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Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 28 Nov 2007 09:02:05 -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/28/t11962651042daj9f3eg163nqt.htm/, Retrieved Thu, 02 May 2024 11:44:39 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=7112, Retrieved Thu, 02 May 2024 11:44:39 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

188

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

-       [(Partial) Autocorrelation Function] [wo4-q2 vervolg] [2007-11-28 16:02:05] [ce4b259486d1abcc1b8c2643f3bb6ec3] [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	2 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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=7112&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]2 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=7112&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=7112&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	2 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
0	1	6.9282	0
1	0.01165	0.0807	0.468003
2	-0.145254	-1.0063	0.840353
3	-0.024488	-0.1697	0.567004
4	-0.058452	-0.405	0.65635
5	-0.035782	-0.2479	0.597367
6	0.039507	0.2737	0.392741
7	0.06925	0.4798	0.316782
8	0.037592	0.2604	0.397818
9	0.137079	0.9497	0.173508
10	-0.147434	-1.0215	0.84392
11	7.1e-05	5e-04	0.499805
12	-0.1455	-1.0081	0.840758
13	-0.070143	-0.486	0.685398
14	0.189223	1.311	0.098051
15	0.065223	0.4519	0.326695
16	-0.022307	-0.1545	0.561087

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 6.9282 & 0 \tabularnewline
1 & 0.01165 & 0.0807 & 0.468003 \tabularnewline
2 & -0.145254 & -1.0063 & 0.840353 \tabularnewline
3 & -0.024488 & -0.1697 & 0.567004 \tabularnewline
4 & -0.058452 & -0.405 & 0.65635 \tabularnewline
5 & -0.035782 & -0.2479 & 0.597367 \tabularnewline
6 & 0.039507 & 0.2737 & 0.392741 \tabularnewline
7 & 0.06925 & 0.4798 & 0.316782 \tabularnewline
8 & 0.037592 & 0.2604 & 0.397818 \tabularnewline
9 & 0.137079 & 0.9497 & 0.173508 \tabularnewline
10 & -0.147434 & -1.0215 & 0.84392 \tabularnewline
11 & 7.1e-05 & 5e-04 & 0.499805 \tabularnewline
12 & -0.1455 & -1.0081 & 0.840758 \tabularnewline
13 & -0.070143 & -0.486 & 0.685398 \tabularnewline
14 & 0.189223 & 1.311 & 0.098051 \tabularnewline
15 & 0.065223 & 0.4519 & 0.326695 \tabularnewline
16 & -0.022307 & -0.1545 & 0.561087 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=7112&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]6.9282[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.01165[/C][C]0.0807[/C][C]0.468003[/C][/ROW]
[ROW][C]2[/C][C]-0.145254[/C][C]-1.0063[/C][C]0.840353[/C][/ROW]
[ROW][C]3[/C][C]-0.024488[/C][C]-0.1697[/C][C]0.567004[/C][/ROW]
[ROW][C]4[/C][C]-0.058452[/C][C]-0.405[/C][C]0.65635[/C][/ROW]
[ROW][C]5[/C][C]-0.035782[/C][C]-0.2479[/C][C]0.597367[/C][/ROW]
[ROW][C]6[/C][C]0.039507[/C][C]0.2737[/C][C]0.392741[/C][/ROW]
[ROW][C]7[/C][C]0.06925[/C][C]0.4798[/C][C]0.316782[/C][/ROW]
[ROW][C]8[/C][C]0.037592[/C][C]0.2604[/C][C]0.397818[/C][/ROW]
[ROW][C]9[/C][C]0.137079[/C][C]0.9497[/C][C]0.173508[/C][/ROW]
[ROW][C]10[/C][C]-0.147434[/C][C]-1.0215[/C][C]0.84392[/C][/ROW]
[ROW][C]11[/C][C]7.1e-05[/C][C]5e-04[/C][C]0.499805[/C][/ROW]
[ROW][C]12[/C][C]-0.1455[/C][C]-1.0081[/C][C]0.840758[/C][/ROW]
[ROW][C]13[/C][C]-0.070143[/C][C]-0.486[/C][C]0.685398[/C][/ROW]
[ROW][C]14[/C][C]0.189223[/C][C]1.311[/C][C]0.098051[/C][/ROW]
[ROW][C]15[/C][C]0.065223[/C][C]0.4519[/C][C]0.326695[/C][/ROW]
[ROW][C]16[/C][C]-0.022307[/C][C]-0.1545[/C][C]0.561087[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=7112&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=7112&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	6.9282	0
1	0.01165	0.0807	0.468003
2	-0.145254	-1.0063	0.840353
3	-0.024488	-0.1697	0.567004
4	-0.058452	-0.405	0.65635
5	-0.035782	-0.2479	0.597367
6	0.039507	0.2737	0.392741
7	0.06925	0.4798	0.316782
8	0.037592	0.2604	0.397818
9	0.137079	0.9497	0.173508
10	-0.147434	-1.0215	0.84392
11	7.1e-05	5e-04	0.499805
12	-0.1455	-1.0081	0.840758
13	-0.070143	-0.486	0.685398
14	0.189223	1.311	0.098051
15	0.065223	0.4519	0.326695
16	-0.022307	-0.1545	0.561087

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.01165	0.0807	0.468003
1	-0.145409	-1.0074	0.840609
2	-0.021309	-0.1476	0.558375
3	-0.080788	-0.5597	0.710861
4	-0.042349	-0.2934	0.61476
5	0.01919	0.133	0.447393
6	0.055258	0.3828	0.351766
7	0.040714	0.2821	0.38955
8	0.157604	1.0919	0.140162
9	-0.137602	-0.9533	0.827401
10	0.065205	0.4518	0.32674
11	-0.193045	-1.3375	0.906311
12	-0.044227	-0.3064	0.619692
13	0.135669	0.9399	0.175977
14	0.016618	0.1151	0.45441
15	0.002643	0.0183	0.492734
16	-0.178243	-1.2349	0.888562

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.01165 & 0.0807 & 0.468003 \tabularnewline
1 & -0.145409 & -1.0074 & 0.840609 \tabularnewline
2 & -0.021309 & -0.1476 & 0.558375 \tabularnewline
3 & -0.080788 & -0.5597 & 0.710861 \tabularnewline
4 & -0.042349 & -0.2934 & 0.61476 \tabularnewline
5 & 0.01919 & 0.133 & 0.447393 \tabularnewline
6 & 0.055258 & 0.3828 & 0.351766 \tabularnewline
7 & 0.040714 & 0.2821 & 0.38955 \tabularnewline
8 & 0.157604 & 1.0919 & 0.140162 \tabularnewline
9 & -0.137602 & -0.9533 & 0.827401 \tabularnewline
10 & 0.065205 & 0.4518 & 0.32674 \tabularnewline
11 & -0.193045 & -1.3375 & 0.906311 \tabularnewline
12 & -0.044227 & -0.3064 & 0.619692 \tabularnewline
13 & 0.135669 & 0.9399 & 0.175977 \tabularnewline
14 & 0.016618 & 0.1151 & 0.45441 \tabularnewline
15 & 0.002643 & 0.0183 & 0.492734 \tabularnewline
16 & -0.178243 & -1.2349 & 0.888562 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=7112&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]0.01165[/C][C]0.0807[/C][C]0.468003[/C][/ROW]
[ROW][C]1[/C][C]-0.145409[/C][C]-1.0074[/C][C]0.840609[/C][/ROW]
[ROW][C]2[/C][C]-0.021309[/C][C]-0.1476[/C][C]0.558375[/C][/ROW]
[ROW][C]3[/C][C]-0.080788[/C][C]-0.5597[/C][C]0.710861[/C][/ROW]
[ROW][C]4[/C][C]-0.042349[/C][C]-0.2934[/C][C]0.61476[/C][/ROW]
[ROW][C]5[/C][C]0.01919[/C][C]0.133[/C][C]0.447393[/C][/ROW]
[ROW][C]6[/C][C]0.055258[/C][C]0.3828[/C][C]0.351766[/C][/ROW]
[ROW][C]7[/C][C]0.040714[/C][C]0.2821[/C][C]0.38955[/C][/ROW]
[ROW][C]8[/C][C]0.157604[/C][C]1.0919[/C][C]0.140162[/C][/ROW]
[ROW][C]9[/C][C]-0.137602[/C][C]-0.9533[/C][C]0.827401[/C][/ROW]
[ROW][C]10[/C][C]0.065205[/C][C]0.4518[/C][C]0.32674[/C][/ROW]
[ROW][C]11[/C][C]-0.193045[/C][C]-1.3375[/C][C]0.906311[/C][/ROW]
[ROW][C]12[/C][C]-0.044227[/C][C]-0.3064[/C][C]0.619692[/C][/ROW]
[ROW][C]13[/C][C]0.135669[/C][C]0.9399[/C][C]0.175977[/C][/ROW]
[ROW][C]14[/C][C]0.016618[/C][C]0.1151[/C][C]0.45441[/C][/ROW]
[ROW][C]15[/C][C]0.002643[/C][C]0.0183[/C][C]0.492734[/C][/ROW]
[ROW][C]16[/C][C]-0.178243[/C][C]-1.2349[/C][C]0.888562[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=7112&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=7112&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	0.01165	0.0807	0.468003
1	-0.145409	-1.0074	0.840609
2	-0.021309	-0.1476	0.558375
3	-0.080788	-0.5597	0.710861
4	-0.042349	-0.2934	0.61476
5	0.01919	0.133	0.447393
6	0.055258	0.3828	0.351766
7	0.040714	0.2821	0.38955
8	0.157604	1.0919	0.140162
9	-0.137602	-0.9533	0.827401
10	0.065205	0.4518	0.32674
11	-0.193045	-1.3375	0.906311
12	-0.044227	-0.3064	0.619692
13	0.135669	0.9399	0.175977
14	0.016618	0.1151	0.45441
15	0.002643	0.0183	0.492734
16	-0.178243	-1.2349	0.888562

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = 1.3 ; par3 = 0 ; par4 = 1 ; par5 = 12 ;

Parameters (R input):

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