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Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 23 Nov 2007 06:33:33 -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/23/t1195824451mj3tq9jvvv6b8ol.htm/, Retrieved Sun, 28 Apr 2024 21:30:46 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=6164, Retrieved Sun, 28 Apr 2024 21:30:46 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

235

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

-     [(Partial) Autocorrelation Function] [Partiel Autocorre...] [2007-11-22 13:00:02] [ced1562ed3c62c3bc1f3b66b8f83b537]
-   PD    [(Partial) Autocorrelation Function] [WS 9] [2007-11-23 13:33:33] [d41d8cd98f00b204e9800998ecf8427e] [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	3 seconds
R Server	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\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 & 3 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6164&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6164&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6164&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	3 seconds
R Server	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
0	1	7.8102	0
1	0.928799	7.2541	0
2	0.868154	6.7805	0
3	0.803135	6.2727	0
4	0.720623	5.6282	0
5	0.648672	5.0663	2e-06
6	0.584666	4.5664	1.2e-05
7	0.517068	4.0384	7.6e-05
8	0.457645	3.5743	0.000347
9	0.398898	3.1155	0.001399
10	0.336035	2.6245	0.005475
11	0.288393	2.2524	0.013953
12	0.247411	1.9323	0.028982
13	0.231137	1.8052	0.037986
14	0.217431	1.6982	0.047284
15	0.193174	1.5087	0.068264
16	0.165794	1.2949	0.100119
17	0.135414	1.0576	0.147201

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 7.8102 & 0 \tabularnewline
1 & 0.928799 & 7.2541 & 0 \tabularnewline
2 & 0.868154 & 6.7805 & 0 \tabularnewline
3 & 0.803135 & 6.2727 & 0 \tabularnewline
4 & 0.720623 & 5.6282 & 0 \tabularnewline
5 & 0.648672 & 5.0663 & 2e-06 \tabularnewline
6 & 0.584666 & 4.5664 & 1.2e-05 \tabularnewline
7 & 0.517068 & 4.0384 & 7.6e-05 \tabularnewline
8 & 0.457645 & 3.5743 & 0.000347 \tabularnewline
9 & 0.398898 & 3.1155 & 0.001399 \tabularnewline
10 & 0.336035 & 2.6245 & 0.005475 \tabularnewline
11 & 0.288393 & 2.2524 & 0.013953 \tabularnewline
12 & 0.247411 & 1.9323 & 0.028982 \tabularnewline
13 & 0.231137 & 1.8052 & 0.037986 \tabularnewline
14 & 0.217431 & 1.6982 & 0.047284 \tabularnewline
15 & 0.193174 & 1.5087 & 0.068264 \tabularnewline
16 & 0.165794 & 1.2949 & 0.100119 \tabularnewline
17 & 0.135414 & 1.0576 & 0.147201 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6164&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]7.8102[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.928799[/C][C]7.2541[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.868154[/C][C]6.7805[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.803135[/C][C]6.2727[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.720623[/C][C]5.6282[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.648672[/C][C]5.0663[/C][C]2e-06[/C][/ROW]
[ROW][C]6[/C][C]0.584666[/C][C]4.5664[/C][C]1.2e-05[/C][/ROW]
[ROW][C]7[/C][C]0.517068[/C][C]4.0384[/C][C]7.6e-05[/C][/ROW]
[ROW][C]8[/C][C]0.457645[/C][C]3.5743[/C][C]0.000347[/C][/ROW]
[ROW][C]9[/C][C]0.398898[/C][C]3.1155[/C][C]0.001399[/C][/ROW]
[ROW][C]10[/C][C]0.336035[/C][C]2.6245[/C][C]0.005475[/C][/ROW]
[ROW][C]11[/C][C]0.288393[/C][C]2.2524[/C][C]0.013953[/C][/ROW]
[ROW][C]12[/C][C]0.247411[/C][C]1.9323[/C][C]0.028982[/C][/ROW]
[ROW][C]13[/C][C]0.231137[/C][C]1.8052[/C][C]0.037986[/C][/ROW]
[ROW][C]14[/C][C]0.217431[/C][C]1.6982[/C][C]0.047284[/C][/ROW]
[ROW][C]15[/C][C]0.193174[/C][C]1.5087[/C][C]0.068264[/C][/ROW]
[ROW][C]16[/C][C]0.165794[/C][C]1.2949[/C][C]0.100119[/C][/ROW]
[ROW][C]17[/C][C]0.135414[/C][C]1.0576[/C][C]0.147201[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6164&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6164&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	7.8102	0
1	0.928799	7.2541	0
2	0.868154	6.7805	0
3	0.803135	6.2727	0
4	0.720623	5.6282	0
5	0.648672	5.0663	2e-06
6	0.584666	4.5664	1.2e-05
7	0.517068	4.0384	7.6e-05
8	0.457645	3.5743	0.000347
9	0.398898	3.1155	0.001399
10	0.336035	2.6245	0.005475
11	0.288393	2.2524	0.013953
12	0.247411	1.9323	0.028982
13	0.231137	1.8052	0.037986
14	0.217431	1.6982	0.047284
15	0.193174	1.5087	0.068264
16	0.165794	1.2949	0.100119
17	0.135414	1.0576	0.147201

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.928799	7.2541	0
1	0.039953	0.312	0.378035
2	-0.059059	-0.4613	0.676874
3	-0.168115	-1.313	0.902953
4	0.01203	0.094	0.462724
5	0.033544	0.262	0.397108
6	-0.04628	-0.3615	0.640497
7	-0.006873	-0.0537	0.521318
8	-0.040287	-0.3147	0.622951
9	-0.064524	-0.5039	0.691943
10	0.0549	0.4288	0.334797
11	0.031887	0.249	0.40208
12	0.164617	1.2857	0.101704
13	-0.008418	-0.0657	0.526104
14	-0.121823	-0.9515	0.827439
15	-0.098083	-0.766	0.776699
16	-0.034825	-0.272	0.606728
17	0.024538	0.1917	0.424326

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.928799 & 7.2541 & 0 \tabularnewline
1 & 0.039953 & 0.312 & 0.378035 \tabularnewline
2 & -0.059059 & -0.4613 & 0.676874 \tabularnewline
3 & -0.168115 & -1.313 & 0.902953 \tabularnewline
4 & 0.01203 & 0.094 & 0.462724 \tabularnewline
5 & 0.033544 & 0.262 & 0.397108 \tabularnewline
6 & -0.04628 & -0.3615 & 0.640497 \tabularnewline
7 & -0.006873 & -0.0537 & 0.521318 \tabularnewline
8 & -0.040287 & -0.3147 & 0.622951 \tabularnewline
9 & -0.064524 & -0.5039 & 0.691943 \tabularnewline
10 & 0.0549 & 0.4288 & 0.334797 \tabularnewline
11 & 0.031887 & 0.249 & 0.40208 \tabularnewline
12 & 0.164617 & 1.2857 & 0.101704 \tabularnewline
13 & -0.008418 & -0.0657 & 0.526104 \tabularnewline
14 & -0.121823 & -0.9515 & 0.827439 \tabularnewline
15 & -0.098083 & -0.766 & 0.776699 \tabularnewline
16 & -0.034825 & -0.272 & 0.606728 \tabularnewline
17 & 0.024538 & 0.1917 & 0.424326 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6164&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]0.928799[/C][C]7.2541[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.039953[/C][C]0.312[/C][C]0.378035[/C][/ROW]
[ROW][C]2[/C][C]-0.059059[/C][C]-0.4613[/C][C]0.676874[/C][/ROW]
[ROW][C]3[/C][C]-0.168115[/C][C]-1.313[/C][C]0.902953[/C][/ROW]
[ROW][C]4[/C][C]0.01203[/C][C]0.094[/C][C]0.462724[/C][/ROW]
[ROW][C]5[/C][C]0.033544[/C][C]0.262[/C][C]0.397108[/C][/ROW]
[ROW][C]6[/C][C]-0.04628[/C][C]-0.3615[/C][C]0.640497[/C][/ROW]
[ROW][C]7[/C][C]-0.006873[/C][C]-0.0537[/C][C]0.521318[/C][/ROW]
[ROW][C]8[/C][C]-0.040287[/C][C]-0.3147[/C][C]0.622951[/C][/ROW]
[ROW][C]9[/C][C]-0.064524[/C][C]-0.5039[/C][C]0.691943[/C][/ROW]
[ROW][C]10[/C][C]0.0549[/C][C]0.4288[/C][C]0.334797[/C][/ROW]
[ROW][C]11[/C][C]0.031887[/C][C]0.249[/C][C]0.40208[/C][/ROW]
[ROW][C]12[/C][C]0.164617[/C][C]1.2857[/C][C]0.101704[/C][/ROW]
[ROW][C]13[/C][C]-0.008418[/C][C]-0.0657[/C][C]0.526104[/C][/ROW]
[ROW][C]14[/C][C]-0.121823[/C][C]-0.9515[/C][C]0.827439[/C][/ROW]
[ROW][C]15[/C][C]-0.098083[/C][C]-0.766[/C][C]0.776699[/C][/ROW]
[ROW][C]16[/C][C]-0.034825[/C][C]-0.272[/C][C]0.606728[/C][/ROW]
[ROW][C]17[/C][C]0.024538[/C][C]0.1917[/C][C]0.424326[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6164&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6164&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	0.928799	7.2541	0
1	0.039953	0.312	0.378035
2	-0.059059	-0.4613	0.676874
3	-0.168115	-1.313	0.902953
4	0.01203	0.094	0.462724
5	0.033544	0.262	0.397108
6	-0.04628	-0.3615	0.640497
7	-0.006873	-0.0537	0.521318
8	-0.040287	-0.3147	0.622951
9	-0.064524	-0.5039	0.691943
10	0.0549	0.4288	0.334797
11	0.031887	0.249	0.40208
12	0.164617	1.2857	0.101704
13	-0.008418	-0.0657	0.526104
14	-0.121823	-0.9515	0.827439
15	-0.098083	-0.766	0.776699
16	-0.034825	-0.272	0.606728
17	0.024538	0.1917	0.424326

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 = 1 ; par5 = 12 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; 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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