[/C][C]-0.09338[/C][C]-0.7924[/C][C]0.215379[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=195408&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=195408&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	-0.649612	-5.5121	0
2	0.202061	1.7145	0.045365
3	-0.009466	-0.0803	0.468104
4	-0.073787	-0.6261	0.266614
5	0.036971	0.3137	0.377325
6	0.02904	0.2464	0.403031
7	-0.025003	-0.2122	0.416291
8	-0.012847	-0.109	0.456749
9	0.023528	0.1996	0.421163
10	-0.042527	-0.3609	0.359634
11	0.142019	1.2051	0.116061
12	-0.217793	-1.848	0.034352
13	0.131464	1.1155	0.13417
14	0.0254	0.2155	0.414982
15	-0.062882	-0.5336	0.297642
16	0.042909	0.3641	0.358426
17	-0.082671	-0.7015	0.242631
18	0.116777	0.9909	0.16253
19	-0.09338	-0.7924	0.215379

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.649612	-5.5121	0
2	-0.380507	-3.2287	0.000937
3	-0.152616	-1.295	0.09973
4	-0.160367	-1.3608	0.088917
5	-0.17724	-1.5039	0.068486
6	-0.073658	-0.625	0.266972
7	-0.007847	-0.0666	0.473549
8	-0.047705	-0.4048	0.343416
9	-0.043469	-0.3688	0.356664
10	-0.080135	-0.68	0.249353
11	0.170049	1.4429	0.07669
12	-0.029884	-0.2536	0.400274
13	-0.121272	-1.029	0.153457
14	0.056422	0.4788	0.316782
15	0.120201	1.0199	0.155586
16	0.065452	0.5554	0.290179
17	-0.136052	-1.1544	0.126069
18	0.038446	0.3262	0.3726
19	0.072783	0.6176	0.269398

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.649612 & -5.5121 & 0 \tabularnewline
2 & -0.380507 & -3.2287 & 0.000937 \tabularnewline
3 & -0.152616 & -1.295 & 0.09973 \tabularnewline
4 & -0.160367 & -1.3608 & 0.088917 \tabularnewline
5 & -0.17724 & -1.5039 & 0.068486 \tabularnewline
6 & -0.073658 & -0.625 & 0.266972 \tabularnewline
7 & -0.007847 & -0.0666 & 0.473549 \tabularnewline
8 & -0.047705 & -0.4048 & 0.343416 \tabularnewline
9 & -0.043469 & -0.3688 & 0.356664 \tabularnewline
10 & -0.080135 & -0.68 & 0.249353 \tabularnewline
11 & 0.170049 & 1.4429 & 0.07669 \tabularnewline
12 & -0.029884 & -0.2536 & 0.400274 \tabularnewline
13 & -0.121272 & -1.029 & 0.153457 \tabularnewline
14 & 0.056422 & 0.4788 & 0.316782 \tabularnewline
15 & 0.120201 & 1.0199 & 0.155586 \tabularnewline
16 & 0.065452 & 0.5554 & 0.290179 \tabularnewline
17 & -0.136052 & -1.1544 & 0.126069 \tabularnewline
18 & 0.038446 & 0.3262 & 0.3726 \tabularnewline
19 & 0.072783 & 0.6176 & 0.269398 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=195408&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]-0.649612[/C][C]-5.5121[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.380507[/C][C]-3.2287[/C][C]0.000937[/C][/ROW]
[ROW][C]3[/C][C]-0.152616[/C][C]-1.295[/C][C]0.09973[/C][/ROW]
[ROW][C]4[/C][C]-0.160367[/C][C]-1.3608[/C][C]0.088917[/C][/ROW]
[ROW][C]5[/C][C]-0.17724[/C][C]-1.5039[/C][C]0.068486[/C][/ROW]
[ROW][C]6[/C][C]-0.073658[/C][C]-0.625[/C][C]0.266972[/C][/ROW]
[ROW][C]7[/C][C]-0.007847[/C][C]-0.0666[/C][C]0.473549[/C][/ROW]
[ROW][C]8[/C][C]-0.047705[/C][C]-0.4048[/C][C]0.343416[/C][/ROW]
[ROW][C]9[/C][C]-0.043469[/C][C]-0.3688[/C][C]0.356664[/C][/ROW]
[ROW][C]10[/C][C]-0.080135[/C][C]-0.68[/C][C]0.249353[/C][/ROW]
[ROW][C]11[/C][C]0.170049[/C][C]1.4429[/C][C]0.07669[/C][/ROW]
[ROW][C]12[/C][C]-0.029884[/C][C]-0.2536[/C][C]0.400274[/C][/ROW]
[ROW][C]13[/C][C]-0.121272[/C][C]-1.029[/C][C]0.153457[/C][/ROW]
[ROW][C]14[/C][C]0.056422[/C][C]0.4788[/C][C]0.316782[/C][/ROW]
[ROW][C]15[/C][C]0.120201[/C][C]1.0199[/C][C]0.155586[/C][/ROW]
[ROW][C]16[/C][C]0.065452[/C][C]0.5554[/C][C]0.290179[/C][/ROW]
[ROW][C]17[/C][C]-0.136052[/C][C]-1.1544[/C][C]0.126069[/C][/ROW]
[ROW][C]18[/C][C]0.038446[/C][C]0.3262[/C][C]0.3726[/C][/ROW]
[ROW][C]19[/C][C]0.072783[/C][C]0.6176[/C][C]0.269398[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=195408&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=195408&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	-0.649612	-5.5121	0
2	-0.380507	-3.2287	0.000937
3	-0.152616	-1.295	0.09973
4	-0.160367	-1.3608	0.088917
5	-0.17724	-1.5039	0.068486
6	-0.073658	-0.625	0.266972
7	-0.007847	-0.0666	0.473549
8	-0.047705	-0.4048	0.343416
9	-0.043469	-0.3688	0.356664
10	-0.080135	-0.68	0.249353
11	0.170049	1.4429	0.07669
12	-0.029884	-0.2536	0.400274
13	-0.121272	-1.029	0.153457
14	0.056422	0.4788	0.316782
15	0.120201	1.0199	0.155586
16	0.065452	0.5554	0.290179
17	-0.136052	-1.1544	0.126069
18	0.038446	0.3262	0.3726
19	0.072783	0.6176	0.269398

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 1 ; 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 (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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Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code