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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Tue, 04 Dec 2007 05:50:12 -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/Dec/04/t1196772186i515uj6qepoe000.htm/, Retrieved Thu, 02 May 2024 12:41:47 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=2371, Retrieved Thu, 02 May 2024 12:41:47 +0000

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No (this computation is public)

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Estimated Impact

240

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

-       [(Partial) Autocorrelation Function] [] [2007-12-04 12:50:12] [67794d83edd3193bd9ea9816803ddb96] [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=2371&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=2371&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2371&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	7.746	0
1	0.126628	0.9809	0.165301
2	0.28789	2.23	0.014751
3	-0.060091	-0.4655	0.678357
4	-0.082331	-0.6377	0.736962
5	-0.154715	-1.1984	0.882267
6	0.012705	0.0984	0.460965
7	0.22588	1.7497	0.042645
8	0.19049	1.4755	0.07265
9	0.217237	1.6827	0.048814
10	0.1009	0.7816	0.218771
11	0.101839	0.7888	0.216655
12	-0.399753	-3.0965	0.998512
13	-0.019745	-0.1529	0.560522
14	-0.136999	-1.0612	0.853572
15	-0.020428	-0.1582	0.5626
16	0.1359	1.0527	0.148355

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 7.746 & 0 \tabularnewline
1 & 0.126628 & 0.9809 & 0.165301 \tabularnewline
2 & 0.28789 & 2.23 & 0.014751 \tabularnewline
3 & -0.060091 & -0.4655 & 0.678357 \tabularnewline
4 & -0.082331 & -0.6377 & 0.736962 \tabularnewline
5 & -0.154715 & -1.1984 & 0.882267 \tabularnewline
6 & 0.012705 & 0.0984 & 0.460965 \tabularnewline
7 & 0.22588 & 1.7497 & 0.042645 \tabularnewline
8 & 0.19049 & 1.4755 & 0.07265 \tabularnewline
9 & 0.217237 & 1.6827 & 0.048814 \tabularnewline
10 & 0.1009 & 0.7816 & 0.218771 \tabularnewline
11 & 0.101839 & 0.7888 & 0.216655 \tabularnewline
12 & -0.399753 & -3.0965 & 0.998512 \tabularnewline
13 & -0.019745 & -0.1529 & 0.560522 \tabularnewline
14 & -0.136999 & -1.0612 & 0.853572 \tabularnewline
15 & -0.020428 & -0.1582 & 0.5626 \tabularnewline
16 & 0.1359 & 1.0527 & 0.148355 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2371&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]7.746[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.126628[/C][C]0.9809[/C][C]0.165301[/C][/ROW]
[ROW][C]2[/C][C]0.28789[/C][C]2.23[/C][C]0.014751[/C][/ROW]
[ROW][C]3[/C][C]-0.060091[/C][C]-0.4655[/C][C]0.678357[/C][/ROW]
[ROW][C]4[/C][C]-0.082331[/C][C]-0.6377[/C][C]0.736962[/C][/ROW]
[ROW][C]5[/C][C]-0.154715[/C][C]-1.1984[/C][C]0.882267[/C][/ROW]
[ROW][C]6[/C][C]0.012705[/C][C]0.0984[/C][C]0.460965[/C][/ROW]
[ROW][C]7[/C][C]0.22588[/C][C]1.7497[/C][C]0.042645[/C][/ROW]
[ROW][C]8[/C][C]0.19049[/C][C]1.4755[/C][C]0.07265[/C][/ROW]
[ROW][C]9[/C][C]0.217237[/C][C]1.6827[/C][C]0.048814[/C][/ROW]
[ROW][C]10[/C][C]0.1009[/C][C]0.7816[/C][C]0.218771[/C][/ROW]
[ROW][C]11[/C][C]0.101839[/C][C]0.7888[/C][C]0.216655[/C][/ROW]
[ROW][C]12[/C][C]-0.399753[/C][C]-3.0965[/C][C]0.998512[/C][/ROW]
[ROW][C]13[/C][C]-0.019745[/C][C]-0.1529[/C][C]0.560522[/C][/ROW]
[ROW][C]14[/C][C]-0.136999[/C][C]-1.0612[/C][C]0.853572[/C][/ROW]
[ROW][C]15[/C][C]-0.020428[/C][C]-0.1582[/C][C]0.5626[/C][/ROW]
[ROW][C]16[/C][C]0.1359[/C][C]1.0527[/C][C]0.148355[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2371&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2371&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	7.746	0
1	0.126628	0.9809	0.165301
2	0.28789	2.23	0.014751
3	-0.060091	-0.4655	0.678357
4	-0.082331	-0.6377	0.736962
5	-0.154715	-1.1984	0.882267
6	0.012705	0.0984	0.460965
7	0.22588	1.7497	0.042645
8	0.19049	1.4755	0.07265
9	0.217237	1.6827	0.048814
10	0.1009	0.7816	0.218771
11	0.101839	0.7888	0.216655
12	-0.399753	-3.0965	0.998512
13	-0.019745	-0.1529	0.560522
14	-0.136999	-1.0612	0.853572
15	-0.020428	-0.1582	0.5626
16	0.1359	1.0527	0.148355

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.126628	0.9809	0.165301
1	0.276285	2.1401	0.018211
2	-0.13364	-1.0352	0.847628
3	-0.157679	-1.2214	0.88664
4	-0.084084	-0.6513	0.741333
5	0.118383	0.917	0.181409
6	0.319751	2.4768	0.008047
7	0.10156	0.7867	0.217284
8	-0.014521	-0.1125	0.544589
9	-0.016784	-0.13	0.551503
10	0.129115	1.0001	0.160634
11	-0.416265	-3.2244	0.998978
12	0.032941	0.2552	0.399736
13	0.155262	1.2027	0.116918
14	-0.125767	-0.9742	0.833063
15	0.059433	0.4604	0.323459
16	0.043679	0.3383	0.368146

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.126628 & 0.9809 & 0.165301 \tabularnewline
1 & 0.276285 & 2.1401 & 0.018211 \tabularnewline
2 & -0.13364 & -1.0352 & 0.847628 \tabularnewline
3 & -0.157679 & -1.2214 & 0.88664 \tabularnewline
4 & -0.084084 & -0.6513 & 0.741333 \tabularnewline
5 & 0.118383 & 0.917 & 0.181409 \tabularnewline
6 & 0.319751 & 2.4768 & 0.008047 \tabularnewline
7 & 0.10156 & 0.7867 & 0.217284 \tabularnewline
8 & -0.014521 & -0.1125 & 0.544589 \tabularnewline
9 & -0.016784 & -0.13 & 0.551503 \tabularnewline
10 & 0.129115 & 1.0001 & 0.160634 \tabularnewline
11 & -0.416265 & -3.2244 & 0.998978 \tabularnewline
12 & 0.032941 & 0.2552 & 0.399736 \tabularnewline
13 & 0.155262 & 1.2027 & 0.116918 \tabularnewline
14 & -0.125767 & -0.9742 & 0.833063 \tabularnewline
15 & 0.059433 & 0.4604 & 0.323459 \tabularnewline
16 & 0.043679 & 0.3383 & 0.368146 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2371&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]0.126628[/C][C]0.9809[/C][C]0.165301[/C][/ROW]
[ROW][C]1[/C][C]0.276285[/C][C]2.1401[/C][C]0.018211[/C][/ROW]
[ROW][C]2[/C][C]-0.13364[/C][C]-1.0352[/C][C]0.847628[/C][/ROW]
[ROW][C]3[/C][C]-0.157679[/C][C]-1.2214[/C][C]0.88664[/C][/ROW]
[ROW][C]4[/C][C]-0.084084[/C][C]-0.6513[/C][C]0.741333[/C][/ROW]
[ROW][C]5[/C][C]0.118383[/C][C]0.917[/C][C]0.181409[/C][/ROW]
[ROW][C]6[/C][C]0.319751[/C][C]2.4768[/C][C]0.008047[/C][/ROW]
[ROW][C]7[/C][C]0.10156[/C][C]0.7867[/C][C]0.217284[/C][/ROW]
[ROW][C]8[/C][C]-0.014521[/C][C]-0.1125[/C][C]0.544589[/C][/ROW]
[ROW][C]9[/C][C]-0.016784[/C][C]-0.13[/C][C]0.551503[/C][/ROW]
[ROW][C]10[/C][C]0.129115[/C][C]1.0001[/C][C]0.160634[/C][/ROW]
[ROW][C]11[/C][C]-0.416265[/C][C]-3.2244[/C][C]0.998978[/C][/ROW]
[ROW][C]12[/C][C]0.032941[/C][C]0.2552[/C][C]0.399736[/C][/ROW]
[ROW][C]13[/C][C]0.155262[/C][C]1.2027[/C][C]0.116918[/C][/ROW]
[ROW][C]14[/C][C]-0.125767[/C][C]-0.9742[/C][C]0.833063[/C][/ROW]
[ROW][C]15[/C][C]0.059433[/C][C]0.4604[/C][C]0.323459[/C][/ROW]
[ROW][C]16[/C][C]0.043679[/C][C]0.3383[/C][C]0.368146[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2371&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2371&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	0.126628	0.9809	0.165301
1	0.276285	2.1401	0.018211
2	-0.13364	-1.0352	0.847628
3	-0.157679	-1.2214	0.88664
4	-0.084084	-0.6513	0.741333
5	0.118383	0.917	0.181409
6	0.319751	2.4768	0.008047
7	0.10156	0.7867	0.217284
8	-0.014521	-0.1125	0.544589
9	-0.016784	-0.13	0.551503
10	0.129115	1.0001	0.160634
11	-0.416265	-3.2244	0.998978
12	0.032941	0.2552	0.399736
13	0.155262	1.2027	0.116918
14	-0.125767	-0.9742	0.833063
15	0.059433	0.4604	0.323459
16	0.043679	0.3383	0.368146

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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Input Parameters & R Code