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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 07 Dec 2007 03:34:01 -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/Dec/07/t1197022878rtua3bru1fxv9ey.htm/, Retrieved Mon, 29 Apr 2024 03:12:24 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=2735, Retrieved Mon, 29 Apr 2024 03:12:24 +0000

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No (this computation is public)

User-defined keywords

Estimated Impact

205

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

-       [(Partial) Autocorrelation Function] [Autocorrelation m...] [2007-12-07 10:34:01] [ca5e0f9f346e091f4d0fe7e17f7dba21] [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=2735&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=2735&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2735&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	6.9282	0
1	0.448265	3.1057	0.001592
2	0.388684	2.6929	0.004863
3	0.169591	1.175	0.122903
4	0.187413	1.2984	0.100171
5	0.163465	1.1325	0.131521
6	0.11892	0.8239	0.207034
7	0.003278	0.0227	0.490986
8	-0.165646	-1.1476	0.871595
9	-0.027916	-0.1934	0.576272
10	-0.19002	-1.3165	0.902871
11	-0.174499	-1.209	0.8837
12	-0.288659	-1.9999	0.974406
13	-0.256638	-1.778	0.959134
14	-0.106972	-0.7411	0.768885
15	-0.104263	-0.7224	0.763209
16	-0.092875	-0.6435	0.738505

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 6.9282 & 0 \tabularnewline
1 & 0.448265 & 3.1057 & 0.001592 \tabularnewline
2 & 0.388684 & 2.6929 & 0.004863 \tabularnewline
3 & 0.169591 & 1.175 & 0.122903 \tabularnewline
4 & 0.187413 & 1.2984 & 0.100171 \tabularnewline
5 & 0.163465 & 1.1325 & 0.131521 \tabularnewline
6 & 0.11892 & 0.8239 & 0.207034 \tabularnewline
7 & 0.003278 & 0.0227 & 0.490986 \tabularnewline
8 & -0.165646 & -1.1476 & 0.871595 \tabularnewline
9 & -0.027916 & -0.1934 & 0.576272 \tabularnewline
10 & -0.19002 & -1.3165 & 0.902871 \tabularnewline
11 & -0.174499 & -1.209 & 0.8837 \tabularnewline
12 & -0.288659 & -1.9999 & 0.974406 \tabularnewline
13 & -0.256638 & -1.778 & 0.959134 \tabularnewline
14 & -0.106972 & -0.7411 & 0.768885 \tabularnewline
15 & -0.104263 & -0.7224 & 0.763209 \tabularnewline
16 & -0.092875 & -0.6435 & 0.738505 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2735&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]0.448265[/C][C]3.1057[/C][C]0.001592[/C][/ROW]
[ROW][C]2[/C][C]0.388684[/C][C]2.6929[/C][C]0.004863[/C][/ROW]
[ROW][C]3[/C][C]0.169591[/C][C]1.175[/C][C]0.122903[/C][/ROW]
[ROW][C]4[/C][C]0.187413[/C][C]1.2984[/C][C]0.100171[/C][/ROW]
[ROW][C]5[/C][C]0.163465[/C][C]1.1325[/C][C]0.131521[/C][/ROW]
[ROW][C]6[/C][C]0.11892[/C][C]0.8239[/C][C]0.207034[/C][/ROW]
[ROW][C]7[/C][C]0.003278[/C][C]0.0227[/C][C]0.490986[/C][/ROW]
[ROW][C]8[/C][C]-0.165646[/C][C]-1.1476[/C][C]0.871595[/C][/ROW]
[ROW][C]9[/C][C]-0.027916[/C][C]-0.1934[/C][C]0.576272[/C][/ROW]
[ROW][C]10[/C][C]-0.19002[/C][C]-1.3165[/C][C]0.902871[/C][/ROW]
[ROW][C]11[/C][C]-0.174499[/C][C]-1.209[/C][C]0.8837[/C][/ROW]
[ROW][C]12[/C][C]-0.288659[/C][C]-1.9999[/C][C]0.974406[/C][/ROW]
[ROW][C]13[/C][C]-0.256638[/C][C]-1.778[/C][C]0.959134[/C][/ROW]
[ROW][C]14[/C][C]-0.106972[/C][C]-0.7411[/C][C]0.768885[/C][/ROW]
[ROW][C]15[/C][C]-0.104263[/C][C]-0.7224[/C][C]0.763209[/C][/ROW]
[ROW][C]16[/C][C]-0.092875[/C][C]-0.6435[/C][C]0.738505[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2735&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2735&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	0.448265	3.1057	0.001592
2	0.388684	2.6929	0.004863
3	0.169591	1.175	0.122903
4	0.187413	1.2984	0.100171
5	0.163465	1.1325	0.131521
6	0.11892	0.8239	0.207034
7	0.003278	0.0227	0.490986
8	-0.165646	-1.1476	0.871595
9	-0.027916	-0.1934	0.576272
10	-0.19002	-1.3165	0.902871
11	-0.174499	-1.209	0.8837
12	-0.288659	-1.9999	0.974406
13	-0.256638	-1.778	0.959134
14	-0.106972	-0.7411	0.768885
15	-0.104263	-0.7224	0.763209
16	-0.092875	-0.6435	0.738505

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.448265	3.1057	0.001592
1	0.234955	1.6278	0.055055
2	-0.091434	-0.6335	0.735284
3	0.084266	0.5838	0.281039
4	0.083499	0.5785	0.282816
5	-0.030229	-0.2094	0.582502
6	-0.119648	-0.8289	0.794381
7	-0.215751	-1.4948	0.92924
8	0.165608	1.1474	0.128458
9	-0.182101	-1.2616	0.893411
10	-0.144256	-0.9994	0.838702
11	-0.087746	-0.6079	0.726947
12	-0.024901	-0.1725	0.568124
13	0.196473	1.3612	0.089903
14	-0.080019	-0.5544	0.709056
15	-0.074188	-0.514	0.695191
16	0.11947	0.8277	0.205965

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.448265 & 3.1057 & 0.001592 \tabularnewline
1 & 0.234955 & 1.6278 & 0.055055 \tabularnewline
2 & -0.091434 & -0.6335 & 0.735284 \tabularnewline
3 & 0.084266 & 0.5838 & 0.281039 \tabularnewline
4 & 0.083499 & 0.5785 & 0.282816 \tabularnewline
5 & -0.030229 & -0.2094 & 0.582502 \tabularnewline
6 & -0.119648 & -0.8289 & 0.794381 \tabularnewline
7 & -0.215751 & -1.4948 & 0.92924 \tabularnewline
8 & 0.165608 & 1.1474 & 0.128458 \tabularnewline
9 & -0.182101 & -1.2616 & 0.893411 \tabularnewline
10 & -0.144256 & -0.9994 & 0.838702 \tabularnewline
11 & -0.087746 & -0.6079 & 0.726947 \tabularnewline
12 & -0.024901 & -0.1725 & 0.568124 \tabularnewline
13 & 0.196473 & 1.3612 & 0.089903 \tabularnewline
14 & -0.080019 & -0.5544 & 0.709056 \tabularnewline
15 & -0.074188 & -0.514 & 0.695191 \tabularnewline
16 & 0.11947 & 0.8277 & 0.205965 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2735&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]0.448265[/C][C]3.1057[/C][C]0.001592[/C][/ROW]
[ROW][C]1[/C][C]0.234955[/C][C]1.6278[/C][C]0.055055[/C][/ROW]
[ROW][C]2[/C][C]-0.091434[/C][C]-0.6335[/C][C]0.735284[/C][/ROW]
[ROW][C]3[/C][C]0.084266[/C][C]0.5838[/C][C]0.281039[/C][/ROW]
[ROW][C]4[/C][C]0.083499[/C][C]0.5785[/C][C]0.282816[/C][/ROW]
[ROW][C]5[/C][C]-0.030229[/C][C]-0.2094[/C][C]0.582502[/C][/ROW]
[ROW][C]6[/C][C]-0.119648[/C][C]-0.8289[/C][C]0.794381[/C][/ROW]
[ROW][C]7[/C][C]-0.215751[/C][C]-1.4948[/C][C]0.92924[/C][/ROW]
[ROW][C]8[/C][C]0.165608[/C][C]1.1474[/C][C]0.128458[/C][/ROW]
[ROW][C]9[/C][C]-0.182101[/C][C]-1.2616[/C][C]0.893411[/C][/ROW]
[ROW][C]10[/C][C]-0.144256[/C][C]-0.9994[/C][C]0.838702[/C][/ROW]
[ROW][C]11[/C][C]-0.087746[/C][C]-0.6079[/C][C]0.726947[/C][/ROW]
[ROW][C]12[/C][C]-0.024901[/C][C]-0.1725[/C][C]0.568124[/C][/ROW]
[ROW][C]13[/C][C]0.196473[/C][C]1.3612[/C][C]0.089903[/C][/ROW]
[ROW][C]14[/C][C]-0.080019[/C][C]-0.5544[/C][C]0.709056[/C][/ROW]
[ROW][C]15[/C][C]-0.074188[/C][C]-0.514[/C][C]0.695191[/C][/ROW]
[ROW][C]16[/C][C]0.11947[/C][C]0.8277[/C][C]0.205965[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2735&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2735&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	0.448265	3.1057	0.001592
1	0.234955	1.6278	0.055055
2	-0.091434	-0.6335	0.735284
3	0.084266	0.5838	0.281039
4	0.083499	0.5785	0.282816
5	-0.030229	-0.2094	0.582502
6	-0.119648	-0.8289	0.794381
7	-0.215751	-1.4948	0.92924
8	0.165608	1.1474	0.128458
9	-0.182101	-1.2616	0.893411
10	-0.144256	-0.9994	0.838702
11	-0.087746	-0.6079	0.726947
12	-0.024901	-0.1725	0.568124
13	0.196473	1.3612	0.089903
14	-0.080019	-0.5544	0.709056
15	-0.074188	-0.514	0.695191
16	0.11947	0.8277	0.205965

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = 2.0 ; par3 = 0 ; par4 = 1 ; par5 = 12 ;

Parameters (R input):

par1 = Default ; par2 = 2.0 ; par3 = 0 ; 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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Input Parameters & R Code