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Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Tue, 27 Nov 2007 10:07:40 -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/2007/Nov/27/t1196182683cmwrgscmsdd1cm1.htm/, Retrieved Sun, 05 May 2024 11:57:39 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=6891, Retrieved Sun, 05 May 2024 11:57:39 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

groep MENS

Estimated Impact

171

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

-       [(Partial) Autocorrelation Function] [Textiel_Q2_autoco...] [2007-11-27 17:07:40] [183840e644503a44411d430a3cdac4ba] [Current]

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Summary of compuational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of compuational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6891&T=0

[TABLE]
[ROW][C]Summary of compuational 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]1 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=6891&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6891&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 compuational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
0	1	8.544	0
1	0.777717	6.6448	0
2	0.667956	5.707	0
3	0.634233	5.4189	0
4	0.537231	4.5901	9e-06
5	0.466557	3.9863	7.9e-05
6	0.391141	3.3419	0.000657
7	0.26343	2.2507	0.013707
8	0.198466	1.6957	0.047102
9	0.132211	1.1296	0.131169
10	0.007068	0.0604	0.476007
11	-0.078718	-0.6726	0.748328
12	-0.231771	-1.9803	0.974278
13	-0.289015	-2.4693	0.992062
14	-0.296692	-2.5349	0.993305
15	-0.296089	-2.5298	0.993214
16	-0.314041	-2.6832	0.995492
17	-0.330171	-2.821	0.996919

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 8.544 & 0 \tabularnewline
1 & 0.777717 & 6.6448 & 0 \tabularnewline
2 & 0.667956 & 5.707 & 0 \tabularnewline
3 & 0.634233 & 5.4189 & 0 \tabularnewline
4 & 0.537231 & 4.5901 & 9e-06 \tabularnewline
5 & 0.466557 & 3.9863 & 7.9e-05 \tabularnewline
6 & 0.391141 & 3.3419 & 0.000657 \tabularnewline
7 & 0.26343 & 2.2507 & 0.013707 \tabularnewline
8 & 0.198466 & 1.6957 & 0.047102 \tabularnewline
9 & 0.132211 & 1.1296 & 0.131169 \tabularnewline
10 & 0.007068 & 0.0604 & 0.476007 \tabularnewline
11 & -0.078718 & -0.6726 & 0.748328 \tabularnewline
12 & -0.231771 & -1.9803 & 0.974278 \tabularnewline
13 & -0.289015 & -2.4693 & 0.992062 \tabularnewline
14 & -0.296692 & -2.5349 & 0.993305 \tabularnewline
15 & -0.296089 & -2.5298 & 0.993214 \tabularnewline
16 & -0.314041 & -2.6832 & 0.995492 \tabularnewline
17 & -0.330171 & -2.821 & 0.996919 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6891&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]0[/C][C]1[/C][C]8.544[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.777717[/C][C]6.6448[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.667956[/C][C]5.707[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.634233[/C][C]5.4189[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.537231[/C][C]4.5901[/C][C]9e-06[/C][/ROW]
[ROW][C]5[/C][C]0.466557[/C][C]3.9863[/C][C]7.9e-05[/C][/ROW]
[ROW][C]6[/C][C]0.391141[/C][C]3.3419[/C][C]0.000657[/C][/ROW]
[ROW][C]7[/C][C]0.26343[/C][C]2.2507[/C][C]0.013707[/C][/ROW]
[ROW][C]8[/C][C]0.198466[/C][C]1.6957[/C][C]0.047102[/C][/ROW]
[ROW][C]9[/C][C]0.132211[/C][C]1.1296[/C][C]0.131169[/C][/ROW]
[ROW][C]10[/C][C]0.007068[/C][C]0.0604[/C][C]0.476007[/C][/ROW]
[ROW][C]11[/C][C]-0.078718[/C][C]-0.6726[/C][C]0.748328[/C][/ROW]
[ROW][C]12[/C][C]-0.231771[/C][C]-1.9803[/C][C]0.974278[/C][/ROW]
[ROW][C]13[/C][C]-0.289015[/C][C]-2.4693[/C][C]0.992062[/C][/ROW]
[ROW][C]14[/C][C]-0.296692[/C][C]-2.5349[/C][C]0.993305[/C][/ROW]
[ROW][C]15[/C][C]-0.296089[/C][C]-2.5298[/C][C]0.993214[/C][/ROW]
[ROW][C]16[/C][C]-0.314041[/C][C]-2.6832[/C][C]0.995492[/C][/ROW]
[ROW][C]17[/C][C]-0.330171[/C][C]-2.821[/C][C]0.996919[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6891&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6891&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
0	1	8.544	0
1	0.777717	6.6448	0
2	0.667956	5.707	0
3	0.634233	5.4189	0
4	0.537231	4.5901	9e-06
5	0.466557	3.9863	7.9e-05
6	0.391141	3.3419	0.000657
7	0.26343	2.2507	0.013707
8	0.198466	1.6957	0.047102
9	0.132211	1.1296	0.131169
10	0.007068	0.0604	0.476007
11	-0.078718	-0.6726	0.748328
12	-0.231771	-1.9803	0.974278
13	-0.289015	-2.4693	0.992062
14	-0.296692	-2.5349	0.993305
15	-0.296089	-2.5298	0.993214
16	-0.314041	-2.6832	0.995492
17	-0.330171	-2.821	0.996919

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.777717	6.6448	0
1	0.159715	1.3646	0.088284
2	0.19089	1.631	0.053602
3	-0.080103	-0.6844	0.752057
4	0.003095	0.0264	0.489486
5	-0.072967	-0.6234	0.732528
6	-0.179264	-1.5316	0.935033
7	-0.004032	-0.0344	0.513693
8	-0.05042	-0.4308	0.666054
9	-0.162544	-1.3888	0.915438
10	-0.08442	-0.7213	0.76348
11	-0.306519	-2.6189	0.994639
12	0.052976	0.4526	0.326079
13	0.047185	0.4031	0.34401
14	0.185298	1.5832	0.058851
15	0.030417	0.2599	0.397844
16	-0.032153	-0.2747	0.607845
17	0.063069	0.5389	0.295811

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.777717 & 6.6448 & 0 \tabularnewline
1 & 0.159715 & 1.3646 & 0.088284 \tabularnewline
2 & 0.19089 & 1.631 & 0.053602 \tabularnewline
3 & -0.080103 & -0.6844 & 0.752057 \tabularnewline
4 & 0.003095 & 0.0264 & 0.489486 \tabularnewline
5 & -0.072967 & -0.6234 & 0.732528 \tabularnewline
6 & -0.179264 & -1.5316 & 0.935033 \tabularnewline
7 & -0.004032 & -0.0344 & 0.513693 \tabularnewline
8 & -0.05042 & -0.4308 & 0.666054 \tabularnewline
9 & -0.162544 & -1.3888 & 0.915438 \tabularnewline
10 & -0.08442 & -0.7213 & 0.76348 \tabularnewline
11 & -0.306519 & -2.6189 & 0.994639 \tabularnewline
12 & 0.052976 & 0.4526 & 0.326079 \tabularnewline
13 & 0.047185 & 0.4031 & 0.34401 \tabularnewline
14 & 0.185298 & 1.5832 & 0.058851 \tabularnewline
15 & 0.030417 & 0.2599 & 0.397844 \tabularnewline
16 & -0.032153 & -0.2747 & 0.607845 \tabularnewline
17 & 0.063069 & 0.5389 & 0.295811 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6891&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]0[/C][C]0.777717[/C][C]6.6448[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.159715[/C][C]1.3646[/C][C]0.088284[/C][/ROW]
[ROW][C]2[/C][C]0.19089[/C][C]1.631[/C][C]0.053602[/C][/ROW]
[ROW][C]3[/C][C]-0.080103[/C][C]-0.6844[/C][C]0.752057[/C][/ROW]
[ROW][C]4[/C][C]0.003095[/C][C]0.0264[/C][C]0.489486[/C][/ROW]
[ROW][C]5[/C][C]-0.072967[/C][C]-0.6234[/C][C]0.732528[/C][/ROW]
[ROW][C]6[/C][C]-0.179264[/C][C]-1.5316[/C][C]0.935033[/C][/ROW]
[ROW][C]7[/C][C]-0.004032[/C][C]-0.0344[/C][C]0.513693[/C][/ROW]
[ROW][C]8[/C][C]-0.05042[/C][C]-0.4308[/C][C]0.666054[/C][/ROW]
[ROW][C]9[/C][C]-0.162544[/C][C]-1.3888[/C][C]0.915438[/C][/ROW]
[ROW][C]10[/C][C]-0.08442[/C][C]-0.7213[/C][C]0.76348[/C][/ROW]
[ROW][C]11[/C][C]-0.306519[/C][C]-2.6189[/C][C]0.994639[/C][/ROW]
[ROW][C]12[/C][C]0.052976[/C][C]0.4526[/C][C]0.326079[/C][/ROW]
[ROW][C]13[/C][C]0.047185[/C][C]0.4031[/C][C]0.34401[/C][/ROW]
[ROW][C]14[/C][C]0.185298[/C][C]1.5832[/C][C]0.058851[/C][/ROW]
[ROW][C]15[/C][C]0.030417[/C][C]0.2599[/C][C]0.397844[/C][/ROW]
[ROW][C]16[/C][C]-0.032153[/C][C]-0.2747[/C][C]0.607845[/C][/ROW]
[ROW][C]17[/C][C]0.063069[/C][C]0.5389[/C][C]0.295811[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6891&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6891&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
0	0.777717	6.6448	0
1	0.159715	1.3646	0.088284
2	0.19089	1.631	0.053602
3	-0.080103	-0.6844	0.752057
4	0.003095	0.0264	0.489486
5	-0.072967	-0.6234	0.732528
6	-0.179264	-1.5316	0.935033
7	-0.004032	-0.0344	0.513693
8	-0.05042	-0.4308	0.666054
9	-0.162544	-1.3888	0.915438
10	-0.08442	-0.7213	0.76348
11	-0.306519	-2.6189	0.994639
12	0.052976	0.4526	0.326079
13	0.047185	0.4031	0.34401
14	0.185298	1.5832	0.058851
15	0.030417	0.2599	0.397844
16	-0.032153	-0.2747	0.607845
17	0.063069	0.5389	0.295811

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 1 ; par2 = 0 ; par3 = 0 ; par4 = 12 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; 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 1:par1) {
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(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-1,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(mytstat,lengthx),6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')

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