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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 02:46:35 -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/t1195724331daat2tk0rdfrfrm.htm/, Retrieved Thu, 02 May 2024 17:01:26 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=5927, Retrieved Thu, 02 May 2024 17:01:26 +0000

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No (this computation is public)

User-defined keywords

Estimated Impact

216

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

-       [(Partial) Autocorrelation Function] [(Partiel)Autocorr...] [2007-11-22 09:46:35] [2cdb7403ed3391afb545b8c0d20da37e] [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	'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 & 2 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=5927&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]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=5927&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5927&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	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
0	1	8.544	0
1	0.912308	7.7948	0
2	0.785179	6.7086	0
3	0.676159	5.7771	0
4	0.604427	5.1642	1e-06
5	0.573941	4.9038	3e-06
6	0.537913	4.5959	9e-06
7	0.473186	4.0429	6.5e-05
8	0.399627	3.4144	0.000523
9	0.377702	3.2271	0.000937
10	0.401449	3.43	0.000498
11	0.458255	3.9153	0.000101
12	0.484761	4.1418	4.6e-05
13	0.394331	3.3692	0.000604
14	0.272712	2.33	0.011286
15	0.168964	1.4436	0.076561
16	0.104127	0.8897	0.188285
17	0.076378	0.6526	0.25804

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 8.544 & 0 \tabularnewline
1 & 0.912308 & 7.7948 & 0 \tabularnewline
2 & 0.785179 & 6.7086 & 0 \tabularnewline
3 & 0.676159 & 5.7771 & 0 \tabularnewline
4 & 0.604427 & 5.1642 & 1e-06 \tabularnewline
5 & 0.573941 & 4.9038 & 3e-06 \tabularnewline
6 & 0.537913 & 4.5959 & 9e-06 \tabularnewline
7 & 0.473186 & 4.0429 & 6.5e-05 \tabularnewline
8 & 0.399627 & 3.4144 & 0.000523 \tabularnewline
9 & 0.377702 & 3.2271 & 0.000937 \tabularnewline
10 & 0.401449 & 3.43 & 0.000498 \tabularnewline
11 & 0.458255 & 3.9153 & 0.000101 \tabularnewline
12 & 0.484761 & 4.1418 & 4.6e-05 \tabularnewline
13 & 0.394331 & 3.3692 & 0.000604 \tabularnewline
14 & 0.272712 & 2.33 & 0.011286 \tabularnewline
15 & 0.168964 & 1.4436 & 0.076561 \tabularnewline
16 & 0.104127 & 0.8897 & 0.188285 \tabularnewline
17 & 0.076378 & 0.6526 & 0.25804 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=5927&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]0.912308[/C][C]7.7948[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.785179[/C][C]6.7086[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.676159[/C][C]5.7771[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.604427[/C][C]5.1642[/C][C]1e-06[/C][/ROW]
[ROW][C]5[/C][C]0.573941[/C][C]4.9038[/C][C]3e-06[/C][/ROW]
[ROW][C]6[/C][C]0.537913[/C][C]4.5959[/C][C]9e-06[/C][/ROW]
[ROW][C]7[/C][C]0.473186[/C][C]4.0429[/C][C]6.5e-05[/C][/ROW]
[ROW][C]8[/C][C]0.399627[/C][C]3.4144[/C][C]0.000523[/C][/ROW]
[ROW][C]9[/C][C]0.377702[/C][C]3.2271[/C][C]0.000937[/C][/ROW]
[ROW][C]10[/C][C]0.401449[/C][C]3.43[/C][C]0.000498[/C][/ROW]
[ROW][C]11[/C][C]0.458255[/C][C]3.9153[/C][C]0.000101[/C][/ROW]
[ROW][C]12[/C][C]0.484761[/C][C]4.1418[/C][C]4.6e-05[/C][/ROW]
[ROW][C]13[/C][C]0.394331[/C][C]3.3692[/C][C]0.000604[/C][/ROW]
[ROW][C]14[/C][C]0.272712[/C][C]2.33[/C][C]0.011286[/C][/ROW]
[ROW][C]15[/C][C]0.168964[/C][C]1.4436[/C][C]0.076561[/C][/ROW]
[ROW][C]16[/C][C]0.104127[/C][C]0.8897[/C][C]0.188285[/C][/ROW]
[ROW][C]17[/C][C]0.076378[/C][C]0.6526[/C][C]0.25804[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=5927&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5927&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	0.912308	7.7948	0
2	0.785179	6.7086	0
3	0.676159	5.7771	0
4	0.604427	5.1642	1e-06
5	0.573941	4.9038	3e-06
6	0.537913	4.5959	9e-06
7	0.473186	4.0429	6.5e-05
8	0.399627	3.4144	0.000523
9	0.377702	3.2271	0.000937
10	0.401449	3.43	0.000498
11	0.458255	3.9153	0.000101
12	0.484761	4.1418	4.6e-05
13	0.394331	3.3692	0.000604
14	0.272712	2.33	0.011286
15	0.168964	1.4436	0.076561
16	0.104127	0.8897	0.188285
17	0.076378	0.6526	0.25804

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.912308	7.7948	0
1	-0.281026	-2.4011	0.990553
2	0.096539	0.8248	0.206079
3	0.111312	0.951	0.172359
4	0.142119	1.2143	0.114281
5	-0.124796	-1.0663	0.85509
6	-0.115753	-0.989	0.837033
7	0.016045	0.1371	0.445668
8	0.311727	2.6634	0.004756
9	0.085458	0.7301	0.233818
10	0.14863	1.2699	0.104078
11	-0.166058	-1.4188	0.919893
12	-0.578441	-4.9422	0.999998
13	0.042667	0.3645	0.358251
14	0.03628	0.31	0.378732
15	0.019456	0.1662	0.434216
16	0.022454	0.1918	0.424198
17	-0.034806	-0.2974	0.616492

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.912308 & 7.7948 & 0 \tabularnewline
1 & -0.281026 & -2.4011 & 0.990553 \tabularnewline
2 & 0.096539 & 0.8248 & 0.206079 \tabularnewline
3 & 0.111312 & 0.951 & 0.172359 \tabularnewline
4 & 0.142119 & 1.2143 & 0.114281 \tabularnewline
5 & -0.124796 & -1.0663 & 0.85509 \tabularnewline
6 & -0.115753 & -0.989 & 0.837033 \tabularnewline
7 & 0.016045 & 0.1371 & 0.445668 \tabularnewline
8 & 0.311727 & 2.6634 & 0.004756 \tabularnewline
9 & 0.085458 & 0.7301 & 0.233818 \tabularnewline
10 & 0.14863 & 1.2699 & 0.104078 \tabularnewline
11 & -0.166058 & -1.4188 & 0.919893 \tabularnewline
12 & -0.578441 & -4.9422 & 0.999998 \tabularnewline
13 & 0.042667 & 0.3645 & 0.358251 \tabularnewline
14 & 0.03628 & 0.31 & 0.378732 \tabularnewline
15 & 0.019456 & 0.1662 & 0.434216 \tabularnewline
16 & 0.022454 & 0.1918 & 0.424198 \tabularnewline
17 & -0.034806 & -0.2974 & 0.616492 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=5927&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]0.912308[/C][C]7.7948[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]-0.281026[/C][C]-2.4011[/C][C]0.990553[/C][/ROW]
[ROW][C]2[/C][C]0.096539[/C][C]0.8248[/C][C]0.206079[/C][/ROW]
[ROW][C]3[/C][C]0.111312[/C][C]0.951[/C][C]0.172359[/C][/ROW]
[ROW][C]4[/C][C]0.142119[/C][C]1.2143[/C][C]0.114281[/C][/ROW]
[ROW][C]5[/C][C]-0.124796[/C][C]-1.0663[/C][C]0.85509[/C][/ROW]
[ROW][C]6[/C][C]-0.115753[/C][C]-0.989[/C][C]0.837033[/C][/ROW]
[ROW][C]7[/C][C]0.016045[/C][C]0.1371[/C][C]0.445668[/C][/ROW]
[ROW][C]8[/C][C]0.311727[/C][C]2.6634[/C][C]0.004756[/C][/ROW]
[ROW][C]9[/C][C]0.085458[/C][C]0.7301[/C][C]0.233818[/C][/ROW]
[ROW][C]10[/C][C]0.14863[/C][C]1.2699[/C][C]0.104078[/C][/ROW]
[ROW][C]11[/C][C]-0.166058[/C][C]-1.4188[/C][C]0.919893[/C][/ROW]
[ROW][C]12[/C][C]-0.578441[/C][C]-4.9422[/C][C]0.999998[/C][/ROW]
[ROW][C]13[/C][C]0.042667[/C][C]0.3645[/C][C]0.358251[/C][/ROW]
[ROW][C]14[/C][C]0.03628[/C][C]0.31[/C][C]0.378732[/C][/ROW]
[ROW][C]15[/C][C]0.019456[/C][C]0.1662[/C][C]0.434216[/C][/ROW]
[ROW][C]16[/C][C]0.022454[/C][C]0.1918[/C][C]0.424198[/C][/ROW]
[ROW][C]17[/C][C]-0.034806[/C][C]-0.2974[/C][C]0.616492[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=5927&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5927&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	0.912308	7.7948	0
1	-0.281026	-2.4011	0.990553
2	0.096539	0.8248	0.206079
3	0.111312	0.951	0.172359
4	0.142119	1.2143	0.114281
5	-0.124796	-1.0663	0.85509
6	-0.115753	-0.989	0.837033
7	0.016045	0.1371	0.445668
8	0.311727	2.6634	0.004756
9	0.085458	0.7301	0.233818
10	0.14863	1.2699	0.104078
11	-0.166058	-1.4188	0.919893
12	-0.578441	-4.9422	0.999998
13	0.042667	0.3645	0.358251
14	0.03628	0.31	0.378732
15	0.019456	0.1662	0.434216
16	0.022454	0.1918	0.424198
17	-0.034806	-0.2974	0.616492

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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