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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 03 Dec 2010 10:43:29 +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/03/t1291372996vm0uxi59fjtoc89.htm/, Retrieved Tue, 07 May 2024 15:22:32 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=104625, Retrieved Tue, 07 May 2024 15:22:32 +0000

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User-defined keywords

Estimated Impact

204

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] [Workshop 9] [2010-12-03 10:43:29] [ecfb965f5669057f3ac5b58964283289] [Current]
-   P         [(Partial) Autocorrelation Function] [Workshop 9] [2010-12-03 10:48:00] [39c51da0be01189e8a44eb69e891b7a1] 
-   P           [(Partial) Autocorrelation Function] [Workshop 9] [2010-12-03 12:19:31] [39c51da0be01189e8a44eb69e891b7a1] 
-    D            [(Partial) Autocorrelation Function] [Autocorrelation A...] [2010-12-21 12:22:09] [f9eaed74daea918f73b9f505c5b1f19e] 
-   P               [(Partial) Autocorrelation Function] [Autocorrelation A...] [2010-12-21 13:51:25] [f9eaed74daea918f73b9f505c5b1f19e] 
-   P               [(Partial) Autocorrelation Function] [Autocorrelation A...] [2010-12-21 14:56:54] [f9eaed74daea918f73b9f505c5b1f19e] 
-    D          [(Partial) Autocorrelation Function] [Autocorrelation ACF] [2010-12-21 11:32:47] [f9eaed74daea918f73b9f505c5b1f19e] 

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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=104625&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=104625&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=104625&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	0.33367	2.5846	0.0061
2	0.148125	1.1474	0.127891
3	0.037858	0.2932	0.385172
4	-0.195877	-1.5173	0.067226
5	-0.365484	-2.831	0.003152
6	-0.565263	-4.3785	2.4e-05
7	-0.393652	-3.0492	0.001706
8	-0.231438	-1.7927	0.03903
9	-0.019435	-0.1505	0.44042
10	0.101469	0.786	0.217488
11	0.319608	2.4757	0.008069
12	0.686578	5.3182	1e-06
13	0.297152	2.3017	0.012419
14	0.169604	1.3137	0.096967
15	0.075551	0.5852	0.280298
16	-0.077209	-0.5981	0.276026
17	-0.268161	-2.0772	0.021038

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.33367 & 2.5846 & 0.0061 \tabularnewline
2 & 0.148125 & 1.1474 & 0.127891 \tabularnewline
3 & 0.037858 & 0.2932 & 0.385172 \tabularnewline
4 & -0.195877 & -1.5173 & 0.067226 \tabularnewline
5 & -0.365484 & -2.831 & 0.003152 \tabularnewline
6 & -0.565263 & -4.3785 & 2.4e-05 \tabularnewline
7 & -0.393652 & -3.0492 & 0.001706 \tabularnewline
8 & -0.231438 & -1.7927 & 0.03903 \tabularnewline
9 & -0.019435 & -0.1505 & 0.44042 \tabularnewline
10 & 0.101469 & 0.786 & 0.217488 \tabularnewline
11 & 0.319608 & 2.4757 & 0.008069 \tabularnewline
12 & 0.686578 & 5.3182 & 1e-06 \tabularnewline
13 & 0.297152 & 2.3017 & 0.012419 \tabularnewline
14 & 0.169604 & 1.3137 & 0.096967 \tabularnewline
15 & 0.075551 & 0.5852 & 0.280298 \tabularnewline
16 & -0.077209 & -0.5981 & 0.276026 \tabularnewline
17 & -0.268161 & -2.0772 & 0.021038 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=104625&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]0.33367[/C][C]2.5846[/C][C]0.0061[/C][/ROW]
[ROW][C]2[/C][C]0.148125[/C][C]1.1474[/C][C]0.127891[/C][/ROW]
[ROW][C]3[/C][C]0.037858[/C][C]0.2932[/C][C]0.385172[/C][/ROW]
[ROW][C]4[/C][C]-0.195877[/C][C]-1.5173[/C][C]0.067226[/C][/ROW]
[ROW][C]5[/C][C]-0.365484[/C][C]-2.831[/C][C]0.003152[/C][/ROW]
[ROW][C]6[/C][C]-0.565263[/C][C]-4.3785[/C][C]2.4e-05[/C][/ROW]
[ROW][C]7[/C][C]-0.393652[/C][C]-3.0492[/C][C]0.001706[/C][/ROW]
[ROW][C]8[/C][C]-0.231438[/C][C]-1.7927[/C][C]0.03903[/C][/ROW]
[ROW][C]9[/C][C]-0.019435[/C][C]-0.1505[/C][C]0.44042[/C][/ROW]
[ROW][C]10[/C][C]0.101469[/C][C]0.786[/C][C]0.217488[/C][/ROW]
[ROW][C]11[/C][C]0.319608[/C][C]2.4757[/C][C]0.008069[/C][/ROW]
[ROW][C]12[/C][C]0.686578[/C][C]5.3182[/C][C]1e-06[/C][/ROW]
[ROW][C]13[/C][C]0.297152[/C][C]2.3017[/C][C]0.012419[/C][/ROW]
[ROW][C]14[/C][C]0.169604[/C][C]1.3137[/C][C]0.096967[/C][/ROW]
[ROW][C]15[/C][C]0.075551[/C][C]0.5852[/C][C]0.280298[/C][/ROW]
[ROW][C]16[/C][C]-0.077209[/C][C]-0.5981[/C][C]0.276026[/C][/ROW]
[ROW][C]17[/C][C]-0.268161[/C][C]-2.0772[/C][C]0.021038[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=104625&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=104625&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	0.33367	2.5846	0.0061
2	0.148125	1.1474	0.127891
3	0.037858	0.2932	0.385172
4	-0.195877	-1.5173	0.067226
5	-0.365484	-2.831	0.003152
6	-0.565263	-4.3785	2.4e-05
7	-0.393652	-3.0492	0.001706
8	-0.231438	-1.7927	0.03903
9	-0.019435	-0.1505	0.44042
10	0.101469	0.786	0.217488
11	0.319608	2.4757	0.008069
12	0.686578	5.3182	1e-06
13	0.297152	2.3017	0.012419
14	0.169604	1.3137	0.096967
15	0.075551	0.5852	0.280298
16	-0.077209	-0.5981	0.276026
17	-0.268161	-2.0772	0.021038

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.33367	2.5846	0.0061
2	0.041398	0.3207	0.374787
3	-0.026303	-0.2037	0.419624
4	-0.233078	-1.8054	0.038014
5	-0.280972	-2.1764	0.016736
6	-0.449056	-3.4784	0.000473
7	-0.198886	-1.5406	0.06434
8	-0.147075	-1.1392	0.129567
9	0.000251	0.0019	0.499227
10	-0.121914	-0.9443	0.174391
11	0.018207	0.141	0.444158
12	0.455462	3.528	0.000405
13	-0.112279	-0.8697	0.193963
14	-0.067449	-0.5225	0.301639
15	-0.010423	-0.0807	0.467961
16	0.128887	0.9984	0.161059
17	0.073993	0.5731	0.284344

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.33367 & 2.5846 & 0.0061 \tabularnewline
2 & 0.041398 & 0.3207 & 0.374787 \tabularnewline
3 & -0.026303 & -0.2037 & 0.419624 \tabularnewline
4 & -0.233078 & -1.8054 & 0.038014 \tabularnewline
5 & -0.280972 & -2.1764 & 0.016736 \tabularnewline
6 & -0.449056 & -3.4784 & 0.000473 \tabularnewline
7 & -0.198886 & -1.5406 & 0.06434 \tabularnewline
8 & -0.147075 & -1.1392 & 0.129567 \tabularnewline
9 & 0.000251 & 0.0019 & 0.499227 \tabularnewline
10 & -0.121914 & -0.9443 & 0.174391 \tabularnewline
11 & 0.018207 & 0.141 & 0.444158 \tabularnewline
12 & 0.455462 & 3.528 & 0.000405 \tabularnewline
13 & -0.112279 & -0.8697 & 0.193963 \tabularnewline
14 & -0.067449 & -0.5225 & 0.301639 \tabularnewline
15 & -0.010423 & -0.0807 & 0.467961 \tabularnewline
16 & 0.128887 & 0.9984 & 0.161059 \tabularnewline
17 & 0.073993 & 0.5731 & 0.284344 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=104625&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]0.33367[/C][C]2.5846[/C][C]0.0061[/C][/ROW]
[ROW][C]2[/C][C]0.041398[/C][C]0.3207[/C][C]0.374787[/C][/ROW]
[ROW][C]3[/C][C]-0.026303[/C][C]-0.2037[/C][C]0.419624[/C][/ROW]
[ROW][C]4[/C][C]-0.233078[/C][C]-1.8054[/C][C]0.038014[/C][/ROW]
[ROW][C]5[/C][C]-0.280972[/C][C]-2.1764[/C][C]0.016736[/C][/ROW]
[ROW][C]6[/C][C]-0.449056[/C][C]-3.4784[/C][C]0.000473[/C][/ROW]
[ROW][C]7[/C][C]-0.198886[/C][C]-1.5406[/C][C]0.06434[/C][/ROW]
[ROW][C]8[/C][C]-0.147075[/C][C]-1.1392[/C][C]0.129567[/C][/ROW]
[ROW][C]9[/C][C]0.000251[/C][C]0.0019[/C][C]0.499227[/C][/ROW]
[ROW][C]10[/C][C]-0.121914[/C][C]-0.9443[/C][C]0.174391[/C][/ROW]
[ROW][C]11[/C][C]0.018207[/C][C]0.141[/C][C]0.444158[/C][/ROW]
[ROW][C]12[/C][C]0.455462[/C][C]3.528[/C][C]0.000405[/C][/ROW]
[ROW][C]13[/C][C]-0.112279[/C][C]-0.8697[/C][C]0.193963[/C][/ROW]
[ROW][C]14[/C][C]-0.067449[/C][C]-0.5225[/C][C]0.301639[/C][/ROW]
[ROW][C]15[/C][C]-0.010423[/C][C]-0.0807[/C][C]0.467961[/C][/ROW]
[ROW][C]16[/C][C]0.128887[/C][C]0.9984[/C][C]0.161059[/C][/ROW]
[ROW][C]17[/C][C]0.073993[/C][C]0.5731[/C][C]0.284344[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=104625&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=104625&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	0.33367	2.5846	0.0061
2	0.041398	0.3207	0.374787
3	-0.026303	-0.2037	0.419624
4	-0.233078	-1.8054	0.038014
5	-0.280972	-2.1764	0.016736
6	-0.449056	-3.4784	0.000473
7	-0.198886	-1.5406	0.06434
8	-0.147075	-1.1392	0.129567
9	0.000251	0.0019	0.499227
10	-0.121914	-0.9443	0.174391
11	0.018207	0.141	0.444158
12	0.455462	3.528	0.000405
13	-0.112279	-0.8697	0.193963
14	-0.067449	-0.5225	0.301639
15	-0.010423	-0.0807	0.467961
16	0.128887	0.9984	0.161059
17	0.073993	0.5731	0.284344

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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Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code