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Author

*The author of this computation has been verified*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Tue, 15 Dec 2009 03:45:27 -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/2009/Dec/15/t1260873992ffar70zp44cw5e2.htm/, Retrieved Wed, 08 May 2024 18:28:43 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=67831, Retrieved Wed, 08 May 2024 18:28:43 +0000

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No (this computation is public)

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Estimated Impact

115

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

-       [(Partial) Autocorrelation Function] [Autocorrelation (...] [2009-12-15 10:45:27] [91da2e1ebdd83187f2515f461585cbee] [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	3 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

\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 & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=67831&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=67831&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67831&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	3 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.278655	-3.1894	0.000892
2	-0.364373	-4.1704	2.7e-05
3	0.132999	1.5222	0.065179
4	0.052286	0.5984	0.27529
5	-0.109944	-1.2584	0.105248
6	0.244717	2.8009	0.002934
7	-0.206749	-2.3663	0.009715
8	0.178613	2.0443	0.021463
9	0.023176	0.2653	0.395614
10	-0.377541	-4.3211	1.5e-05
11	-0.112042	-1.2824	0.100988
12	0.721879	8.2623	0
13	-0.219746	-2.5151	0.006555
14	-0.258647	-2.9604	0.001824
15	0.019283	0.2207	0.412834
16	0.066222	0.7579	0.224923
17	-0.053258	-0.6096	0.271602
18	0.155607	1.781	0.038615
19	-0.141414	-1.6186	0.053974
20	0.19404	2.2209	0.014038
21	-0.067586	-0.7736	0.220293

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.278655 & -3.1894 & 0.000892 \tabularnewline
2 & -0.364373 & -4.1704 & 2.7e-05 \tabularnewline
3 & 0.132999 & 1.5222 & 0.065179 \tabularnewline
4 & 0.052286 & 0.5984 & 0.27529 \tabularnewline
5 & -0.109944 & -1.2584 & 0.105248 \tabularnewline
6 & 0.244717 & 2.8009 & 0.002934 \tabularnewline
7 & -0.206749 & -2.3663 & 0.009715 \tabularnewline
8 & 0.178613 & 2.0443 & 0.021463 \tabularnewline
9 & 0.023176 & 0.2653 & 0.395614 \tabularnewline
10 & -0.377541 & -4.3211 & 1.5e-05 \tabularnewline
11 & -0.112042 & -1.2824 & 0.100988 \tabularnewline
12 & 0.721879 & 8.2623 & 0 \tabularnewline
13 & -0.219746 & -2.5151 & 0.006555 \tabularnewline
14 & -0.258647 & -2.9604 & 0.001824 \tabularnewline
15 & 0.019283 & 0.2207 & 0.412834 \tabularnewline
16 & 0.066222 & 0.7579 & 0.224923 \tabularnewline
17 & -0.053258 & -0.6096 & 0.271602 \tabularnewline
18 & 0.155607 & 1.781 & 0.038615 \tabularnewline
19 & -0.141414 & -1.6186 & 0.053974 \tabularnewline
20 & 0.19404 & 2.2209 & 0.014038 \tabularnewline
21 & -0.067586 & -0.7736 & 0.220293 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=67831&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]-0.278655[/C][C]-3.1894[/C][C]0.000892[/C][/ROW]
[ROW][C]2[/C][C]-0.364373[/C][C]-4.1704[/C][C]2.7e-05[/C][/ROW]
[ROW][C]3[/C][C]0.132999[/C][C]1.5222[/C][C]0.065179[/C][/ROW]
[ROW][C]4[/C][C]0.052286[/C][C]0.5984[/C][C]0.27529[/C][/ROW]
[ROW][C]5[/C][C]-0.109944[/C][C]-1.2584[/C][C]0.105248[/C][/ROW]
[ROW][C]6[/C][C]0.244717[/C][C]2.8009[/C][C]0.002934[/C][/ROW]
[ROW][C]7[/C][C]-0.206749[/C][C]-2.3663[/C][C]0.009715[/C][/ROW]
[ROW][C]8[/C][C]0.178613[/C][C]2.0443[/C][C]0.021463[/C][/ROW]
[ROW][C]9[/C][C]0.023176[/C][C]0.2653[/C][C]0.395614[/C][/ROW]
[ROW][C]10[/C][C]-0.377541[/C][C]-4.3211[/C][C]1.5e-05[/C][/ROW]
[ROW][C]11[/C][C]-0.112042[/C][C]-1.2824[/C][C]0.100988[/C][/ROW]
[ROW][C]12[/C][C]0.721879[/C][C]8.2623[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]-0.219746[/C][C]-2.5151[/C][C]0.006555[/C][/ROW]
[ROW][C]14[/C][C]-0.258647[/C][C]-2.9604[/C][C]0.001824[/C][/ROW]
[ROW][C]15[/C][C]0.019283[/C][C]0.2207[/C][C]0.412834[/C][/ROW]
[ROW][C]16[/C][C]0.066222[/C][C]0.7579[/C][C]0.224923[/C][/ROW]
[ROW][C]17[/C][C]-0.053258[/C][C]-0.6096[/C][C]0.271602[/C][/ROW]
[ROW][C]18[/C][C]0.155607[/C][C]1.781[/C][C]0.038615[/C][/ROW]
[ROW][C]19[/C][C]-0.141414[/C][C]-1.6186[/C][C]0.053974[/C][/ROW]
[ROW][C]20[/C][C]0.19404[/C][C]2.2209[/C][C]0.014038[/C][/ROW]
[ROW][C]21[/C][C]-0.067586[/C][C]-0.7736[/C][C]0.220293[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=67831&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67831&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	-0.278655	-3.1894	0.000892
2	-0.364373	-4.1704	2.7e-05
3	0.132999	1.5222	0.065179
4	0.052286	0.5984	0.27529
5	-0.109944	-1.2584	0.105248
6	0.244717	2.8009	0.002934
7	-0.206749	-2.3663	0.009715
8	0.178613	2.0443	0.021463
9	0.023176	0.2653	0.395614
10	-0.377541	-4.3211	1.5e-05
11	-0.112042	-1.2824	0.100988
12	0.721879	8.2623	0
13	-0.219746	-2.5151	0.006555
14	-0.258647	-2.9604	0.001824
15	0.019283	0.2207	0.412834
16	0.066222	0.7579	0.224923
17	-0.053258	-0.6096	0.271602
18	0.155607	1.781	0.038615
19	-0.141414	-1.6186	0.053974
20	0.19404	2.2209	0.014038
21	-0.067586	-0.7736	0.220293

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.278655	-3.1894	0.000892
2	-0.479234	-5.4851	0
3	-0.212148	-2.4282	0.008267
4	-0.21365	-2.4453	0.0079
5	-0.256461	-2.9353	0.001968
6	0.13587	1.5551	0.061167
7	-0.191119	-2.1875	0.015242
8	0.368999	4.2234	2.2e-05
9	0.185058	2.1181	0.018028
10	-0.211593	-2.4218	0.008407
11	-0.559114	-6.3993	0
12	0.254803	2.9164	0.002084
13	0.169789	1.9433	0.027061
14	0.163518	1.8715	0.03175
15	-0.120872	-1.3834	0.084442
16	-0.03562	-0.4077	0.342085
17	-0.085634	-0.9801	0.164414
18	-0.08955	-1.0249	0.153639
19	0.039486	0.4519	0.326029
20	0.010815	0.1238	0.450839
21	-0.034814	-0.3985	0.345468

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.278655 & -3.1894 & 0.000892 \tabularnewline
2 & -0.479234 & -5.4851 & 0 \tabularnewline
3 & -0.212148 & -2.4282 & 0.008267 \tabularnewline
4 & -0.21365 & -2.4453 & 0.0079 \tabularnewline
5 & -0.256461 & -2.9353 & 0.001968 \tabularnewline
6 & 0.13587 & 1.5551 & 0.061167 \tabularnewline
7 & -0.191119 & -2.1875 & 0.015242 \tabularnewline
8 & 0.368999 & 4.2234 & 2.2e-05 \tabularnewline
9 & 0.185058 & 2.1181 & 0.018028 \tabularnewline
10 & -0.211593 & -2.4218 & 0.008407 \tabularnewline
11 & -0.559114 & -6.3993 & 0 \tabularnewline
12 & 0.254803 & 2.9164 & 0.002084 \tabularnewline
13 & 0.169789 & 1.9433 & 0.027061 \tabularnewline
14 & 0.163518 & 1.8715 & 0.03175 \tabularnewline
15 & -0.120872 & -1.3834 & 0.084442 \tabularnewline
16 & -0.03562 & -0.4077 & 0.342085 \tabularnewline
17 & -0.085634 & -0.9801 & 0.164414 \tabularnewline
18 & -0.08955 & -1.0249 & 0.153639 \tabularnewline
19 & 0.039486 & 0.4519 & 0.326029 \tabularnewline
20 & 0.010815 & 0.1238 & 0.450839 \tabularnewline
21 & -0.034814 & -0.3985 & 0.345468 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=67831&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]-0.278655[/C][C]-3.1894[/C][C]0.000892[/C][/ROW]
[ROW][C]2[/C][C]-0.479234[/C][C]-5.4851[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]-0.212148[/C][C]-2.4282[/C][C]0.008267[/C][/ROW]
[ROW][C]4[/C][C]-0.21365[/C][C]-2.4453[/C][C]0.0079[/C][/ROW]
[ROW][C]5[/C][C]-0.256461[/C][C]-2.9353[/C][C]0.001968[/C][/ROW]
[ROW][C]6[/C][C]0.13587[/C][C]1.5551[/C][C]0.061167[/C][/ROW]
[ROW][C]7[/C][C]-0.191119[/C][C]-2.1875[/C][C]0.015242[/C][/ROW]
[ROW][C]8[/C][C]0.368999[/C][C]4.2234[/C][C]2.2e-05[/C][/ROW]
[ROW][C]9[/C][C]0.185058[/C][C]2.1181[/C][C]0.018028[/C][/ROW]
[ROW][C]10[/C][C]-0.211593[/C][C]-2.4218[/C][C]0.008407[/C][/ROW]
[ROW][C]11[/C][C]-0.559114[/C][C]-6.3993[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.254803[/C][C]2.9164[/C][C]0.002084[/C][/ROW]
[ROW][C]13[/C][C]0.169789[/C][C]1.9433[/C][C]0.027061[/C][/ROW]
[ROW][C]14[/C][C]0.163518[/C][C]1.8715[/C][C]0.03175[/C][/ROW]
[ROW][C]15[/C][C]-0.120872[/C][C]-1.3834[/C][C]0.084442[/C][/ROW]
[ROW][C]16[/C][C]-0.03562[/C][C]-0.4077[/C][C]0.342085[/C][/ROW]
[ROW][C]17[/C][C]-0.085634[/C][C]-0.9801[/C][C]0.164414[/C][/ROW]
[ROW][C]18[/C][C]-0.08955[/C][C]-1.0249[/C][C]0.153639[/C][/ROW]
[ROW][C]19[/C][C]0.039486[/C][C]0.4519[/C][C]0.326029[/C][/ROW]
[ROW][C]20[/C][C]0.010815[/C][C]0.1238[/C][C]0.450839[/C][/ROW]
[ROW][C]21[/C][C]-0.034814[/C][C]-0.3985[/C][C]0.345468[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=67831&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67831&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	-0.278655	-3.1894	0.000892
2	-0.479234	-5.4851	0
3	-0.212148	-2.4282	0.008267
4	-0.21365	-2.4453	0.0079
5	-0.256461	-2.9353	0.001968
6	0.13587	1.5551	0.061167
7	-0.191119	-2.1875	0.015242
8	0.368999	4.2234	2.2e-05
9	0.185058	2.1181	0.018028
10	-0.211593	-2.4218	0.008407
11	-0.559114	-6.3993	0
12	0.254803	2.9164	0.002084
13	0.169789	1.9433	0.027061
14	0.163518	1.8715	0.03175
15	-0.120872	-1.3834	0.084442
16	-0.03562	-0.4077	0.342085
17	-0.085634	-0.9801	0.164414
18	-0.08955	-1.0249	0.153639
19	0.039486	0.4519	0.326029
20	0.010815	0.1238	0.450839
21	-0.034814	-0.3985	0.345468

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = 0.0 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 0.0 ; par3 = 1 ; 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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code