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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 22 Nov 2007 08:05:01 -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/22/t1195743412mpqq8s5t9f5ml2c.htm/, Retrieved Thu, 02 May 2024 21:06:12 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=6038, Retrieved Thu, 02 May 2024 21:06:12 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

W10Q2G7

Estimated Impact

194

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

-       [(Partial) Autocorrelation Function] [autocorrelation f...] [2007-11-22 15:05:01] [65108f21b143a71c6470aac06bd65b08] [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=6038&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=6038&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6038&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	0.691161	5.9053	0
2	0.47474	4.0562	6.2e-05
3	0.345826	2.9547	0.002105
4	0.22661	1.9362	0.02836
5	0.142299	1.2158	0.113989
6	0.072478	0.6193	0.268838
7	0.052157	0.4456	0.328593
8	-0.062708	-0.5358	0.70313
9	-0.109011	-0.9314	0.822639
10	-0.177536	-1.5169	0.933191
11	-0.293017	-2.5035	0.992734
12	-0.288053	-2.4611	0.991893
13	-0.263069	-2.2477	0.986191
14	-0.213873	-1.8273	0.964132
15	-0.142811	-1.2202	0.886837
16	-0.078247	-0.6685	0.747053
17	-0.121684	-1.0397	0.849037

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 8.544 & 0 \tabularnewline
1 & 0.691161 & 5.9053 & 0 \tabularnewline
2 & 0.47474 & 4.0562 & 6.2e-05 \tabularnewline
3 & 0.345826 & 2.9547 & 0.002105 \tabularnewline
4 & 0.22661 & 1.9362 & 0.02836 \tabularnewline
5 & 0.142299 & 1.2158 & 0.113989 \tabularnewline
6 & 0.072478 & 0.6193 & 0.268838 \tabularnewline
7 & 0.052157 & 0.4456 & 0.328593 \tabularnewline
8 & -0.062708 & -0.5358 & 0.70313 \tabularnewline
9 & -0.109011 & -0.9314 & 0.822639 \tabularnewline
10 & -0.177536 & -1.5169 & 0.933191 \tabularnewline
11 & -0.293017 & -2.5035 & 0.992734 \tabularnewline
12 & -0.288053 & -2.4611 & 0.991893 \tabularnewline
13 & -0.263069 & -2.2477 & 0.986191 \tabularnewline
14 & -0.213873 & -1.8273 & 0.964132 \tabularnewline
15 & -0.142811 & -1.2202 & 0.886837 \tabularnewline
16 & -0.078247 & -0.6685 & 0.747053 \tabularnewline
17 & -0.121684 & -1.0397 & 0.849037 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6038&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]0.691161[/C][C]5.9053[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.47474[/C][C]4.0562[/C][C]6.2e-05[/C][/ROW]
[ROW][C]3[/C][C]0.345826[/C][C]2.9547[/C][C]0.002105[/C][/ROW]
[ROW][C]4[/C][C]0.22661[/C][C]1.9362[/C][C]0.02836[/C][/ROW]
[ROW][C]5[/C][C]0.142299[/C][C]1.2158[/C][C]0.113989[/C][/ROW]
[ROW][C]6[/C][C]0.072478[/C][C]0.6193[/C][C]0.268838[/C][/ROW]
[ROW][C]7[/C][C]0.052157[/C][C]0.4456[/C][C]0.328593[/C][/ROW]
[ROW][C]8[/C][C]-0.062708[/C][C]-0.5358[/C][C]0.70313[/C][/ROW]
[ROW][C]9[/C][C]-0.109011[/C][C]-0.9314[/C][C]0.822639[/C][/ROW]
[ROW][C]10[/C][C]-0.177536[/C][C]-1.5169[/C][C]0.933191[/C][/ROW]
[ROW][C]11[/C][C]-0.293017[/C][C]-2.5035[/C][C]0.992734[/C][/ROW]
[ROW][C]12[/C][C]-0.288053[/C][C]-2.4611[/C][C]0.991893[/C][/ROW]
[ROW][C]13[/C][C]-0.263069[/C][C]-2.2477[/C][C]0.986191[/C][/ROW]
[ROW][C]14[/C][C]-0.213873[/C][C]-1.8273[/C][C]0.964132[/C][/ROW]
[ROW][C]15[/C][C]-0.142811[/C][C]-1.2202[/C][C]0.886837[/C][/ROW]
[ROW][C]16[/C][C]-0.078247[/C][C]-0.6685[/C][C]0.747053[/C][/ROW]
[ROW][C]17[/C][C]-0.121684[/C][C]-1.0397[/C][C]0.849037[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6038&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6038&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	0.691161	5.9053	0
2	0.47474	4.0562	6.2e-05
3	0.345826	2.9547	0.002105
4	0.22661	1.9362	0.02836
5	0.142299	1.2158	0.113989
6	0.072478	0.6193	0.268838
7	0.052157	0.4456	0.328593
8	-0.062708	-0.5358	0.70313
9	-0.109011	-0.9314	0.822639
10	-0.177536	-1.5169	0.933191
11	-0.293017	-2.5035	0.992734
12	-0.288053	-2.4611	0.991893
13	-0.263069	-2.2477	0.986191
14	-0.213873	-1.8273	0.964132
15	-0.142811	-1.2202	0.886837
16	-0.078247	-0.6685	0.747053
17	-0.121684	-1.0397	0.849037

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.691161	5.9053	0
1	-0.005673	-0.0485	0.519263
2	0.037842	0.3233	0.373687
3	-0.047583	-0.4066	0.657236
4	-0.009359	-0.08	0.531758
5	-0.033966	-0.2902	0.613758
6	0.040953	0.3499	0.36371
7	-0.194763	-1.6641	0.949806
8	0.014997	0.1281	0.449199
9	-0.132876	-1.1353	0.870016
10	-0.176017	-1.5039	0.931538
11	0.049212	0.4205	0.33769
12	-0.011869	-0.1014	0.540249
13	0.020352	0.1739	0.431218
14	0.080833	0.6906	0.245992
15	0.005879	0.0502	0.480039
16	-0.169336	-1.4468	0.923884
17	0.050824	0.4342	0.332696

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.691161 & 5.9053 & 0 \tabularnewline
1 & -0.005673 & -0.0485 & 0.519263 \tabularnewline
2 & 0.037842 & 0.3233 & 0.373687 \tabularnewline
3 & -0.047583 & -0.4066 & 0.657236 \tabularnewline
4 & -0.009359 & -0.08 & 0.531758 \tabularnewline
5 & -0.033966 & -0.2902 & 0.613758 \tabularnewline
6 & 0.040953 & 0.3499 & 0.36371 \tabularnewline
7 & -0.194763 & -1.6641 & 0.949806 \tabularnewline
8 & 0.014997 & 0.1281 & 0.449199 \tabularnewline
9 & -0.132876 & -1.1353 & 0.870016 \tabularnewline
10 & -0.176017 & -1.5039 & 0.931538 \tabularnewline
11 & 0.049212 & 0.4205 & 0.33769 \tabularnewline
12 & -0.011869 & -0.1014 & 0.540249 \tabularnewline
13 & 0.020352 & 0.1739 & 0.431218 \tabularnewline
14 & 0.080833 & 0.6906 & 0.245992 \tabularnewline
15 & 0.005879 & 0.0502 & 0.480039 \tabularnewline
16 & -0.169336 & -1.4468 & 0.923884 \tabularnewline
17 & 0.050824 & 0.4342 & 0.332696 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6038&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]0.691161[/C][C]5.9053[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]-0.005673[/C][C]-0.0485[/C][C]0.519263[/C][/ROW]
[ROW][C]2[/C][C]0.037842[/C][C]0.3233[/C][C]0.373687[/C][/ROW]
[ROW][C]3[/C][C]-0.047583[/C][C]-0.4066[/C][C]0.657236[/C][/ROW]
[ROW][C]4[/C][C]-0.009359[/C][C]-0.08[/C][C]0.531758[/C][/ROW]
[ROW][C]5[/C][C]-0.033966[/C][C]-0.2902[/C][C]0.613758[/C][/ROW]
[ROW][C]6[/C][C]0.040953[/C][C]0.3499[/C][C]0.36371[/C][/ROW]
[ROW][C]7[/C][C]-0.194763[/C][C]-1.6641[/C][C]0.949806[/C][/ROW]
[ROW][C]8[/C][C]0.014997[/C][C]0.1281[/C][C]0.449199[/C][/ROW]
[ROW][C]9[/C][C]-0.132876[/C][C]-1.1353[/C][C]0.870016[/C][/ROW]
[ROW][C]10[/C][C]-0.176017[/C][C]-1.5039[/C][C]0.931538[/C][/ROW]
[ROW][C]11[/C][C]0.049212[/C][C]0.4205[/C][C]0.33769[/C][/ROW]
[ROW][C]12[/C][C]-0.011869[/C][C]-0.1014[/C][C]0.540249[/C][/ROW]
[ROW][C]13[/C][C]0.020352[/C][C]0.1739[/C][C]0.431218[/C][/ROW]
[ROW][C]14[/C][C]0.080833[/C][C]0.6906[/C][C]0.245992[/C][/ROW]
[ROW][C]15[/C][C]0.005879[/C][C]0.0502[/C][C]0.480039[/C][/ROW]
[ROW][C]16[/C][C]-0.169336[/C][C]-1.4468[/C][C]0.923884[/C][/ROW]
[ROW][C]17[/C][C]0.050824[/C][C]0.4342[/C][C]0.332696[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6038&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6038&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	0.691161	5.9053	0
1	-0.005673	-0.0485	0.519263
2	0.037842	0.3233	0.373687
3	-0.047583	-0.4066	0.657236
4	-0.009359	-0.08	0.531758
5	-0.033966	-0.2902	0.613758
6	0.040953	0.3499	0.36371
7	-0.194763	-1.6641	0.949806
8	0.014997	0.1281	0.449199
9	-0.132876	-1.1353	0.870016
10	-0.176017	-1.5039	0.931538
11	0.049212	0.4205	0.33769
12	-0.011869	-0.1014	0.540249
13	0.020352	0.1739	0.431218
14	0.080833	0.6906	0.245992
15	0.005879	0.0502	0.480039
16	-0.169336	-1.4468	0.923884
17	0.050824	0.4342	0.332696

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 ;

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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