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Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 30 Nov 2007 10:20:40 -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/30/t1196442624md11bqx759647kn.htm/, Retrieved Sun, 28 Apr 2024 16:25:19 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=7753, Retrieved Sun, 28 Apr 2024 16:25:19 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Intermediaire goederen

Estimated Impact

165

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

-       [(Partial) Autocorrelation Function] [Workshop 8 Q1] [2007-11-30 17:20:40] [6dd0685065b0babfa744248f2bd1b94f] [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=7753&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=7753&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=7753&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	8.9443	0
1	0.274333	2.4537	0.008156
2	-0.053482	-0.4784	0.68315
3	-0.047371	-0.4237	0.663538
4	-0.098739	-0.8831	0.810098
5	0.033955	0.3037	0.381072
6	0.062011	0.5546	0.290343
7	0.012483	0.1117	0.45569
8	-0.115647	-1.0344	0.847961
9	-0.054753	-0.4897	0.687166
10	-0.177282	-1.5857	0.941619
11	0.148306	1.3265	0.094226
12	0.512577	4.5846	8e-06
13	-0.057995	-0.5187	0.697306
14	-0.210476	-1.8826	0.968302
15	-0.123988	-1.109	0.864619
16	-0.101522	-0.908	0.816708
17	0.033411	0.2988	0.38292
18	0.05606	0.5014	0.308729

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 8.9443 & 0 \tabularnewline
1 & 0.274333 & 2.4537 & 0.008156 \tabularnewline
2 & -0.053482 & -0.4784 & 0.68315 \tabularnewline
3 & -0.047371 & -0.4237 & 0.663538 \tabularnewline
4 & -0.098739 & -0.8831 & 0.810098 \tabularnewline
5 & 0.033955 & 0.3037 & 0.381072 \tabularnewline
6 & 0.062011 & 0.5546 & 0.290343 \tabularnewline
7 & 0.012483 & 0.1117 & 0.45569 \tabularnewline
8 & -0.115647 & -1.0344 & 0.847961 \tabularnewline
9 & -0.054753 & -0.4897 & 0.687166 \tabularnewline
10 & -0.177282 & -1.5857 & 0.941619 \tabularnewline
11 & 0.148306 & 1.3265 & 0.094226 \tabularnewline
12 & 0.512577 & 4.5846 & 8e-06 \tabularnewline
13 & -0.057995 & -0.5187 & 0.697306 \tabularnewline
14 & -0.210476 & -1.8826 & 0.968302 \tabularnewline
15 & -0.123988 & -1.109 & 0.864619 \tabularnewline
16 & -0.101522 & -0.908 & 0.816708 \tabularnewline
17 & 0.033411 & 0.2988 & 0.38292 \tabularnewline
18 & 0.05606 & 0.5014 & 0.308729 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=7753&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]8.9443[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.274333[/C][C]2.4537[/C][C]0.008156[/C][/ROW]
[ROW][C]2[/C][C]-0.053482[/C][C]-0.4784[/C][C]0.68315[/C][/ROW]
[ROW][C]3[/C][C]-0.047371[/C][C]-0.4237[/C][C]0.663538[/C][/ROW]
[ROW][C]4[/C][C]-0.098739[/C][C]-0.8831[/C][C]0.810098[/C][/ROW]
[ROW][C]5[/C][C]0.033955[/C][C]0.3037[/C][C]0.381072[/C][/ROW]
[ROW][C]6[/C][C]0.062011[/C][C]0.5546[/C][C]0.290343[/C][/ROW]
[ROW][C]7[/C][C]0.012483[/C][C]0.1117[/C][C]0.45569[/C][/ROW]
[ROW][C]8[/C][C]-0.115647[/C][C]-1.0344[/C][C]0.847961[/C][/ROW]
[ROW][C]9[/C][C]-0.054753[/C][C]-0.4897[/C][C]0.687166[/C][/ROW]
[ROW][C]10[/C][C]-0.177282[/C][C]-1.5857[/C][C]0.941619[/C][/ROW]
[ROW][C]11[/C][C]0.148306[/C][C]1.3265[/C][C]0.094226[/C][/ROW]
[ROW][C]12[/C][C]0.512577[/C][C]4.5846[/C][C]8e-06[/C][/ROW]
[ROW][C]13[/C][C]-0.057995[/C][C]-0.5187[/C][C]0.697306[/C][/ROW]
[ROW][C]14[/C][C]-0.210476[/C][C]-1.8826[/C][C]0.968302[/C][/ROW]
[ROW][C]15[/C][C]-0.123988[/C][C]-1.109[/C][C]0.864619[/C][/ROW]
[ROW][C]16[/C][C]-0.101522[/C][C]-0.908[/C][C]0.816708[/C][/ROW]
[ROW][C]17[/C][C]0.033411[/C][C]0.2988[/C][C]0.38292[/C][/ROW]
[ROW][C]18[/C][C]0.05606[/C][C]0.5014[/C][C]0.308729[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=7753&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=7753&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	8.9443	0
1	0.274333	2.4537	0.008156
2	-0.053482	-0.4784	0.68315
3	-0.047371	-0.4237	0.663538
4	-0.098739	-0.8831	0.810098
5	0.033955	0.3037	0.381072
6	0.062011	0.5546	0.290343
7	0.012483	0.1117	0.45569
8	-0.115647	-1.0344	0.847961
9	-0.054753	-0.4897	0.687166
10	-0.177282	-1.5857	0.941619
11	0.148306	1.3265	0.094226
12	0.512577	4.5846	8e-06
13	-0.057995	-0.5187	0.697306
14	-0.210476	-1.8826	0.968302
15	-0.123988	-1.109	0.864619
16	-0.101522	-0.908	0.816708
17	0.033411	0.2988	0.38292
18	0.05606	0.5014	0.308729

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.274333	2.4537	0.008156
1	-0.139218	-1.2452	0.891653
2	0.00831	0.0743	0.470468
3	-0.103384	-0.9247	0.821046
4	0.098254	0.8788	0.191068
5	0.004122	0.0369	0.485339
6	0.001175	0.0105	0.495822
7	-0.135522	-1.2121	0.885488
8	0.039793	0.3559	0.361419
9	-0.219712	-1.9652	0.973567
10	0.321925	2.8794	0.002555
11	0.376338	3.3661	0.000587
12	-0.410503	-3.6717	0.999783
13	-0.086484	-0.7735	0.779258
14	0.065436	0.5853	0.280006
15	-0.037778	-0.3379	0.631838
16	-0.007799	-0.0698	0.527721
17	-0.028265	-0.2528	0.599468
18	0.041565	0.3718	0.355525

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.274333 & 2.4537 & 0.008156 \tabularnewline
1 & -0.139218 & -1.2452 & 0.891653 \tabularnewline
2 & 0.00831 & 0.0743 & 0.470468 \tabularnewline
3 & -0.103384 & -0.9247 & 0.821046 \tabularnewline
4 & 0.098254 & 0.8788 & 0.191068 \tabularnewline
5 & 0.004122 & 0.0369 & 0.485339 \tabularnewline
6 & 0.001175 & 0.0105 & 0.495822 \tabularnewline
7 & -0.135522 & -1.2121 & 0.885488 \tabularnewline
8 & 0.039793 & 0.3559 & 0.361419 \tabularnewline
9 & -0.219712 & -1.9652 & 0.973567 \tabularnewline
10 & 0.321925 & 2.8794 & 0.002555 \tabularnewline
11 & 0.376338 & 3.3661 & 0.000587 \tabularnewline
12 & -0.410503 & -3.6717 & 0.999783 \tabularnewline
13 & -0.086484 & -0.7735 & 0.779258 \tabularnewline
14 & 0.065436 & 0.5853 & 0.280006 \tabularnewline
15 & -0.037778 & -0.3379 & 0.631838 \tabularnewline
16 & -0.007799 & -0.0698 & 0.527721 \tabularnewline
17 & -0.028265 & -0.2528 & 0.599468 \tabularnewline
18 & 0.041565 & 0.3718 & 0.355525 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=7753&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]0.274333[/C][C]2.4537[/C][C]0.008156[/C][/ROW]
[ROW][C]1[/C][C]-0.139218[/C][C]-1.2452[/C][C]0.891653[/C][/ROW]
[ROW][C]2[/C][C]0.00831[/C][C]0.0743[/C][C]0.470468[/C][/ROW]
[ROW][C]3[/C][C]-0.103384[/C][C]-0.9247[/C][C]0.821046[/C][/ROW]
[ROW][C]4[/C][C]0.098254[/C][C]0.8788[/C][C]0.191068[/C][/ROW]
[ROW][C]5[/C][C]0.004122[/C][C]0.0369[/C][C]0.485339[/C][/ROW]
[ROW][C]6[/C][C]0.001175[/C][C]0.0105[/C][C]0.495822[/C][/ROW]
[ROW][C]7[/C][C]-0.135522[/C][C]-1.2121[/C][C]0.885488[/C][/ROW]
[ROW][C]8[/C][C]0.039793[/C][C]0.3559[/C][C]0.361419[/C][/ROW]
[ROW][C]9[/C][C]-0.219712[/C][C]-1.9652[/C][C]0.973567[/C][/ROW]
[ROW][C]10[/C][C]0.321925[/C][C]2.8794[/C][C]0.002555[/C][/ROW]
[ROW][C]11[/C][C]0.376338[/C][C]3.3661[/C][C]0.000587[/C][/ROW]
[ROW][C]12[/C][C]-0.410503[/C][C]-3.6717[/C][C]0.999783[/C][/ROW]
[ROW][C]13[/C][C]-0.086484[/C][C]-0.7735[/C][C]0.779258[/C][/ROW]
[ROW][C]14[/C][C]0.065436[/C][C]0.5853[/C][C]0.280006[/C][/ROW]
[ROW][C]15[/C][C]-0.037778[/C][C]-0.3379[/C][C]0.631838[/C][/ROW]
[ROW][C]16[/C][C]-0.007799[/C][C]-0.0698[/C][C]0.527721[/C][/ROW]
[ROW][C]17[/C][C]-0.028265[/C][C]-0.2528[/C][C]0.599468[/C][/ROW]
[ROW][C]18[/C][C]0.041565[/C][C]0.3718[/C][C]0.355525[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=7753&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=7753&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	0.274333	2.4537	0.008156
1	-0.139218	-1.2452	0.891653
2	0.00831	0.0743	0.470468
3	-0.103384	-0.9247	0.821046
4	0.098254	0.8788	0.191068
5	0.004122	0.0369	0.485339
6	0.001175	0.0105	0.495822
7	-0.135522	-1.2121	0.885488
8	0.039793	0.3559	0.361419
9	-0.219712	-1.9652	0.973567
10	0.321925	2.8794	0.002555
11	0.376338	3.3661	0.000587
12	-0.410503	-3.6717	0.999783
13	-0.086484	-0.7735	0.779258
14	0.065436	0.5853	0.280006
15	-0.037778	-0.3379	0.631838
16	-0.007799	-0.0698	0.527721
17	-0.028265	-0.2528	0.599468
18	0.041565	0.3718	0.355525

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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